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Ann Catrin Apstein-Müller (auch Ann Catrin Bolton * 13. April 1973 in Gräfelfing) ist eine deutsche Lyrikerin und Übersetzerin. Sie lebt und arbeitet in Augsburg.

Leben und Werk
Ann Catrin Apstein-Müller wuchs in einem Münchner Vorort auf, wo sie 1992 ihr Abitur machte. Es folge ein Studium der Germanistik und Amerikanistik und des Medienrechts an der Ludwig-Maximilians-Universität München. An das Studium schloss sich eine Ausbildung zur Buchhändlerin in München an. Nach zehn Jahren Teilzeitarbeit im Buchhandel, während derer sie ihre freiberufliche Tätigkeit aufbaute, arbeitet sie heute als Autorin und freie Übersetzerin für Literatur und Fachtexte. Mit dem Schreiben begann sie bereits im Grundschulalter, in der intensivsten Phase zwischen 2000 und 2013 verarbeitete sie darin vor allem eigene Lebenssituationen und Beobachtungen, verbunden mit Einflüssen aus Musik, Film und Literatur.

Seit 2005 ist sie vor allem als Übersetzerin aus dem Slowenischen und Englischen tätig, so hat sie zahlreiche belletristische Werke und Theaterstücke slowenischer Autoren ins Deutsche übersetzt. Im November 2015 publizierte sie ihren ersten eigenen Gedichtband mit dem Titel Sonnenhonig in der Reihe 100 Gedichte im Martin Werhand Verlag. Ihre zweite Lyrikpublikation erschien ein Jahr später unter dem Namen Degravitation im selben Verlag. Neben Gedichten, erste lyrische Texte erschienen bereits im Jahr 2002 in der Anthologie-Reihe Junge Lyrik im Martin Werhand Verlag, hat Ann Catrin Apstein-Müller auch Kurzprosa veröffentlicht, unter anderem in der deutschen Literaturzeitschrift Dichtungsring.

Veröffentlichte Übersetzungen

Bücher
 Aleš Šteger, Preußenpark: Berliner Skizzen, Suhrkamp Verlag, Frankfurt am Main 2009, ISBN 978-3-518-12569-4 (Orig.: Berlin, Beletrina 2007)
 Pero Simić, Tito – Geheimnis des Jahrhunderts, Orbis 2012, ISBN 978-961-6372-75-6 (Orig.: Tito – skrivnost stoletja, Orbis 2010)
 Tadej Golob, Der Goldene Zahn, Schruf&Stipetic, Berlin 2015, ISBN 978-3-944359-12-0 (Orig.: Zlati zob, Mladinska knjiga 2011)
 Evald Flisar, Der Zauberlehrling, Hermagoras, Klagenfurt 2015, ISBN 978-3-7086-0856-3 (Orig.: Čarovnikov vajenec, 9. izd., KUD Sodobnost International, 2013)
 Davorin Lenko, Körper im Dunkeln, DSP/Litterae Slovenicae; Ljubljana 2016, ISBN 978-961-6547-98-7 (Orig.: Telesa v temi, Center za slovensko književnost 2013)
 Miha Mazzini, Deutsche Lotterie, Transit Buchverlag 2016, ISBN 978-3-88747-334-1 (Orig.: Nemška loterija, Beletrina 2010)
 Marko Sosič, Tito, amor mijo, Drava, Klagenfurt 2016, ISBN 978-3-85435-775-9 (i. V. Orig.: Tito, amor mijo, Litera 2005)
 Evald Flisar, Über den Wolken, Klagenfurt 2017, ISBN 978-3-7086-0932-4 (i. V. Orig.: Besede nad oblaki)
 Anita Šumer, Verrückt nach Sauerteig, Unimedica, Kandern, 2019 ISBN 978-3-96257-104-7 (i. V. Orig.: Drožomanija)
 Jana Bauer, Die kleine Gruselfee, Frankfurt am Main 2019, ISBN 978-3-7373-5636-7 (i. V. Orig.: Groznovilca v Hudi hosti)
 Maja Gal Štromar, Denk an mich, auch in guten Zeiten, Bad Herrenalb, Edition CONVERSO, 2020, ISBN 978-3-9819763-8-0 (i. V. Orig.: Misli name, ko ti je lepo)
 Veronika Dintinjana, Gelb brennt der Forsythienstrauch, Ljubljana : Društvo slovenskih pisateljev, 2020, ISBN 978-961-6995-62-7 (i. V. Orig.: Rumeno gori grm forzici)
 Tone Škrjanec, Haut, Ljubljana : Društvo slovenskih pisateljev, 2021, ISBN 978-961-6995-79-5 (i. V. Orig.: Koža)

Theaterstücke
 Simona Semenič, 5jungs.net, Kaiserverlag, Wien 2009.
 Simona Semenič, Sie da, sehen Sie uns (denn) wirklich nie oder (tun Sie s) etwa doch?, Volkstheater Wien 2010.
 Evald Flisar, Und Leonardo?, Theater im Keller, Graz, DEA Oktober 2012.

Beiträge in Büchern und Zeitschriften
 Aleš Šteger, Tacitus in der U-Bahn-Station, in: Sprache im technischen Zeitalter 183, Köln 2007.
 Aleš Šteger, Erbarmen! Erbarmen! Herr Professor, verstehen Sie das Leben?, in: Osteuropa 2-3/2009, Berlin 2009.
 Aleš Šteger, Die Erschaffung der verlorenen Zeit, in: Branko Lenart, Styrians, Kultur in Leibnitz, Leibnitz 2009.
 Aleš Šteger, Wozu?, in: Josef Trattner, Sofa, Schlebrügge.Editor, Wien 2010.
 Milan Kleč, Schieler, in: Ostragehege 59, Dresden 2010.
 Stanka Hrastelj, 9 Gedichte für das Projekt European Borderlands des LCB, 2010.
 Aleš Šteger, Gegen die Phantome, Vortrag Europäische Literaturtage 2010, Wachau, Österreich
 Ana Pepelnik, 11 Gedichte für lyrikline.org
 Tadej Golob, Schweinsfüße (Auszug), Slovene Studies 34/1-2, Bowling Green 2012.

Eigene Werke

Bücher
 Sonnenhonig: 100 Gedichte. Martin Werhand Verlag, Melsbach 2015, ISBN 978-3-943910-20-9.
 Degravitation: 50 Gedichte in Deutsch – 50 Poems in English. Martin Werhand Verlag, Melsbach 2016, ISBN 978-3-943910-23-0.

Eigene Beiträge in Literatur- und Fachzeitschriften
 Gedichte. In: Junge Lyrik III. Martin Werhand Verlag, 2002, ISBN 3-9806390-3-7.
 Notamerica. Kurzprosa. In: Torso 12. Berlin/ München 2003.
 e = mc². Kurzprosa. In: Dichtungsring. Nr. 36, Bonn 2008.
 Wieder vereint/Reunited. Kurzprosa. In: Beatrix Brockman (Hrsg.): The Vanderbilt Berlin Wall Project. Nashville /Tennessee 2009, ISBN 978-0-557-10819-0.
 Gedichte In: anthologie blauer salon – eins. glauche-löwe-milserliteraturprojekte gbr, Duisburg 2009, ISBN 978-3-9813131-0-9.

Literatur
 Ann Catrin Apstein-Müller In: Deutsches Literatur-Lexikon. Das 20. Jahrhundert - Nachtragsband: A - E Volume 1, Verlag Walter de Gruyter, 2020, ISBN 978-3-11-063218-7
 Ann Catrin Apstein-Müller In: Nicolai Riedel Bibliographisches Handbuch der deutschsprachigen Lyrik 1945–2020, Metzler, Heidelberg, 2023, S. 514, ISBN 978-3-662-65460-6

Weblinks
 Wortstromer Übersetzung & Lektorat, Ann Catrin Bolton & Piers Bolton Offizielle Webseite

Einzelnachweise

Autor
Übersetzer aus dem Englischen
Übersetzer aus dem Slowenischen
Übersetzer ins Deutsche
Lyrik
Literatur (21. Jahrhundert)
Literatur (Deutsch)
Schriftsteller (Augsburg)
Deutscher
Geboren 1973
Frau

redpajama_set_name: RedPajamaWikipedia


Survivors of Suicide got its start in the Philadelphia area in 1983. Two women, Sunnie Baron-Freeman and Anne Clark, who had experienced a suicide in each of their families were separately looking for other people who had suffered this tragedy. They sought a "safe place" with people who had "been there." They "connected" through contacts with the Self-Help Clearing House in Philadelphia. They decided to start a support group in Philadelphia where those with similar experiences could share their survivor journeys. Once the Philadelphia group was up and running, a second group opened up in Chester County.
In 1987, Mary Ellen Carpenter from Delaware County suffered the suicide of her son and needed a place to share her grief and learn more about this incomprehensible tragedy. At the suggestion of Sunnie Freeman she opened up a group in Delaware County. Groups followed in Bucks County, Montgomery County, and in southern New Jersey.
Survivors of Suicide, Inc. is now a 501(c)(3) organization with a Board of Directors, all of whom are survivors. The President is Gail Dohrn, Vice President Pat Lufkin, Secretary Olga Thornton and Treasurer, Tony Salvatore.


Network and spectrum are pretty expensive things. Huge costs go in deploying networks. An operator who is ready to incur costs expects good return on investment.
But the costs are so huge that it takes years for an operator to look at profits. Also they cannot charge heavily for service because they have incurred huge costs. So there is a trade off between what we expect and what we get.
Typically, voice networks are pretty much controlled. Each voice call is given a radio channel and if all the channels in a certain area are occupied user starts feeling the congestion. This was one of the challenges with the voice network that service providers used to face or still facing. Now with data coming in, that challenges have increased many folds.
Data is a best effort service. That is at a given point of time, a user doing data from his mobile may consume more than one channel. Since spectrum is limited, networks easily get choked up. Thanks to 3G, since voice calls are on one radio technology and data on other, at least my voice calls are safe.
Why are unlimited plans a distant dream? Its simple economics! More you give, more they ask. It has been result of many research's that 5-10% of subscribers that use unlimited plans consume 70-80% of network bandwidth. This certainly is not fair. Assume that in a give region there is geek sitting and consuming all the bandwidth, doesn't our insanity levels go high? AT&T had burnt its hands with unlimited plans. First the networks are congested, next subscribers are not happy and the result no unlimited plans. Even if the plans are advertised "unlimited", they are not "truly" unlimited.
The wide variety of mobiles that are available in the market is also adds up to the network congestion. The mobiles should be carefully designed not to burden the network with signaling. With so many applications running on mobile devices the connections are always up and resources are continuously consumed. This is for the exact reason why IPhone developers where give crash course by AT&T.
It's nobody's business to tell subscriber how to use what is given to him. But its time users get smart and start utilizing the resources efficiently. Instead of burning the networks with downloading movies on mobile phone why not switch over to wifi? Just a thought!
Excellent write up, many kudos. You are doing a great job, I think its our Indian mentality to (mis)use something that's unlimited. I guess in that case operators aren't left with any option but to give users FUP (but I also feel that service provider should term it as "Unlimited" with it has fair usage policy behind it).


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'I Don't Want My Son To See Me Die' — The Fear Of In-Person Teaching During A Pandemic
Elizabeth Broadbent
November 24, 2020, 8:00 PM ·6 min read
She's small, pretty, this image of a kind, young high school teacher summoned on my phone screen. She came to Scary Mommy to talk about face-to-face teaching during the COVID-19 pandemic. But she didn't want to tell tales of crumbling infrastructure (though her school has it) or lack of ventilation (her classroom suffers from that, too).
She wanted to talk about the havoc COVID-19 has wreaked on her mental health.
Because she lives in a right-to-work state, governed by what she calls "a culture of fear" about unions, this teacher has to remain anonymous. "They will fire me," she tells Scary Mommy. She and her colleagues have been specifically threatened with termination if they speak to media.
Teachers Had It Hard Before Face-to-Face Teaching During a Pandemic
She reminds us that teaching was never an easy profession — and this makes face-to-face teaching even more dangerous. We also know that schools have always been a hotbed of germs. "Teachers get weird stuff," she says — a high school teacher who washes her hands and sanitizes constantly. "I had mono in my mid-thirties." She once had a kid whose parents sent him to school knowing he had influenza: he had to come if he wanted to play sports that night. He infected several kids in her classroom, including her.
Even without a pandemic, she says, people need to realize that teachers are "sitting in a room with thirty kids for ninety minutes at a time." In fact, ABC News ranks teaching as "the dirtiest job" when it comes to germs and microbes. Dr. Harley Rotbart, professor emeritus of pediatrics at the University of Colorado and author of the book Germ Proof Your Kid, tells CNN that schools are "germ candy stores" and says that "schools are full of 'hot zones' for germs." They estimate that the average high school student, the demographic this teacher teaches, can be expected to contract three to four colds a year. They are also at high risk for the flu.
Face-to-Face Teaching Scarier With Little Leadership
First, she says, in the early stages of the pandemic, came the doom-scrolling through Reddit, Facebook, The New York Times, The BCC, and The Washington Post. Then came the dawning realization that her school district, and the neighboring ones, had no real plans— they were not told what instruction would look like, either face-to-face or virtual, until the end of July (classes were slated to start mid-August but pushed back). They were not assigned classes until mid-August; the number of students in those classes wasn't clear until after school started. Even without face-to-face teaching, the stress wore on her with no clear plans, no sense of the future, and "a sense of zero leadership, from the top down."
But Face-to-Face Teaching Made Everything Worse
mixetto/Getty
"Everything is hard," she tells Scary Mommy. She talked about everything from her own fears to calling administration on teachers who walk around maskless. "I've told on colleagues," she says. "It's not something I want to do, but it's a life-or-death situation." Administration hasn't done enough to stop it from happening, she says.
She reports that her anxiety levels have skyrocketed during face-to-face teaching. This isn't a shock. Randi Weingarten, president of the American Federation of Teachers, one of the largest teachers unions in the country, tells NBC, "Teachers are exhausted." Across the country, teachers report stress and burnout; in Utah, principals say their teachers are "having panic attacks" juggling online and face-to-face teaching, like our teacher is being asked to do.
When asked what exactly she was anxious about, the teacher says first, she's anxious that she will get COVID — or that her son will get it. "We don't know the long term effects," she says. "My kids deserves the same long life as your kid. The fact that a kid needs to come to school to 'get socialized' and puts my kid at risk enrages me… I want a say. I want a choice. It doesn't need to be like this. We have a stake in this, too."
"I don't want my son to see me die," she continues. "I think about that a lot. I thought about it on the way to work today."
But It's Not Just The Anxiety
"I'm just tired," she says. "I'm exhausted. I drink more than I should. Everything is hard, grading is hard, talking to parents is hard. I come home and I can barely parent my own child [from the stress]." The Minnesota Star-Tribune reports that a recent study found teacher stress is so bad that one-third of teachers in the state, who do face-to-face teaching and virtual at the same time, are contemplating quitting.
But the teacher and her colleagues, she says, are careful to do the best job that they can amid the stress and anxiety of face-to-face teaching. They put a on a good face for the students, who she's very careful to point out are not to blame for this. "We're acting the entire time," she says. "I'm putting on a performance the entire day. You stow your personal life. I'm not angry at the kids."
"I did not sign up to be an infectious disease doctor," she says. "I did not sign up to risk my life. I would risk my life for a school shooter. But this is not the same as a school shooter. Disease in schools is a choice."
She Knows What The Critics Say
The criticism when teachers complain, she says, is always there, but it's become worse during the pandemic. "They say, well, you should get another job. Then who will educate these kids? Where will they come from? We choose to teach. It's a — I hate this word, it's overused — it's a calling. We feel called to do this. I don't want to miss out on this. I don't want to miss these experiences."
She also knows she's lucky to have a job during the pandemic when so many are unemployed. But she says it's not true that everyone who works is being asked to risk their life. It's not the same, she argues, as sitting in a room with the same 30 people, breathing the same air, for 90 minutes, with improper ventilation — a situation most disease experts would agree is high-risk.
Though she has no plans to quit, she can't help but wonder how long she can survive under the intense strain of it all.
"I love my job," she says, "but I love my life and my family more."
See the original article on ScaryMommy.com
Melinda Gates: Why women's voices must be at the center of rebuilding after COVID-19
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redpajama_set_name: RedPajamaCommonCrawl


For our students, studying in The Hague can make a big difference. The Hague is proud to be known as the international city of peace and justice. With the presence of the government, parliament, ministries, national and international courts, countless European institutions, embassies and companies, The Hague has a prestigious international stature.
The Hague offers a broad choice of appealing academic programmes in an international environment. Students broaden their view of the world and quickly develop a substantial network of international contacts. But at the same time, The Hague is a compact city, where just about everything is close to everything else. What students learn during their studies they can often put into practice straight away in the international environment offered by The Hague. The teaching is supplemented by guest lectures given by highly respected professionals who work in and around The Hague and by the many opportunities for internships offered by the city.
All our programmes in The Hague have their own study association. These associations organise study trips, lectures and numerous social activities. This means that students can quickly build up a group of friends based on their stidy programme, and they start to build a network that will stand them in good stead for the rest of their lives.
Beehive Student Centre, situated directly opposite Wijnhaven building, offers students a place to meet each other, to study, to work out and get advice from experts from Student Support Services. There are office spaces and meeting rooms available for student and study associatons.
The Hague is an attractive place to live. There are good reasons why it is rated as one of the most attractive student cities in world rankings. There is so much going on in The Hague. The Hague has eleven kilometres of sandy beach within cycling distance of the historic city centre. This is the perfect place to take a breather.
The Hague is a fantastic place to combine studying with a lively social life, personal development and an investment in building your future.


chez zero: Why, China, why?
Here's another wonderfully thoughtful post from one of my heroes.
She has lots of great info about how to avoid toys made in China, links to great stores that carry European toys (like one of our favorites, Oompa Toys), info about toy companies that work in China but have strict oversight policies, and ideas for making toys. I commented on her post, basically asking her to adopt me, but I haven't heard back yet.
Thank you SO much for sharing that - I've bookmarked that page and also sent the link to all my mommy friends. It was indeed very inspiring!


Editor's Note: If you're looking for a delicious vegan dessert recipe, then you need to keep this sweet little number in mind. From its light dusting of cinnamon-sugar to its ice cream filing, this Churro Ice Cream Sandwich recipe is the perfect answer for those hot summer nights. The no-bake dessert can even be made in stages, as the dough can be mixed and stored in the refrigerator for up to one week before frying it. Vegans and non-vegans alike will love indulging in this unique and delicious treat, so you just might want to make an extra batch!
We move a lot of soft serve at V Street. Sometimes when we're anxious to get on to a new flavor, we end with a little left over. On one particularly creative evening, we decided to freeze the leftovers into little rounds. The next morning, we prepped some tasty churro pastry dough, rolled it into little disks, and fried them off so we could roll them in cinnamon sugar and stack them around the ice cream pucks. And so was born the ultimate ice cream sandwich.
Combine 2 cups water, the salt, brown sugar, baking powder, and olive oil in a medium saucepan and bring to a boil over medium heat. Whisk in the flour, stirring constantly just until fully combined, about 30 seconds.
Transfer the dough to a plate, cover with plastic wrap, and let cool to room temperature, about 20 minutes.
Line a sheet pan with parchment paper. On a floured work surface, roll the dough out into a 1/2-inch sheet and use a cookie cutter to stamp out twelve 2-inch circles. Arrange the churros on the baking pan. Cover the pan tightly in plastic wrap and freeze until ready to fry, up to 1 week.
Line a plate with paper towels. Combine the granulated sugar and cinnamon in a small bowl and set aside. Preheat a fryer to 375 degrees F or heat 2 inches of the oil in a large skillet or saucepan over high heat until the oil begins to ripple. Fry the churros, 2 to 4 at a time, for 4 minutes or until golden brown.
Remove the churros from the heat and drain on the paper towel–lined plate for 1 minute to remove any excess oil. Lightly roll the churros in the cinnamon sugar. Place on a rack to cool for at least 5 minutes.
Place a scoop of your favorite ice cream on a cooled churro and press a second churro on top to make a sandwich. Serve immediately.
I've never heard of a churro ice cream sandwich, but I must say, I'm quite intrigued! This is definitely a recipe I'll have to try once summer rolls around.


text:
Brown fat programme could signal new treatment options in obesity and type 2 diabetes
US researchers believe a program that converts white fat to brown fat could be pivotal in providing new treatments for obesity and type 2 diabetes.
This "browning program" was discovered by scientists from the Perelman School of Medicine at the University of Pennsylvania.
By converting energy-hoarding white fat cells into fat-burning brown fat cells, the body can be protected from obesity and type 2 diabetes.
"It's conceivable that one would be able to target this pathway with a drug, to push white fat to become brown fat and thereby treat obesity," said lead author Dr Zoltan P. Arany, PhD, whose findings have been published online ahead of print in Genes and Development.
The browning of white fat cells is normally suppressed by a series of proteins, the researchers discovered, but when they deleted a protein called FLCN in the white fat cells of mice, it led to the activation of the set of genes needed for the browning program.
When FLCN was deleted, the white fat cells became visibly browner. Additionally their cellular structures altered to accommodate more mitochondria – the small oxygen reactions that supply chemical energy and convert energy to heat in brown fat.
Arany and colleagues believe they can reproduce this browning effect using a drug that boosts the activity of a cellular metabolism called PGC-1β.
"In principle, a drug that boosts the activity of PGC-1β or some of its target genes might serve as a therapeutic activator of the browning program to curb obesity and treat or prevent diabetes," said Arany.
Earlier this year, University of Tennessee researchers discovered in a separate study that a chemical called Beta-LGND2 reduced obesity and metabolic diseases in mice through turning white fat into brown fat.
Drinking plain water could help reduce diabetes risk
Beta blockers co-therapy with intensive glycemic treatment lowers cardiovascular events
Sitting less and walking more could reduce fasting insulin levels by 11 per cent
Local authorities urged to encourage people to attend NHS Health Checks


In this episode, a lot of cute things happen. Cute kid, cute village, cute baby Digimon, cute fighting, cute flashback... cute way to spend time not doing anything.
About halfway through watching this episode, it dawned on me that absolutely nothing was going to happen. My worst fears were realized when not only did Patamon not digivolve, but they didn't even turn the island back toward Infinity Mountain. Without a dangerous enemy, huge action scene or trademark evolution sequence, there's no sense of pace to it. It just kinda goes... and then it kinda stops.
The good news is that TK finally has an episode all to himself, waiting far too long considering that there's been something like three Joe episodes already. I'll get to him in a second, but the episode is the first time it hit me over the head: he really does have the same voice actress as Haruhi Suzumiya. Maybe I just wasn't paying attention to him before, but when TK is the only one in the episode, it's really obvious and even a bit distracting at times. Digimon predates Haruhi by several years, but that's what happens when you let a show fade into history like that. It's much more amusing in reverse, like Takaya in Persona 3 sounding like the Digimon Emperor.
Appropriate that the first few minutes of the show feature the melancholy of Takeru Takaishi as he and Patamon wander alone, helpless and frightened. The railroad crossing from Haruhi even makes a cameo appearance! There are a few cute moments early on, like TK speculating on Patamon's Champion form (all involving pigs for some reason), but nothing can brace you for what lies in Primary Village.
Let's run through this: TK and Patamon enjoying the fluffy bouncy side of Primary Village is fun. The little baby Digimon are squishy and adorable. The flashback with Matt is sweet. The fighting between Elecmon and Patamon is silly. Their subsequent tug-of-war is just plain cute. It's like Haruhi called for the land to be covered in moe. It would all be a nice respite from the more serious side of the show... if we didn't just get one last episode.
At least we get a more rounded glimpse of TK. Either he's in denial about the danger of this world or he still hasn't completely grasped it yet. It creates an interesting duality when he's alone. Normally, he reaches his breaking point faster than anybody as he and Patamon burst into tears pretty quickly, desperately wishing the others would show up. Once they hit Primary Village, they're quick to forget their problems and have a blast with no concern for anything else.
He also really hates violence, even the toothless fight between Patamon and Elecmon. It's suggested that fighting within his family has led him to this. It's funny that I spent the first part of the episode in awe that this little kid eventually turns into the TK from season two, yet completely forgot that this disdain for violence is totally consistent with TK from season two. It seemed confusing to show digivice shots intimating that Patamon was close to evolving but TK wasn't going to have it, but that may have been because I knew it wasn't going to happen here. Or that evolving to take down someone like Elecmon would have just been unfair.
Elecmon's just stupid. He drops the babies' dinner at the first sign of trouble, assumes TK and Patamon are hostile trespassers without talking to them first, he starts a fight with Patamon that endangers his charges, agrees to a tug-of-war that he is less certain to win, then assumes that TK and Patamon are friendly just because Patamon beat him in a contest of strength. Someone get these kids in foster care.
Something could be said about this episode explaining the nature of how Digimon are born, providing some information that could be useful down the line, but it doesn't say anything about Digimon dying or being reborn. That would have been useful... not that there's any chance one of the beloved Digimon might actually die.
Patamon imagining what Biyomon would do in his situation has a cute punchline (evolve to Birdramon and fly the hell away), and provides the only evolution sequence in the whole episode, but choosing Biyomon is really out of nowhere. There's speculation that Patamon views Biyomon as a big sister, but a little more elaboration would be nice.
Patamon finds a note under a digiegg that he claims is digicode, even though it is clearly written in hiragana. Such treatment of the Japanese language is an unfortunate remnant of Saturday morning dubbed anime, but it's particularly gruesome since there is actually a written digicode language based off of hiragana, featured in both episodes where Izzy nestles into his laptop.
The ignorance over the Japanese language is forgiven with the sumo parody, complete with the mawashi belts and TK in a full gyouji get-up.
It's almost a breath of fresh air to see Devimon again, even if it's just briefly to give Leomon marching orders and await the final battle. We should not be so happy to see such a trite villain in such a trite scene.
This episode was alright. Nothing spectacular, nothing awful. Just alright. It's best parts came after the conflict between Patamon and Elecmon was done and over with. Beforehand it was pretty light hearted and whimsical but that fit seeing as it's just TK, the youngest child, with Patamon, a childish Rookie, in a village filled with freshly hatched infant digimon being taken care of by another Rookie who's trying to act all grown up. I loved the moment where Patamon spontaneously starts crying and that gets TK's own crying to stop, and of course the pig Digimon evolution joke that followed. "I AM NOT A PIG, TK!"
It's actually kind of sad that TK seemed to be suggesting that he wanted to talk things out with Devimon and reach a nonviolent solution to the big conflict as they managed with this one, but that's obviously not going to happen. However, Elecmon getting inspired to spread the gospel of friendship and band every good Digimon on the island together does pay off two episodes later. The highlight was the scene showing all the kids on their way back towards where Infinity Mountain is, and then Devimon making his plans. Really gets you pumped up for the upcoming finale to this story. And that ending with Leomon just standing there...chilling.
One big dub nitpick, though? Elecmon's voice doesn't sound young enough, and his acting was questionable at points. Especially "Intruders, invaders!" Yeesh!
Adventure Episode 09: Subzero Ice Punch!


Alas, poor Nicky and her woes of gardening in Montana in the spring. Being English, she likely thinks of carpeted green fields studded with daffodils, crocus, muscari, friendly hedgehogs, and quaint talking bunnies. Then, of course, she married Barry and moved to Montana and spring has never been the same since. Now she has porcupines, May blizzards, and a menagerie of animals that line up to get in the house. Since Trooper the bucket calf got to spend some quality time inside, the lot of them seem to think that just anyone on four legs should be able to come in the front door.
As for gardening, spring bulbs, and overall floral beautification, Nicky is having an even harder go of things. Last year, the cheeky Badger dug up all of her newly planted daffodils bulbs, causing him to froth with delight. So when Nick and her mum created new bulb pots to brighten the front porch, they thought they'd nipped the Badger problem in the bud. Until Nicky returned home to find fresh floral carnage.
Badger was initially blamed, and rightly so as he is generally the destructive force against all things of delicate beauty, but not this time. This time it was Sunfish, Barry's yearling paint colt, that was the culprit. Sunfish has ridiculously strong lips, and like the destructive Badger, he cannot lay off the springtime bulbs. Even worse, he pillaged the flower pots while Nicky's mum was there, but she covered for him repotting what he had torn asunder. And as the final insult, Sunfish had the audacity to laugh his fool head off!
So should you perchance happen by Nicky and Barry's front porch, make certain to compliment whatever remains of the ill-fated potted bulbs. They've withstood dogs, horses, and Montana spring, so they've earned their moment in the sun (however long Badger and Sunfish will let that be).
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First off, it's REVERSIBLE. With an incredibly soft gray wubby fabric on one side and crisp cotton twill on the other, you are truly getting two jackets in one. Snap front closure, wide collar and zipper close pocket on the twill side.
Care | Machine wash cold, tumble dry low. Do not iron.


text:
\section{Introduction}

Liquid  democracy \citep{blum2016liquid} is an influential proposal in recent debates on democratic reforms in both Europe and the US. Several grassroots campaigns, as well as local parties, experimented with this novel type of decision making procedure. Examples include the German Piratenpartei\footnote{\url{https://www.piratenpartei.de/}} and the EU Horizon 2020 project WeGovNow~\citep{boella2018wegovnow}, which have incorporated the LiquidFeedback\footnote{\url{https://liquidfeedback.org/}} platform in their decision making, as well as grass-roots organizations such as the Democracy Earth Foundation\footnote{\url{https://www.democracy.earth/}}. Liquid democracy is a form of proxy voting \citep{miller1969program,Tullock_1992,Alger_2006,green2015direct,cohensius2017proxy} where, in contrast to classical proxy voting, proxies are delegable (or transitive, or transferable). Suppose we are voting on a binary issue, then each voter can either cast her vote directly, or she can delegate her vote to a proxy, who can again either vote directly or, in turn, delegate to yet another proxy, and so forth. Ultimately, the voters that decided not to delegate cast their ballots, which now carry the weight given by the number of voters who entrusted them as proxy, directly or indirectly.

\paragraph{Contribution}
The starting point of our analysis is an often cited feature of liquid democracy:
transitive delegations reduce the level of duplicated effort required by direct voting, by freeing voters from the need to invest effort in order to vote accurately. The focus of the paper is the decision-making problem that voters, who are interested in casting an accurate vote, face between voting directly, and thereby incurring a cost in terms of effort invested to learn about the issue at hand, or delegating to another voter in their network, thereby avoiding costs.
We define a game-theoretic model, called {\em delegation game}, to represent this type of interaction. We establish pure strategy Nash equilibrium existence results for classes of delegation games, and study the quality of equilibria in terms of the average accuracy they enable for the population of voters, both analytically and through simulations. Proofs of the two main results (Theorems \ref{thm:NE-deterministic} and \ref{thm:delegation-games-NE}) are presented in full, while we provide proofs of the simpler secondary results as an Appendix only.

By means of simulations we also study the effects of different network structures on delegation games in terms of: performance against direct voting, average accuracy and the probability of a correct majority vote, the number and quality of voters acting as ultimate proxies (so-called gurus) and, finally, the presence of delegation cycles.
To the best of our knowledge, this is the first paper providing a comprehensive study of liquid democracy from a game-theoretic angle.

\paragraph{Related Work}
Although the idea of delegable proxy was already sketched by \citet{dodgson84principles}, only a few very recent papers have studied aspects of liquid democracy in the (computational) social choice theory \citep{brandt16handbook} literature. \citet{kling2015voting} provide an analysis of election data from the main platform implementing a liquid democracy voting system (Liquid Feedback) for the German Piratenpartei. They focus on network theoretic properties emerging from the structure of delegations---with particular attention to the number of highly influential gurus or `super-voters'. Inspired by their experimental analysis, \citet{golz2018fluid} propose and analyze a variant of the liquid democracy scheme able to restrict reliance on super-voters. \citet{skowron17proportional} study an aspect of the Liquid Feedback platform concerning the order in which proposals are ranked and by which they are brought to the attention of the community. \citet{boldi2011viscous} investigate applications of variants of the liquid democracy voting method (called viscous democracy) to recommender systems.
\citet{brill2018interactive} presents some research directions in the context of liquid democracy.
A general, more philosophical discussion of liquid democracy is provided by \citet{blum2016liquid}.

More directly related to our investigations is the work by \citet{christoff17binary} and, especially, by \citet{kahng18liquid}.
The first paper studies liquid democracy as an aggregator---a function mapping profiles of binary opinions to a collective opinion---in the judgment aggregation and binary voting tradition \citep{Grossi_2014,endriss16judgment}.
The focus of that paper are the unintended effects that transferable proxies may have
due to delegation cycles, and due to the failure of rationality constraints normally satisfied by direct voting.

The second paper addresses one of the most cited selling arguments for liquid democracy: delegable proxies guarantee that better informed agents can exercise more weight on group decisions, thereby increasing their quality. Specifically, \citet{kahng18liquid} study the level of accuracy that can be guaranteed by liquid democracy (based on vote delegation with weighted majority) vs. direct voting by majority. Their key result consists in showing that no `local' procedure to select proxies can guarantee that liquid democracy is, at the same time, never less accurate (in large enough graphs)
and sometimes strictly
more accurate
than direct voting.
In contrast to their work,
we assume that agents incur costs (effort) when voting directly, and on that basis we develop a game-theoretic model. Also, we assume agents aim at tracking their own type rather than an external ground truth, although we do assume such a restriction in our simulations to better highlight how the two models are related and to obtain insights applicable to both.

\section{Preliminaries}

\subsection{Types, Individual Accuracy and Proximity}

We are concerned with a finite set of agents (or voters, or players) $N = \set{1, \ldots, n}$ having to decide whether $x = 1$ or $x = 0$. For each agent one of these two outcomes is better, but the agent is not necessarily aware which one. We refer to this hidden optimal outcome as the {\em type of agent $i$} and denote it by $\tau_i \in \set{0,1}$. Agents want to communicate their type truthfully to the voting mechanism, but they know it only imperfectly. This is captured by the \emph{accuracy} $q_i$ of an agent $i$:
$q_i$ determines the likelihood that, if $i$ votes directly, she votes according to her type $\tau_i$.
We assume that an agent's accuracy is always $\geq 0.5$, i.e., at least as good as a coin toss.

We distinguish two settings depending on whether the agents' types are deterministic or probabilistic.
A {\em deterministic type profile} $T=\tuple{\tau_1, \ldots, \tau_n}$ simply collects each agent's type.
In {\em probabilistic type profiles} types are independent random variables drawn according to a distribution ${\mathbb P}$. Given a probabilistic type profile, the likelihood that any two agents $i,j\in N$ are of the same type is called the {\em proximity} $p_{i,j}$ where
$p_{i,j}={\mathbb P}(\tau(i)=\tau(j)) = {\mathbb P}(\tau(i) = 1)\cdot {\mathbb P}(\tau(j) = 1) +  (1- {\mathbb P}(\tau(i) = 1)) \cdot  (1- {\mathbb P}(\tau(j) = 1))$. In the probabilistic setting we assume agents know such value although, importantly, they do not know ${\mathbb P}$.
In a deterministic type profile, we have $p_{i,j}= 1$ if $\tau_i=\tau_j$ and $p_{i,j}= 0$ otherwise. Following standard equilibrium theory, our theoretical results assume agents act as if they have access to the accuracy of each agent. More realistically, in our simulations we assume agents have access to such information only with respect to neighbors on an underlying interaction structure.

\subsection{Interaction Structure and Delegations}

Agents are nodes in a network (directed graph) represented by a relation $R \subseteq N^2$. For $i \in N$ the neighborhood of $i$ in $\langle N, R \rangle$ is denoted $R(i)$, i.e., the agents that are directly connected to $i$.
Agents have the choice of either voting themselves, thereby relying solely on their own accuracy, or delegating to an agent in their neighborhood. A {\em delegation profile} is a vector ${\bf d} = \tuple{d_1, \ldots, d_n} \in N^n$. Given a delegation profile ${\bf d}$ we denote by $d_i$ the \emph{proxy} selected by $i$ in ${\bf d}$. Clearly a delegation profile can be viewed as a functional graph on $N$ or, equivalently, as a map in ${\bf d}: N \to N$ where ${\bf d}(i) = d_i$. When the iterated application of ${\bf d}$ from $i$ reaches a fixed point we denote such fixed point as $d^*_i$ and call it $i$'s {\em guru} (in ${\bf d}$).
In the following, we write $N^*$ to denote the set of voters whose delegation does not lay on a path ending on a cycle, i.e., the set of voters $i$ for which $d^*_i$ exists.
We write ${\bf d}' = ({\bf d}_{-i},j)$ as a short form for ${\bf d}' = \tuple{d_1, \ldots, d_{i-1}, j, d_{i+1},\dots, d_n} $.

As agents may only be able to observe and interact with their direct network neighbors, structural properties of the interaction network may play a role in the model dynamics. In our simulations we will focus on undirected graphs (that is, $R$ will be assumed to be symmetric, as social ties are normally mutual) consisting of one single connected component (that is, $N^2$ is included in the reflexive transitive closure of $R$).
Under these assumptions, we consider four typical network structures that are well represented in the literature on social network analysis (cf. \citealt{jackson08social}): 1) the {\em random} network, in which each pair of nodes has a given probability of being connected \citep{erdos1959random}; 2) the {\em regular} network, in which all nodes have the same degree; 3) the {\em small world} network, which features a small average path length and high clustering \citep{watts1998collective}; and 4) the {\em scale free} network, which exhibits a power law degree distribution \citep{barabasi1999emergence}.\footnote{Although random and regular graphs are not generally applicable to real-world settings, they serve as a useful baseline to illustrate the effects of network structure on delegations.
}

\iffalse

\subsection{Individual Accuracy and Delegation}

Agents have the choice of either voting themselves or delegating to an agent in their neighborhood.
Agents that vote themselves have to rely on their ability to judge the available alternatives, i.e., their ability to determine their own type.
This is captured by the \emph{accuracy} $q_i$ of an agent $i$:
$q_i$ determines the likelihood that---if $i$ decides to vote herself---she votes according to her type $\tau_i$.
We assume that an agent's accuracy is always $\geq 0.5$, i.e., at least as good as a coin toss.

A {\em delegation profile} is a vector ${\bf d} = \tuple{d_1, \ldots, d_n} \in N^n$. Given a delegation profile ${\bf d}$ we denote by $d_i$ the \emph{proxy} selected by $i$ in ${\bf d}$. Clearly a delegation profile can be viewed as a functional graph on $N$ or, equivalently, as a map in ${\bf d}: N \to N$ where ${\bf d}(i) = d_i$. When the iterated application of ${\bf d}$ from $i$ reaches a fixpoint we denote such fixpoint as $d^*_i$ and call it $i$'s {\em guru} (in ${\bf d}$).
In the following, we write $N^*$ to denote the set of voters whose delegation does lay on a path ending on a cycle, i.e., the set of voters $i$ for which $d^*_i$ exists.
We write ${\bf d}' = ({\bf d}_{-i},j)$ as a short form for ${\bf d}' = \tuple{d_1, \ldots, d_{i-1}, j, d_{i+1},\dots, d_n} $.

\fi

\section{A Model of Rational Delegations}

\subsection{Individual Accuracy under Delegable Proxy}

Each agent $i$ has to choose between two options: either to vote herself with accuracy $q_i$ or to delegate, thereby inheriting the accuracy of another voter (unless $i$ is involved in a delegation cycle).
These choices are recorded in the delegation profile ${\bf d}$ and can be used to compute the individual accuracy for each agent $i\in N^*$ as follows:
\begin{align} \label{eq:accuracy}
    \small
  \hspace{-0.3cm}  q^*_i({\bf d}) =
    \begin{cases}
    q_{d^*_i}\cdot p_{i,d^*_i}

    + (1-q_{d^*_i}) \cdot (1-p_{i,d^*_i}) & \text{if }i\in N^* \\
    0.5 &\text{if }i\notin N^*
    \end{cases}
\end{align}
In \eqref{eq:accuracy}
$i$'s accuracy equals the likelihood that $i$'s guru has the same type and votes accurately plus the likelihood that $i$'s guru has the opposite type and fails to vote accurately. Note that if $i$ votes directly, i.e., $d_i=i$, then $q^*_i({\bf d}) = q_i$. Observe that if $i$'s delegation leads to a cycle ($i\notin N^*$), $i$'s accuracy is set to $0.5$. The rationale for this assumption is the following. If an agent delegates into a cycle, even though she knows her own accuracy and she actively engages with the voting mechanism by expressing a delegation, she fails to pass information about her type to the mechanism. No information is therefore available to decide about her type.

It may be worth observing that, by \eqref{eq:accuracy}, in a deterministic type profile we have that $p_{i,j}\in\{0,1\}$ and therefore $i$'s accuracy reduces to: $q_{d^*_i}$ if $i\in N^*$ and $\tau(i)=\tau(d^*_i)$; $1-q_{d^*(i)}$ if $i\in N^*$ and $\tau(i)\neq\tau(d^*_i)$; and $0.5$ if $i\notin N^*$.

\iffalse
\begin{align} \label{eq:accuracy_deterministic}
    q^*_i({\bf d}) = \begin{cases}
    q_{d^*(i)} &\text{if }i\in N^* \text{ and }\tau(i)=\tau(d^*_i)\text{,}\\
    1-q_{d^*(i)} & \text{if }i\in N^* \text{ and }\tau(i)\neq\tau(d^*_i)\text{,}\\
    0.5 &\text{if }i\notin N^*.
    \end{cases}
\end{align}
Let us immediately establish a basic fact about delegations in our model: assuming a weak rationality condition for all agents, an agent can identify some delegations that have a guaranteed positive impact on her accuracy, even if her proxy further delegates to agents she has no information about.
\fi

Before introducing our game theoretic analysis, we make the following observation. Agents have at their disposal an intuitive strategy to improve their accuracy: simply delegate to a more accurate neighbor. We say that a delegation profile ${\bf d}$ is \emph{positive} if for all $j\in N$ either $d_j=j$ or $q^*_j({\bf d})> q_j$.
Furthermore, we say that a delegation from $i$ to a neighbor $j$ is
\emph{locally positive} if $q_j\cdot p_{i,j} + (1-q_j)\cdot (1-p_{i,j})>q_i$.

\begin{proposition}
Let ${\bf d}$ be a positive delegation profile.
Further, let $s,t\in N$, $d_s=s$, and ${\bf d}'=({\bf d}_{-s},t)$, i.e., agent $s$ votes directly in ${\bf d}$ and delegates to $t$ in ${\bf d}'$.
If the delegation from $s$ to $t$ is locally positive, then
${\bf d}'$ is positive (proof in Appendix~\ref{appendix:proof}).
\label{prop:positive}
\end{proposition}
However, locally positive delegations do not necessarily correspond to optimal delegations.
This can be easily seen
in an example where agent $i$ is not a neighbor of a very competent agent $j$, but would have to delegate via an intermediate agent $k$ (who delegates to $j$). If this intermediate agent $k$ has a lower accuracy than $i$, then the delegation from $i$ to $k$ would not be locally positive, even though it is an optimal choice. So utility-maximization may require information which is inherently non-local (accuracy of `far' agents).

\subsection{Delegation Games}

We assume that each agent $i$ has to invest an effort $e_i$ to manifest her accuracy $q_i$.
If she delegates, she does not have to spend effort.
Agents aim therefore at maximizing the trade-off between the accuracy they can achieve (either by voting directly or through proxy) and the effort they spend. Under this assumption, the binary decision set-up with delegable proxy we outlined above can be used to define a natural game---called {\em delegation game}---$G = \tuple{N, {\mathbb P}, R, \Sigma_i, u_i}$, with $i \in N$, where $N$ is the set of agents, ${\mathbb P}$ is the (possibly degenerate) distribution from which the types of the agents in $N$ are drawn, $R$ the underlying network as defined above, $\Sigma_i\in  N$ is the set of strategies of agent $i$ (voting, or choosing a specific proxy), and
\begin{align}
    u_i({\bf d}) =
    \begin{cases} q^*_i({\bf d})  &\text{if } d_i\neq i\\
    q_i - e_i &\text{if } d_i= i\\

    \end{cases} \label{eq:utility}
\end{align}
is agent $i$'s utility function. The utility $i$ extracts from a delegation profile equals the accuracy she inherits through proxy or, if she votes, her accuracy minus the effort spent.\footnote{No utility is accrued for gaining voting power in our model.} In delegation games we assume that $q_i-e_i\geq 0.5$ for all $i\in N$. This is
because if $q_i-e_i < 0.5$, then $i$ would prefer a random effortless choice over taking a decision with effort.

A few comments about the setup of \eqref{eq:utility} are in order. First of all, as stated earlier, we assume agents to be truthful. They do not aim at maximizing the chance their type wins the vote, but rather to relay their type to the mechanism as accurately as possible.\footnote{Notice however that our modeling of agents' utility remains applicable in this form even if agents are not truthful but the underlying voting rule makes truthfulness a dominant strategy---such as majority in the binary voting setting used here.}
Secondly, notice that the utility an agent extracts from a delegation profile may equal the accuracy of a random coin toss when the agent's delegation ends up into a delegation cycle (cf. \eqref{eq:accuracy}). If this happens the agent fails to relay information about her type, even though she acted in order to do so. This justifies the fact that $0.5$ is also the lowest payoff attainable in a delegation game.

The following classes of delegation games will be used in the paper:
games with {\em deterministic profiles}, i.e., where ${\mathbb P}$ is degenerate and all players are assigned a crisp type from $\set{0,1}$; {\em homogeneous} games, where all players have the same (deterministic) type;\footnote{This is the type of interaction studied, albeit not game-theoretically, by \citet{kahng18liquid} and normally assumed by jury theorems \citep{grofman83thirteen}.} and {\em effortless voting} games, where for each $i \in N$ we have $e_i = 0$.

As an example, a homogeneous game in matrix form is given in Table~\ref{table:dgame}, where $N = \set{1,2}$, $R = N^2$ and the distribution yields the deterministic type profile $T = \tuple{1,1}$. Interestingly, if we assume that $q_i - e_i > 0.5$ with $i \in \set{1,2}$, and that\footnote{We use here the usual notation $-i$ to denote
 $i$'s opponent.} $q_{-i} > q_i - e_i$ (i.e., the opponent's accuracy is higher than the player's individual accuracy minus her effort), then the game shares the ordinal preference structure of the class of anti-coordination games: players need to avoid coordination on the same strategy (one should vote and the other delegate), with two coordination outcomes (both players voting or both delegating) of which the second (the delegation cycle) is worst for both players. Notice that, were the underlying network not complete (i.e., $R \subset N^2$), the matrix would be shrunk by removing the rows and columns corresponding to the delegation options no longer available.

\bgroup
\def1.1{1.1}
\begin{table}[tb]
	\centering
	\begin{tabular}{rP{2.2cm}|P{2.2cm}|}
		 & \multicolumn{1}{c}{vote} & \multicolumn{1}{c}{delegate (to $1$)} \\ \cline{2-3}
		\multicolumn{1}{r|}{vote} & $q_1-e_1, q_2-e_2$ & $q_1-e_1,q_1 $ \\ \cline{2-3}
		\multicolumn{1}{r|}{delegate (to $2$)} & $q_2,q_2-e_2 $ & $0.5,0.5$ \\ \cline{2-3}
	\end{tabular}
	\caption{A two-player delegation game. The row player is agent $1$ and the column player is agent $2$.}
	\label{table:dgame}

\end{table}
\egroup

The introduction of effort has significant consequences on the delegation behavior of voters, and we will study it in depth in the coming sections. It is worth noting immediately that the assumptions of Proposition~\ref{prop:positive} no longer apply, since agents may prefer to make delegations that are not locally positive due to the decreased utility of voting directly.

\subsection{Existence of Equilibria in Delegation Games}

In this section we study the existence of pure strategy Nash Equilibria (NE) in two classes of delegation games. NE describe how ideally rational voters would resolve the effort/accuracy trade-off. Of course,  such voters have common knowledge of the delegation game structure---including, therefore, common knowledge of the accuracies of `distant' agents in the underlying network. Our simulations will later lift some of such epistemic assumptions built into NE.

\paragraph{Deterministic Types}

In the following we provide a NE existence result for games with deterministic type profiles.
\begin{theorem}
Delegation games with deterministic type profiles always have a (pure strategy) NE.\label{thm:NE-deterministic}
\end{theorem}
\begin{proof}
First of all, observe that since the profile is deterministic, for each pair of agents $i$ and $j$, $p_{i,j} \in \set{0,1}$.
The proof is by construction.
First, we partition the set of agents $N$ into $N_1 = \set{i \in N \mid \tau(i) = 1}$ and $N_0 = \set{i \in N \mid \tau(i) = 0}$.
We consider these two sets separately; without loss of generality let us consider $N_1$.
Further we consider the network $R_1=\{(i,j)\in N_1\times N_1: (i,j)\in R\}$.
Since $(N_1,R_1)$ can be seen as a directed graph, we can partition it into Strongly Connected Components (SCCs).
If we shrink each SCC into a single vertex, we obtain the condensation of this graph; note that such a graph is a directed acyclic graph (DAG).
We construct a delegation profile ${\bf d}$ by traversing this DAG bottom up, i.e., starting with leaf SCCs.

Let $S\subseteq N_1$ be a set of agents corresponding to a leaf SCC in the condensation DAG.
We choose an agent $i$ in $S$ that has maximum $q_i-e_i$.
Everyone in $S$ (including $i$) delegates to $i$.
Now let $S\subseteq N_1$ be a set of agents corresponding to an inner node SCC in the condensation DAG and assume that we have already defined the delegation for all SCCs that can be reached from $S$.
As before, we identify an agent $i\in S$ with maximum $q_i-e_i$.
Further, let $T\subseteq N_1\setminus S$ be the set of all voters $j$ that can be reached from $S$ in $(N_1,R_1)$, and for which $q^*_j>q_i-e_i$.
We distinguish two cases.
(i) If $T\neq \emptyset$, then we choose an agent $k\in T$ with $q^*_k=\max_{j\in T} q^*_j$ and all agents in $S$ directly or indirectly delegate to $k$.
(ii) If $T=\emptyset$, all agents in $S$ delegate to $i$.
This concludes our construction (as for $N_0$ the analogous construction applies); let ${\bf d}$ be the corresponding delegation profile.

It remains to verify that this is indeed a NE:
Let $i$ be some agent in an SCC $S$, and, without loss of generality, let $i\in N_1$.
Observe that since we have a deterministic profile, if agent $i$ changes her delegation to $j$, then $i$'s utility changes to $q_j^*({\bf d})$ if $i\in N_1$ and $1-q_j^*({\bf d})$ if $i\in N_0$.
First, note that for all agents $k\in N$, $q^*_k({\bf d})\geq q_k-e_k \geq 0.5$.
Hence, we can immediately exclude that for agent $i$ delegating to an agent in $j\in N_0$ is (strictly) beneficial, as it would yield an accuracy of at most $1-q^*_j\leq 0.5$.
Towards a contradiction assume there is a beneficial deviation to an agent $j\in N_1$, i.e., there is an agent $j\in R(i)\cap N_1$ with $q^*_j({\bf d}) > q_i^*({\bf d})$.
Let us now consider the three cases: (1) $d_i=i$, (2) $d^*_i\in S$ but $d_i\neq i$, and (3) $d^*_i\notin S$.
In case (1), everyone in $S$ delegates to $i$. Hence, if $j\in S$, a cycle would occur yielding a utility of $0.5$, which is not sufficient for a beneficial deviation.
If a delegation to $j\notin S$ is possible but was not chosen, then by construction $q^*_j \leq q_i-e_i$ and hence this deviation is not beneficial. We conclude that in case (1) such an agent $j$ cannot exist.
In case (2), everyone in $S$ delegates to $d^*_i$. Hence, if $j\in S$, then $d^*_j=d^*_i$, a contradiction. If $j\notin S$, the same reasoning as before applies and hence also here we obtain a contradiction.
In case (3), by construction, $d^*_i\notin S$ had been chosen to maximise accuracy, hence $j\in S$.
Since for all $k\in S$, $d_k^*=d_i^*$, only a deviation to $i$ itself can be beneficial, i.e., $j=i$. However, since $d^*_i$ was chosen because $q^*_{d^*(i)} > q_i-e_i$, no beneficial deviation is possible.
\end{proof}
\noindent
It follows that also homogeneous games always have NE.

\paragraph{Effortless Voting}

Effortless voting ($e_i=0$ for all $i\in N$) is applicable whenever effort is spent in advance of the decision and further accuracy improvements are not possible.

\begin{theorem}
Delegation games with effortless voting always have a (pure strategy) NE.\label{thm:delegation-games-NE}
\end{theorem}
\begin{proof}
We prove this statement by showing that the following procedure obtains a NE:
We start with a strategy profile in which all players vote directly, i.e., player $i$'s strategy is $i$.
Then, we iteratively allow players to choose their individual best response strategy to the current strategy profile.
Players act sequentially in arbitrary order.
If there are no more players that can improve their utility by changing their strategy, we have found a NE.
We prove convergence of this procedure by showing that a best response that increases the player's utility never decreases the utility of other players.

We proceed by induction.
Assume that all previous best responses have not reduced any players' utility (IH).
Assume player $i$ now chooses a best response that increases her utility.
Let ${\bf d}$ be the delegation profile; further, let $d^*_i=s$.
By assumption, $i$'s utility started with $q_i-e_i=q_i$ and has not decreased since, i.e., $u_i({\bf d})\geq q_i$.
Since $i$'s best response strictly increases $i$'s utility, it cannot be a delegation to herself.
So let a delegation to $j \neq i$ be $i$'s best response and consider profile ${\bf d}'=({\bf d}_{-i},j)$.
Further, let $d_j^*=t$, i.e., $i$ now delegates to $j$ and by transitivity to $t$, i.e., $d_i'^*=d_j'^*=t$.
Let $k$ be some player other than $i$.
We define the delegation path of $k$ as the sequence $({\bf d}(k), {\bf d}({\bf d}(k)), {\bf d}({\bf d}({\bf d}(k))),\dots)$.
If $k$'s delegation path does not contain $i$, then $k$'s utility remains unchanged, i.e., $u_k({\bf d}')\geq u_k({\bf d})$.
If $k$'s delegation path contains $i$, then $k$ now delegates by transitivity to $t$, i.e., we have $d_k^*=s$ and $d_k'^*=t$.
By \eqref{eq:utility}, we have
\begin{align}
&u_k({\bf d}) = q_s\cdot p_{k,s} + (1-q_{s})\cdot (1-p_{k,s}) \quad\text{ and}\label{eq:uked}\\
&u_k({\bf d}') = q_t\cdot p_{k,t} + (1-q_{t})\cdot (1-p_{k,t}).\label{eq:uke'd'}
\end{align}
We have to show that $k$'s utility does not decrease, i.e., $u_k({\bf d}') \geq u_k({\bf d})$, under the assumption that $i$ chooses a best response, i.e., $u_i({\bf d}') > u_i({\bf d})$,
 with:
\begin{align}
&u_i({\bf d}) = q_s\cdot p_{i,s} + (1-q_{s})\cdot (1-p_{i,s}) \quad\text{ and}\label{eq:uied}\\
&u_i({\bf d}') = q_t\cdot p_{i,t} + (1-q_{t})\cdot (1-p_{i,t}).\label{eq:uie'd'}
\end{align}
In the following we will often use the fact that, for $a,b\in[0,1]$, if $ab+(1-a)(1-b)\geq 0.5$, then either $a,b\in[0,0.5]$ or $a,b\in[0.5,1]$.
By IH, since accuracies are always at least 0.5, it holds that $u_i({\bf d})\geq q_i\geq 0.5$ and by \eqref{eq:uied} we have $q_s \cdot p_{i,s} + (1-q_s)\cdot (1-p_{i,s}) \geq 0.5 $ and hence $p_{i,s}\geq 0.5$.
Analogously, \eqref{eq:uked} implies that $p_{k,s}\geq 0.5$.

Furthermore, we use the fact that
\begin{equation}
p_{k,i} = p_{k,s}p_{s,i}+(1-p_{k,s})(1-p_{s,i}) + (- 2 (2x_k-1) \cdot (2 x_i - 1) \cdot (x_s - 1) x_s)
\label{eq:fact1}
\end{equation}
where $x_j = {\mathbb P}(\tau(j) = 1)$ for $j \in \set{k,i,s}$. Observe that, by the definition of utility in \eqref{eq:utility}, the assumptions made on ${\bf d}$ and ${\bf d}'$, and the fact that for $a,b\in[0,1]$, if $ab+(1-a)(1-b)\geq 0.5$, then either $a,b\in[0,0.5]$ or $a,b\in[0.5,1]$. So we have that either  $x_j \geq 0.5$ for $j \in \set{k, i, s}$, or $x_j \leq 0.5$ for $j \in \set{k, i, s}$. We work on the first case. The other case is symmetric. Let also $\gamma_{k,s,i} = - 2 (2x_k-1) \cdot (2 x_i - 1) \cdot (x_s - 1) x_s$. From the above it follows that $0.5 \geq \gamma_{k,i,s} \geq 0$. Furthermore, given that $p_{i,s} = p_{s,i} \geq 0.5$, we can also conclude that $p_{k,i}\geq 0.5$.
Now by substituting
\begin{equation*}
p_{k,s} = p_{k,i}p_{i,s}+(1-p_{k,i})(1-p_{i,s}) + (\underbrace{- 2 (2x_k -1) \cdot (2 x_s - 1) \cdot (x_i - 1) x_i}_{\gamma_{k,i,s}})
\end{equation*}
in \eqref{eq:uked}, we obtain
\begin{equation}
u_k({\bf d}) = (2 p_{k,i}-1) (\overbrace{2q_sp_{i,s}-q_s-p_{i,s}+1}^{u_i({\bf d})}) + 1 - p_{k,i} + \gamma_{k,i,s}(2q_s - 1).
\label{eq:uked=uied}
\end{equation}

Similarly, using the appropriate instantiation of \eqref{eq:fact1} for $x_j$ with $j \in \set{k,i,t}$, by substituting
$
p_{k,i}\cdot p_{i,t}+(1-p_{k,i})(1-p_{i,t}) + \gamma_{k,i,t}
$
for $p_{k,t}$ in \eqref{eq:uke'd'} we obtain
\begin{equation}
u_k({\bf d}') = (2 p_{k,i}-1)\cdot (\overbrace{2q_tp_{i,t}-q_t-p_{i,t}+1}^{u_i({\bf d}')}) +  1 - p_{k,i} + \gamma_{k,i,t}(2q_t - 1).
\label{eq:uke'd'=uie'd'}
\end{equation}
Now observe that, since $p_{k,i}\geq 0.5$ we have that $(2 p_{k,i}-1)\geq 0$. It remains to compare $\gamma_{k,i,s}(2q_s - 1)$ with $\gamma_{k,i,t}(2q_t - 1)$, showing the latter is greater than the former. Observe that both expressions have a positive sign. We use the fact that $ab+(1-a)(1-b) < cd+(1-c)(1-d)$ implies $cd > ab$ under the assumption that $a,b,c,d\in[0.5,1]$. On the basis of this, and given that $u_i({\bf d}')> u_i({\bf d})$, we obtain that $q_s\cdot p_{i,s} < q_t\cdot p_{i,t}$ and therefore that $q_s\cdot x_s < q_t\cdot x_t$, from which we can conclude that
\begin{equation*}
\begin{split}
&\big(\overbrace{- 2 (2x_k -1) \cdot (2 x_s - 1) \cdot (x_i - 1) x_i}^{\gamma_{k,i,s}}\big)\cdot(2q_s - 1) \\
&< \big(\underbrace{- 2 (2x_k -1) \cdot (2 x_t - 1) \cdot (x_i - 1) x_i}_{\gamma_{k,i,t}}\big) \cdot(2q_t - 1).
\end{split}
\label{eq:extra}
\end{equation*}
It follows that the assumption $u_i({\bf d}')> u_i({\bf d})$ (player $i$ chose a best response that increased her utility) together with Equations~(\ref{eq:uked=uied}) and~(\ref{eq:uke'd'=uie'd'}) implies that $u_k({\bf d}')> u_k({\bf d})$ (and {\em a fortiori} that $u_k({\bf d}') \geq u_k({\bf d})$). We have therefore shown that if some player chooses a best response, the utility of other players does not decrease. This completes the proof.
\end{proof}
\iffalse
\begin{proposition}
There exist delegation games without (pure strategy) NE.
\end{proposition}
\begin{proof}
Embedding a $3$-player matching penny (for $N \geq 3$) showing that best-response dynamics leads to cycles from every possible profile.

\note[Davide]{the construction is possible in cases in which proximity is not symmetric, possibly a case we want to rule out.}

\note[Martin]{Is a proof like this still possible in our new setting?}
\end{proof}
\fi

\paragraph{Discussion}

The existence of NE in general delegation games remains an interesting open problem. It should be noted that the proof strategies of both Theorems~\ref{thm:NE-deterministic} and~\ref{thm:delegation-games-NE} do not work in the general case. Without a clear dichotomy of type it is not possible to assign delegations for all agents in an SCC (as we do in the proof of Theorem~\ref{thm:NE-deterministic}). And the key property upon which the proof of Theorem \ref{thm:delegation-games-NE} hinges (that a best response of an agent does not decrease the utility of other agents) fails in the general case due to the presence of non-zero effort.
Finally, it should also be observed that Theorem \ref{thm:delegation-games-NE} (as well as Proposition~\ref{prop:positive})
essentially depend on the assumption that types are \emph{independent} random variables. If this is not the case (e.g., because voters' preferences are correlated), delegation chains can become undesirable.

\begin{example}
Consider the following example with agents $1$, $2$ and $3$. The probability distribution ${\mathbb P}$ is defined as
${\mathbb P}(\tau(1)=1\wedge \tau(2)=1\wedge \tau(3)=0)=0.45$,
${\mathbb P}(\tau(1)=0\wedge \tau(2)=1\wedge \tau(3)=1)=0.45$, and
${\mathbb P}(\tau(1)=1\wedge \tau(2)=1\wedge \tau(3)=1)=0.1.
$
Consequently, $p_{1,2}=0.55$, $p_{2,3}=0.55$, and $p_{1,3}=0.1$.
Let us assume that the agents' accuracies are $q_1=0.5001$, $q_2=0.51$, and $q_3=0.61$.
A delegation from agent 1 to 2 is locally positive as $q_2\cdot p_{1,2}+(1-q_2)\cdot (1-p_{1,2}) = 0.501 > q_1$.
Furthermore, a delegation from 2 to 3 is locally positive as $q_3\cdot p_{2,3}+(1-q_3)\cdot (1-p_{2,3}) = 0.511 > q_2$.
However, the resulting delegation from $1$ to $3$ is not positive since $q_3\cdot p_{1,3}+(1-q_3)\cdot (1-p_{1,3}) = 0.412$.
\end{example}

\subsection{Quality of Equilibria in Delegation Games}

In delegation games players are motivated to maximize the tradeoff between the accuracy they acquire and the effort they spend for it. A natural measure for the quality of a delegation profile is, therefore, how accurate or informed a random voter becomes as a result of the delegations in the profile, that is, the average accuracy (i.e., $\bar{q}^*({\bf d}) = \frac{1}{n}\sum_{i\in N} q^*_i({\bf d})$) players enjoy in that profile. One can also consider the utilitarian social welfare $\mathsf{SW}({\bf d}) = \sum_{i \in N} u_i({\bf d})$ of a delegation profile ${\bf d}$. This relates to average accuracy as follows:
\[
\bar{q}^*({\bf d}) = \frac{\mathsf{SW}({\bf d}) + \sum_{i \mid d(i) = i} e_i}{n}.
\]

It can immediately be noticed that equilibria do not necessarily maximize
average accuracy.
On the contrary, in the following example NE yields an average accuracy
of close to $0.5$, whereas an average accuracy
of almost $1$ is achievable.

\begin{example} \label{ex:quality}
Consider an $n$-player delegation game where all players have the same type and
$(i,j) \in R$ for all $j$ and all $i>1$, i.e., player 1 is a sink in $R$ and cannot delegate to anyone, but all others can delegate to everyone.
Further, we have $e_1=0$ and $e_i=0.5-\epsilon$ for $i\geq 2$. The respective accuracies are $q_1=0.5+2\epsilon$ and $q_i=1$.
If player $i\geq 2$ does not delegate, her utility is $0.5+\epsilon$. Hence, it is always more desirable to delegate to player $1$ (which yields a utility of $0.5+2\epsilon$ for $i$). Consider now the profiles in which all players delegate to player $1$ (either directly or transitively). Player $1$ can only vote directly (with utility $0.5+2\epsilon$). All such profiles are NE with average accuracy $0.5+2\epsilon$.
If, however, some player $j\geq 2$ chose to vote herself, all players (except $1$) would delegate to $j$ thereby obtaining an average accuracy of $1-\frac{0.5-2\epsilon}{n}$, which converges to $1$ for $n\to\infty$. This is not a NE, as $j$ could increase her utility by delegating to $1$.
\end{example}

The findings of the example can be made more explicit by considering a variant of the price of anarchy for delegation games, based on the above notion of average accuracy. That is, for a given delegation game $G$, the price of anarchy ($\textit{PoA}$) of $G$ is given by
\[
\textit{PoA}(G) = \frac{\max_{{\bf d} \in N^n} \bar{q}^*({\bf d})}{\min_{{\bf d} \in \textit{NE}(G)} \bar{q}^*({\bf d})},
\]
where $\textit{NE}(G)$ denotes the set of pure-strategy NE of $G$.

\begin{fact}
PoA is bounded below by $1$ and above by $2$ (see Apendix~\ref{appendix:proof}).
\end{fact}

An informative performance metrics for liquid democracy is the difference between the group accuracy after delegations versus the group accuracy achieved by direct voting. This measure, called {\em gain}, was introduced and studied by \citet{kahng18liquid}. Here we adapt it to our setting as follows:
$
    \mathsf{G}(G)  = \left(\min_{{\bf d} \in \textit{NE}(G)} \bar{q}^*({\bf d})\right) - \bar{q}
$
where $\bar{q} = \bar{q}^*(\tuple{1, \ldots, n})$.
That is, the gain in the delegation game $G$ is the average accuracy of the worst NE minus the average accuracy of
the profile in which no voter delegates. It turns out that the full performance range is possible:
\begin{fact}
$\mathsf{G}$ is bounded below by $-0.5$ and above by $0.5$ (see Apendix~\ref{appendix:proof}).
\end{fact}

The above bounds for PoA and gain provide only a very partial picture of the performance of liquid democracy when modeled as a delegation game. The next section provides a more fine-grained perspective on the effects of delegations.

\section{Simulations}

We simulate the delegation game described above in a variety of settings. We restrict ourselves to homogeneous games. This allows us to relate our results to those of \citet{kahng18liquid}. Our experiments serve to both verify and extend the theoretical results of the previous section. In particular we simulate the best response dynamics employed in the proof of Theorem \ref{thm:delegation-games-NE} and show that these dynamics converge even in the setting with effort, which we could not establish analytically.
In addition, we investigate the dynamics of a one-shot game scenario, in which all agents need to select their proxy simultaneously at once.

\paragraph{Setup}
We generate graphs of size $N=250$ of each of the four topologies \textit{random}, \textit{regular}, \textit{small world}, and \textit{scale free}, for different average degrees, while ensuring that the graph is connected.
Agents' individual accuracy and effort are initialized randomly with $q_i \in [0.5,1]$ and $q_i - e_i \geq 0.5$.
We average results over 2500 simulations for each setting (25 randomly generated graphs $\times$ 100 initializations). Agents correctly observe their own accuracy and effort, and the accuracy of their neighbors. The game is homogeneous, so proximities are $1$.

Each agent $i$ selects from her neighborhood $R(i)$ (which includes $i$ herself) the agent $j$ that maximizes her expected utility following \eqref{eq:utility}. We compare two scenarios. The {\em iterated best response} scenario follows the procedure of the proof of Theorem~\ref{thm:delegation-games-NE}, in which agents sequentially update their proxy to best-respond to the current profile ${\bf d}$ using knowledge of their neighbors' accuracy $q_i^*({\bf d})$. In the {\em one-shot game} scenario all agents choose their proxy only once, do so simultaneously, and based only on their neighbors' accuracy. The latter setup captures more closely the epistemic limitations that agents face in liquid democracy.

\subsection{Iterated Best Response Dynamics}

These experiments complement our existence theorems. They offer insights into the effects of delegations on average voter's accuracy in equilibrium, and on the effects of different network structures on how such equilibria are achieved.

We initialize $q_i \sim \mathcal{N}(0.75,0.05)$ and first investigate the case in which $e_i = 0$ for all $i$ (effortless voting). Across all combinations of network types and average degrees ranging from 4 to 24, we find that the best response dynamics converges, as predicted by Theorem~\ref{thm:delegation-games-NE}, and does so optimally with $d_i^* = \argmax_{j} q_j$ for all $i$. We observe minimal differences between network types, but see a clear inverse relation between average degree and the
number of iterations required to converge
(Table~\ref{tab:convergence_rate}, top). Intuitively, more densely connected networks facilitate agents in identifying their optimal proxies (further details are provided in Appendix~\ref{appendix:simulation}).

We accumulate results across all network types and compare the effortless setting to the case in which effort is taken into account. When we include effort $e_i \sim \mathcal{N}(0.025,0.01)$, we still observe convergence in all cases and, interestingly, the number of iterations required does not change significantly (Table~\ref{tab:convergence_rate}, bottom). Although the process no longer results in an optimal equilibrium, each case still yields a single guru $j$ with $q_j \approx \max_k q_k$ (less than $1\%$ error) for all $k \in N$. In this scenario, the inclusion of effort means that a best response update of agent $i$ no longer guarantees non-decreasing accuracy and utility for all other agents, which was a key property in the proof of Theorem \ref{thm:delegation-games-NE}. This effect becomes stronger as the average network degree increases, and as a result higher degree networks allow a greater discrepancy between the maximal average accuracy achievable and the average accuracy obtained at stabilization (Table~\ref{tab:br_accuracy})

\begin{table}[tb]
    \caption{Total number of best response updates by individual agents and corresponding full passes over the network required for convergence. Reported are the mean (std.dev.) over all network types. \textit{Note}: not all agents update their delegation at each full pass, but any single update requires an additional pass to check whether the best response still holds.}
    \label{tab:convergence_rate}
    \begin{widetable}{\columnwidth}{l|cccccc}
    Degree & 4 & 8 & 12 & 16 & 20 & 24 \\
    \hline
    BR updates & 298.1 & 261.7 & 254.2 & 251.6 & 250.6 & 250.0 \\
    (effortless) & (18.2) & (11.1) & (6.9) & (4.5) & (3.3) & (2.6) \\[0.2em]
    Full passes & 3.6 & 3.0 & 2.9 & 2.8 & 2.7 & 2.5 \\
    (effortless) & (0.5) & (0.1) & (0.2) & (0.4) & (0.5) & (0.5) \\[0.2em]
    \hline
    BR updates & 294.7 & 259.4 & 252.9 & 250.9 & 250.2 & 249.9 \\
    (with effort) & (18.4) & (10.6) & (6.6) & (4.8) & (4.9) & (4.3) \\[0.2em]
    Full passes & 3.6 & 3.0 & 2.8 & 2.6 & 2.4 & 2.4 \\
    (with effort) & (0.5) & (0.3) & (0.6) & (0.8) & (0.9) & (1.0)
    \end{widetable}
\end{table}

\begin{table}[tb]
    \caption{Comparing the maximum accuracy across all agents and the mean accuracy under delegation ${\bf d}$ for different network degrees, averaged across network types. The differences are statistically significant (paired t-test, $p=0.05$).}
    \label{tab:br_accuracy}
    \begin{widetable}{\columnwidth}{l|cccccc}
    Degree & 4 & 8 & 12 & 16 & 20 & 24 \\
    \hline
    $\max_j q_j$ & 0.8908 & 0.8908 & 0.8904 & 0.8909 & 0.8904 & 0.8910 \\
    $\bar{q}^*({\bf d})$ & 0.8906 & 0.8903 & 0.8897 & 0.8899 & 0.8890 & 0.8893
    \end{widetable}

\end{table}

In lower degree graphs (e.g. degree 4) we further observe differences in convergence speed between the four different network types which coincide with differences between the average path lengths in those graphs: a shorter average distance between nodes yields a lower number of best response updates.
This is intuitive, as larger distances between nodes mean longer delegation chains, but we have not yet conducted statistical tests to verify this hypothesis.

\subsection{One-Shot Delegation Games}

Here we study one-shot interactions in a delegation game:
all agents select their proxy (possibly themselves) simultaneously among their neighbors; no further response is possible. This contrasts the previous scenario in which agents could iteratively improve their choice based on the choices of others.
While \citet{kahng18liquid} study a probabilistic model, we instead assume that agents deterministically select as proxy the agent $j \in R(i)$ that maximizes their utility, as above. We compare $\bar{q}$ and $\bar{q}^*$ (the average network accuracy without and with delegation, respectively), as well as the probability of a correct majority vote under both direct democracy $P_D$ and liquid democracy $P_L$ where gurus carry as weight the number of agents for whom they act as proxy. The difference $P_L - P_D$ is again similar to the notion of {\em gain} \citep{kahng18liquid}. In line with Condorcet's jury theorem (see for instance \citealt{grofman83thirteen}) $P_D \rightarrow 1$ as $N \rightarrow \infty$, and indeed for $N=250$ we obtain $P_D \approx 1$.

First we again look at the effortless setting. Figure~\ref{fig:acc_maj_n250} (top) shows both metrics for the four different network types and for different average degrees.
\begin{figure}[tb]
	\centering

	\includegraphics[width=0.9\linewidth]{acc_maj_full.pdf}
	\caption{{\bf Top:} Without effort. {\bf Bottom:} With effort $e_i \sim \mathcal{N}(0.025, 0.01)$. {\bf Left:} mean accuracy under liquid democracy, $\bar{q}^*({\bf d})$. The solid (dashed) line shows the mean (std. dev.) of the initial accuracy $q$; the dotted line shows $\max_i q_i$. {\bf Right:} probability of a correct majority vote under ${\bf d}$.}
	\label{fig:acc_maj_n250}

\end{figure}
We observe that while $\bar{q}^*({\bf d})$ increases as the network degree increases (and in fact is always higher than $\bar{q}$ without delegation), the probability of a correct majority outcome, $P_L$, simultaneously decreases. This confirms the analysis of \citet{kahng18liquid}. We also observe that the number of gurus decreases exponentially as the degree increases (Figure~\ref{fig:perc_dist_n250_q0.75_e0}, left). Simply put, giving all voting weight to a small group of gurus increases the chance of an incorrect majority vote, assuming that gurus have a less than perfect accuracy.

\begin{figure}[tb]
    \centering
    \includegraphics[width=0.9\linewidth]{{perc_dist_n250_q0.75_e0}.pdf}
    \caption{Percentage of guru nodes under ${\bf d}$ (left) and mean distance between (non-guru) nodes and their gurus (right).}
    \label{fig:perc_dist_n250_q0.75_e0}

\end{figure}

When we include effort (Figure~\ref{fig:acc_maj_n250}, bottom), thereby moving away from the model of \citet{kahng18liquid}, we observe a drastic decrease in average network accuracy combined with a lower probability of a correct majority outcome under liquid democracy, with both decreasing as network degree increases. The main reason is the existence of delegation cycles in this case. This contrasts the best response setting above where agents could iteratively reconsider their choice of proxy and thus avoid cycles. Now, even with relatively low effort (mean 0.025), up to {\em half} of all agents are stuck in a cycle (and thereby fail to pass information about their type) when the degree increases.
This confirms results on the probability of delegation cycles from \citet{christoff17binary} and stresses the importance of cycle resolution in concrete implementations of liquid democracy.

Figure~\ref{fig:acc_maj_n250} further highlights differences between the four network types. Scale free networks yield a lower probability of a correct majority outcome across all degrees, as well as a larger number of gurus with a lower average accuracy and longer delegation chains (Figure~\ref{fig:perc_dist_n250_q0.75_e0}, right). Intuitively, this indicates that one-shot interactions in scale free networks are more likely to end up in a local optimum. In contrast, small world networks have short average distances
and thus agents are more likely to be close to their optimal guru.
Finally, our experiments highlight a key feature of liquid democracy: the trade-off between a reduction in (total) effort against a loss in average voting accuracy.

\section{Conclusions and Future Work}

The paper introduced delegation games as a first game-theoretic model of liquid democracy. Both our theoretical and experimental results showed that voting effort is a key ingredient for understanding how delegations form and what their effects are.
Our empirical findings provided further insights
into the influence of interaction networks on the quality of collective decisions in liquid democracy.

The paper opens up several directions of research.
A general NE existence theorem is the main open question. Our model can then be generalized in many directions, e.g.: by making agents' utility dependent on voting outcomes; by dropping the independence assumption on agents' types; or by assuming the voting mechanism has better than $0.5$ accuracy in identifying the types of agents involved in cycles.

\iffalse
\section{Acknowledgements}
We are indebted to the anonymous reviewers of IJCAI/ECAI'18 and  AAAI'19 for many helpful comments on earlier versions of this paper.
We are also grateful to the participants of the LAMSADE seminar at Paris Dauphine University, and the THEMA seminar at University Cergy-Pontoise where this work was presented, for many helpful comments and suggestions.
Daan Bloembergen has received funding in the framework of the joint programming initiative ERA-Net Smart Energy Systems' focus initiative Smart Grids Plus, with support from the European Union's Horizon 2020 research and innovation programme under grant agreement No 646039.
Davide Grossi was partially supported by EPSRC under grant EP/M015815/1.
Martin Lackner was supported by the European Research Council (ERC) under grant number 639945 (ACCORD) and by the Austrian Science Foundation FWF, grant P25518 and Y698.
\fi

redpajama_set_name: RedPajamaArXiv


text:
How Apple Creates Hype for Their Events (Without Irritating Customers
Want to generate product hype like the pros? Here are a few key takeaways from Apple's iPhone 7 launch last week.
By Ken SterlingExecutive vice president, BigSpeak@ken_sterling
My iPhone 5 is in pretty rough shape.
The glass screen protector is chipped, cracked and has air bubbles. Underneath, the screen is cracked in 3 places--only held together by my screen protector, which really looks like it has a case of dreaded outer-space Measles.
Our president, Barrett, texted me earlier: "Partner, let's upgrade you to the iPhone 7!" I texted back, "Thanks, lovin' size and shape of 5--not sure I'm lovin' this headphone issue."
AT&T was on the ball too--an email just popped into my inbox exclaiming: "Congratulations! You're eligible for an upgrade to the iPhone 7!"
No thank you AT&T--I'll give up my iPhone 5 when you pry it from my cold, dead hands. (I'm partial to the flat edges, which allow me to actually balance the phone on its side.)
My grandpa used to say "never stop at no," and I'm a revenue generation guy. I eat, drink, and sleep persuasion, marketing and sales 24/7.
I'm constantly researching what it takes to get people to say "yes," so naturally, I asked myself, what would it take to get me to say yes, in this case to making the decision to upgrade.
I looped in Amber and Tasha from our marketing team: "Hey, what's Apple doing to promote their launch of the iPhone 7?"
As we worked to review the launch, though, we realized that Apple was actually doing a great job of PR and product presentation. Here's what we learned--and what you can learn--from the iPhone 7 launch:
1. Rumors are much more fun than facts
Ever notice that it's always a "rumor" that gets the new iPhone release hype train rolling?
Some leak from an unknown source "happens" to have the scoop. Or an Apple team member "accidentally" leaves their beta version in a bar. Hey Apple Security team, ever heard of an app called Find My iPhone?
Oh, wait, maybe you didn't want the phone to be recovered but instead left in the hands of a tech reporter. Oops--free publicity.
2. Involve notable companies and people to build credibility
Apparently, you don't need to work at Apple to launch Apple products.
Sia performed her new hit at the launch. Famed Nintendo designer Shigeru Miyamoto announced a Mario game. Instagram's head of design touted the radical new camera features.
The press event was held in the Bill Graham Auditorium, named after the trend-setting, boundary-pushing music promoter--at this point it should probably be renamed "Apple Auditorium."
3. Highlight benefits and downplay what's missing
By now, you've surely heard a lot about the "longest battery life ever" and the "courage" it took to go cordless and yank the headphone jack.
But here's what you didn't hear a lot of (Apple fans, plug your ears):
Competitors' batteries last longer--some phones now charge in just a few minutes, even wirelessly.
Wireless headphones are nothing new.
Neither is a double camera (or the depth-of-field feature, which was featured on an HTC phone two years ago).
I'm sure Apple wants to make sure these are things that many future iPhone 7 owners will likely never, ever know about.
4. Musicians always get the guys
As I already mentioned, Sia made an appearance. But music has always been a major part of Apple's approach to marketing--it's "part of their DNA"--making a huge impact on growth and revenue over the years.
The iPod is credited with creating significant traction in the market back in the early 00s, and reaffirming those creative roots is a smart move.
5. Have spin doctors on hand
It's always a good idea to have a cleanup crew on hand when new products launch.
Apple accidentally leaked some product announcements on Twitter during the event, but had the wherewithal to delete them before anything bad happened (unless, of course, you consider no headphone jack a bad thing).
So what can we learn from all this? Apple nailed their brand image, and because of it, the launch felt like the birth of something new and special.
Despite negative rumors about features, they did a great job of selling the phone's impressive tech.
On the flipside, calling their headphone move "courageous" seemed, I don't know... desperate? Shouldn't courage speak for itself?
The crystal purity that the brand once enjoyed is seeming to crack slightly about the edges--much like the battered screen of my iPhone 5, which, all things considered, I'm keeping.
Sorry, Tim.
The opinions expressed here by Inc.com columnists are their own, not those of Inc.com.


text:
Home inSight Making Iran Great Again
Making Iran Great Again
Michael Ledeen • January 30, 2018
SOURCEPJ Media
Bit by bit, we are getting a fuller picture of how Tehran's tyrants have wrecked the country.
For the most part, the reports in the American press have recounted the economic woes leading up to the nationwide uprising. That focus is due to two related misunderstandings: first, that revolution is driven by economic misery, and second, that such insurrections are a desperate effort to change conditions before all is lost. Those who believe this "explanation" demean the Iranians risking their lives while chanting "down with Khamenei" and "we do not want to be ruled by mullahs."
If misery caused revolution, North Korea would be in the throes of turmoil, but it isn't. Revolution is not an act of desperation, but an act of hope, which is why it is overwhelmingly the work of young people, who believe they can recreate their country.
The wreckage of Iran testifies to the failure of the theocratic regime, which most every Iranian can see whether or not he is suffering economically. To be sure, there is plenty of economic misery: an unemployment rate around forty percent; the bankruptcy of innumerable funds, including Iran's equivalent of Social Security; the bankruptcy of numerous factories; and of course the bankruptcy of many banks. Iranians know that their currency is in spectacular free fall. By new year's day (late March), the rial will likely be worth one one-thousandth what it was under the shah. Even so, workers at some big factories haven't been paid for six months, and some of them are on strike.
But the insurrection that has swept the country in the past month — and which continues to flare up daily — is not merely a call for economic improvement. The Iranian people are suffering from a vast breakdown of the entire system, and they detest the clerics who run it. The other day, more than 25 cities were shut down by pollution. There is a nationwide water crisis, threatening agriculture and sanitation.
The clerical ruling class is blamed for these many failures, and the "Islamic Revolution" has long since lost its mass appeal. Attendance at mosques is way down, and most of the attendees are there because they are ordered there.
The insurrection is thus not merely the product of economic misery, as so many analysts would have it. The human symbol of the revolution, after all, is Vida Movahed, a woman holding her hijab on a stick, her hair flowing over her shoulders. She isn't asking for a salary increase or for her bank to function properly. She's calling for the end of the Islamic Republic.
There are Twitter videos showing other women sans veils directly challenging security forces in the name of their movement, "White Wednesdays."
From all appearances, Supreme Leader Ali Khamenei and his henchmen have no intention of addressing their citizens' rage, even assuming they know how to do it. They are up to their necks in war, from Lebanon, Syria, Afghanistan, and Iraq to numerous targets across Africa. For evidence of their complicity in recent terrorist massacres, we need only look to last week's devastating assault on a Kabul hotel. Tehran's global radio and television network reported the attack within minutes, well before the Afghan government was able to report it.
According to Radio Free Europe, the regime is upping the ante a further $2.5 billion:
Ali Asghar Yousefnejad, a member of Iranian Parliament and the spokesperson for Iran's special parliamentary committee that deals with the country's budget, told the country's official news agency IRNA on Tuesday that the $2.5 billion is in addition to what the military will receive once the fiscal year begins in March.
The Iranian people do not welcome this expansion of military activities, nor, I suspect, do most of them believe the announcement (via official media) that the Revolutionary Guards are fighting Islamic State forces in western Iran. As the Baghdad Post notes, many analysts believe it is disinformation designed to frighten the populace into supporting the regime. Notably, for several years demonstrators have chanted "talk to us about Iran, not about Gaza" at regime officials who speak about spreading the Islamic Revolution.
Yes, the Iranian people are having a tough time making ends meet, but that does not begin to account for the massive uprising. They are disgusted with a failed regime, don't want their husbands and sons sent to battle in Arab lands, and, above all, want an end to the Islamic Republic.
Dr. Michael Ledeen is a Jewish Policy Center Fellow and the Freedom Scholar at the Foundation for the Defense of Democracies. The article first appeared in PJ Media.


Thank you thank you thank you! I had been using ODCompletion for years until the switch to Intel and it was sorely missed. Apple's completion is fine to find method names, but it's nowhere close to ODCompletion when you are typing code in a file where most of the names you use are already in use somewhere else in the file.


text:
Nadia Podoroska (* 10. Februar 1997 in Rosario) ist eine argentinische Tennisspielerin.

Karriere
Podoroska, die im Alter von fünf Jahren mit dem Tennissport begann, spielt am liebsten auf Hartplätzen. Auf der ITF Women's World Tennis Tour gab sie 2011 ihren Einstand und gewann 2013 ihr erstes Profiturnier. Bislang hat sie 14 ITF-Titel im Einzel und sieben im Doppel holen können.
2016 debütierte sie in Rabat in der Qualifikation zu einem WTA-Turnier, musste aber in der ersten Runde aufgeben. Im Anschluss an ihren bis dahin größten Titelgewinn bei einem ITF-Turnier der $25.000-Kategorie in Denain, glückte ihr in Bukarest der erstmalige Sprung in ein WTA-Hauptfeld. Dort war sie jedoch zum Auftakt gegen Danka Kovinić chancenlos. Bei den US Open startete sie daraufhin erstmals in der Qualifikation zu einem Grand-Slam-Turnier und rückte auf Anhieb in die Hauptrunde vor, ehe sie sich in ihrer ersten Begegnung Annika Beck geschlagen geben musste.

2017 konnte Podoroska nach erfolgreicher Qualifikation in Monterrey auf Hartplatz gegen Madison Brengle ihren ersten Erfolg in einem WTA-Hauptfeld erringen und gewann anschließend beim Sandplatzturnier in Bogotá an der Seite von Beatriz Haddad Maia ihren ersten WTA-Titel im Doppel, nachdem sich die beiden im Endspiel gegen Verónica Cepede Royg und Magda Linette durchgesetzt hatten. Aufgrund einer Verletzung am Handgelenk musste Podoroska die Saison aber nach ihrer Erstrundenniederlage in Bukarest frühzeitig beenden und kehrte erst im März 2018 wieder auf die Tour zurück.

Anfang 2020 zeigte sie sich stark formverbessert und begann das Jahr mit zwei ITF-Titeln im Einzel sowie einer Halbfinalteilnahme bei einem Turnier der WTA Challenger Series in Newport Beach. Nach der coronabedingten Saisonunterbrechung, erzielte Podoroska zunächst das Halbfinale beim hochdotierten WTA Challenger Prag, bei dem sie zudem das Endspiel im Doppel erreichte. Danach gewann sie in Saint-Malo bei einem ITF-Turnier der $60.000-Kategorie ihren bis dahin größten Einzeltitel und qualifizierte sich ohne Satzverlust für das Hauptfeld der verschobenen French Open. Dort spielte sie sich bis ins Viertelfinale, in dem sie mit Elina Switolina erstmals eine Spielerin aus den Top 10 der Weltrangliste schlagen konnte und damit die erste Qualifikantin im Halbfinale der French Open wurde. Dort musste sie sich der späteren Siegerin Iga Świątek geschlagen geben. Durch den Erfolg verbesserte sie sich in der Weltrangliste um fast 100 Plätze unter die Top-50.

2014 gab Podoroska bei der 0:4-Playoff-Niederlage gegen Russland ihren Einstand für die argentinische Fed-Cup-Mannschaft. Seitdem hat sie 17 Begegnungen für ihr Land bestritten, von denen sie zwölf gewinnen konnte (Einzelbilanz 11:1).

Turniersiege

Einzel

Doppel

Abschneiden bei Grand-Slam-Turnieren

Dameneinzel

Damendoppel

Juniorinneneinzel

Juniorinnendoppel

Auszeichnungen
 WTA Neuling des Jahres – 2020

Weblinks

Einzelnachweise

Billie-Jean-King-Cup-Spielerin (Argentinien)
Olympiateilnehmer (Argentinien)
Teilnehmer der Olympischen Sommerspiele 2020
Teilnehmer an den Panamerikanischen Spielen (Argentinien)
Teilnehmer an den Südamerikaspielen (Argentinien)
Panamerikaspielesieger (Tennis)
Argentinier
Geboren 1997
Frau


Bill Nye, "The Science Guy," Jessie Deeter, the producer of Who Killed The Electric Car? and Revenge of the Electric Car, and our own Chelsea Sexton took to the stage at the close of public night at the Plug-in 2010 Conference. With this line-up, it was more than 66 percent the same as last year, when Nye, Sexton and Electric Car director Chris Paine answered audience questions. Given the "preaching to the choir," audience-led nature of the event, we thought there would probably be a lot of readers who would want to "attend," digitally, so we're posting an audio recording of the entire two-hour event after the jump. What does it contain?
How about a short preview (verbal, not video) of Revenge of the Electric Car? Deeter said that the film will focus on three main stories: General Motors and the Chevrolet Volt, Tesla Motors, Nissan and the Leaf and electric car mechanic Gadget. How about the panelists' predictions of the percentage of new cars that are plug-ins by 2020? Nye said he doesn't think it'll be 10 percent, Sexton said it'll totally be determined by how many the OEMs are willing to build. How about lots of disparaging comments about adding sound to silent electric cars? How about Nye calling lithium supply worries the "reddest of herrings"? How about one member of the audience proudly saying he's been driving an EV1 since 1998, and Nye replying, "You must be exhausted"? Zing! All these classics and more await you after the jump.
Or download the MP3 here (40MB, 2 hours).


text:
Q: Push notifications not sending due to JSON error in server I cannot figure out why the json is incorrect. I used curl command and it worked perfectly fine. Any reason why this error occurs? I included the error message on the bottom. All other forums are saying to add /parse to the end of the server URL, but I have already done that.
Parse.Cloud.define("TestNotification", function(request, response){
var query = new Parse.Query(Parse.Installation);
  query.equalTo("appName", "NewApp");

  Parse.Push.send({
      where: query,
      data:{
          title: request.params.title,
          alert: request.params.alert
      }
    }, { useMasterKey: true })
    .then(function() {
      response.success();
    }, function(error) {
      response.error(error);
  });
});

curl
curl -X POST -H "X-Parse-Application-Id: xxxxxxx"  -H "X-Parse-Master-Key: xxxxxx" -H "Content-Type: application/json" -d '{"where":{"channels":{"$in":["testchannel"]}},"data":{"alert": "test push"}}' https://xxxxx.herokuapp.com/parse/push
angular(where I am calling the cloud code)
Parse.Cloud.run('TestNotification', {title: "title", alert: "alert"}).then(function(result) {
                    console.log(result);

                },
                function(error) {
                    console.log(error);
                });

Error
message: 'Received an error with invalid JSON from Parse: Cannot POST /push\n' } } code=141, code=107, message=Received an error with invalid JSON from Parse: Cannot POST /push

redpajama_set_name: RedPajamaStackExchange