text:
\section{INTRODUCTION}

The dueling bandit is a variation of the classic multi-armed bandit problem in which the actions are noisy comparisons between arms, rather than observations from the arms themselves \citep{karmedduelingbandit}.  Each action provides $1$ bit indicating which of two arms is probably better.  For example, the arms could represent objects and the bits could be responses from people asked to compare pairs of objects.
In this paper, we focus on the pure {\em exploration} problem of finding the ``best'' arm from noisy pairwise comparisons. This problem is different from the {\em explore-exploit} problem studied in \citet{karmedduelingbandit}. There can be different notions of ``best'' in the dueling framework, including the Condorcet and Borda criteria (defined below).

Most of the dueling-bandit algorithms are primarily concerned with finding the Condorcet winner
(the arm that is probably as good or better than every other arm).
There are two drawbacks to this.  First, a Condorcet winner does not exist unless the underlying probability matrix governing the outcomes of pairwise comparisons satisfies certain restrictions. These restrictions may not be met in many situations. In fact, we show that a Condorcet winner doesn't exist in our experiment with real data presented below.  Second, the best known upper bounds on the sample complexity of finding the Condorcet winner (assuming it exists) grow quadratically (at least) with the number of arms.  This makes Condorcet algorithms impractical for large numbers of arms.

To address these drawbacks, we consider the Borda criterion instead.  The Borda
score of an arm is the probability that the arm is preferred to another arm
chosen uniformly at random. A Borda winner (arm with the largest Borda score)
always exists for every possible probability matrix. We assume throughout this paper that there exists a unique Borda winner. Finding the Borda winner with probability at least $1-\delta$ can be reduced to solving an instance of the standard multi-armed bandit problem resulting in a sufficient sample complexity of $\mathcal{O}\left(\sum_{i>1} (s_1-s_i)^{-2} \log\left( \log((s_1-s_i)^{-2})/\delta\right) \right)$, where $s_i$ denotes Borda score of arm $i$ and
$s_1>s_2>\cdots>s_n$ are the scores in descending order \citep{karnin2013almost,lilucb}. In favorable cases, for instance, if $s_1-s_i
\geq c$, a constant for all $i>1$, then this sample complexity is linear in $n$ as opposed to the quadratic sample complexity necessary to find the Condorcet winner. In this paper we show that this upper bound is essentially tight, thereby apparently ``closing'' the Borda winner identification problem. However, in this paper we consider a specific type of structure that is motivated by its existence in real datasets that complicates this apparently simple story. In particular, we show that the reduction to a standard multi-armed bandit problem can result in very bad performance when compared to an algorithm that exploits this observed structure.

We explore the sample complexity dependence in more detail and consider
structural constraints on the matrix (a particular form of sparsity natural to
this problem) that can significantly reduce the sample complexity. The sparsity model
captures the commonly observed behavior in elections in which there are a small
set of ``top'' candidates that are competing to be the winner but only differ on
a small number of attributes, while a large set of ``others'' are mostly irrelevant
as far as predicting the winner is concerned in the sense that they would always
lose in a pairwise matchup against one of the ``top'' candidates.

This motivates a new algorithm called Successive Elimination with Comparison
Sparsity (SECS).  SECS takes advantage of this structure by determining which of
two arms is better on the basis of their performance with respect to a sparse
set of ``comparison'' arms. Experimental results with real data demonstrate the
practicality of the sparsity model and show that SECS can provide significant
improvements over standard approaches.

The main contributions of this paper are as follows:\\[-14pt]
\begin{itemize}
    \item A distribution dependent lower bound for the sample complexity of identifying the Borda winner that essentially shows that the Borda reduction to the standard multi-armed bandit problem (explained in detail later) is essentially optimal up to logarithmic factors, given no prior structural information.
    \item A new structural assumption for the $n$-armed
        dueling bandits problem in which the top arms can be distinguished by duels with a sparse set of other arms.
    \item An algorithm for the dueling bandits problem under this assumption, with
        theoretical performance guarantees showing significant sample complexity improvements compared to naive reductions to standard multi-armed bandit algorithms.
   \item Experimental results, based on real-world applications, demonstrating
        the superior performance of our algorithm compared to existing methods.
\end{itemize}

\section{PROBLEM SETUP}
\label{problemsetupsection}
The \textit{n-armed dueling bandits problem} \citep{karmedduelingbandit} is a modification of the \textit{n-armed bandit problem}, where instead of pulling a single arm, we choose a pair of arms $(i,j)$ to duel, and receive one bit indicating which of the two is better or preferred, with the probability of $i$ winning the duel is equal to a constant $p_{i,j}$ and that of $j$ equal to $p_{j,i}=1-p_{i,j}$. We define the \textit{probabilty matrix} $P=[p_{i,j}]$, whose $(i,j)$th entry is $p_{i,j}$.

Almost all existing $n$-armed dueling bandit methods \citep{karmedduelingbandit, beatthemean, rucb,urvoy2013generic,ailon2014reducing} focus on the explore-exploit problem and furthermore make a variety of assumptions on the preference matrix $P$. In
particular, those works assume the existence of a Condorcet winner: an arm, $c$, such that
$p_{c,j}>\frac{1}{2}$ for all $j \neq c$. The \textit{Borda} winner is an arm $b$
that satisfies $\sum_{j\neq b} p_{b,j} \geq \sum_{j\neq i} p_{i,j}$ for all $i=1,\cdots,n$. In
other words, the Borda winner is the arm with the highest average probability of
winning against other arms, or said another way, the arm that has the highest
probability of winning against an arm selected uniformly at random from the
remaining arms. The Condorcet winner has been given more attention than the
Borda, the reasons being: 1) Given a choice between the Borda and the Condorcet
winner, the latter is preferred in a direct comparison between the two. 2) As
pointed out in \citet{urvoy2013generic,rucb} the Borda winner can be found by reducing the dueling bandit problem to a standard multi-armed bandit problem as follows.

\begin{definition} \label{bordareduction}{\em Borda Reduction.} The action of pulling arm $i$ with reward $\frac{1}{n-1}\sum_{j\neq i} p_{i,j}$ can be simulated by dueling arm $i$ with another arm chosen uniformly at random.
\end{definition}
However, we feel that the Borda problem has received far less attention than it
deserves. Firstly, the Borda winner \textit{always exists}, the Condorcet does
not. For example, a Condorcet winner does not exist in the MSLR-WEB10k datasets considered in this paper. Assuming the existence of a Condorcet winner severely restricts the class
of allowed $P$ matrices: only those $P$ matrices are allowed which have a row
with all entries $\geq \frac{1}{2}$. In fact,
\citet{karmedduelingbandit,beatthemean} require that the comparison probabilities
$p_{i,j}$ satisfy additional transitivity conditions that are often violated in
practice. Secondly, there are many cases where the Borda winner and the
Condorcet winner are distinct, and the Borda winner would be preferred in many
cases. Lets assume that arm $c$ is the Condorcet winner, with
$p_{c,i}=0.51$ for $i\neq c$. Let arm $b$ be the Borda winner with $p_{b,i}=1$ for
$i\neq b,c$, and $p_{b,c}=0.49$. It is reasonable that arm $c$ is only marginally
better than the other arms, while arm $b$ is significantly preferred over all
other arms except against arm $c$ where it is marginally rejected. In this
example - chosen extreme to highlight the pervasiveness of situations where the
Borda arm is preferred - it is clear that arm $b$ should be the winner: think of
the arms representing objects being contested such as t-shirt designs, and the
$P$ matrix is generated by showing users a pair of items and asking them to
choose the better among the two. This example also shows that the Borda winner
is more robust to estimation errors in the $P$ matrix (for instance, when the
$P$ matrix is estimated by asking a small sample of the entire population to vote
among pairwise choices). The Condorcet winner is sensitive to entries in
the Condorcet arm's row that are close to $\frac{1}{2}$, which is not the case for
the Borda winner. Finally, there are important cases (explained
next) where the winner can be found in fewer number of duels than would be
required by Borda reduction.

\section{MOTIVATION} \label{motivationSection}

\begin{table*}
\begin{equation}
    P_1 =
    \begin{blockarray}{cccccccc}
        & 1 & 2 & 3 & \cdots & n & s_i & s_1-s_i\\
        \begin{block}{c(ccccc)cc} 1 & \frac{1}{2} & \frac{1}{2}&
            \frac{3}{4} & \cdots & \frac{3}{4}+\epsilon &
            \frac{\frac{1}{2}+\epsilon}{n-1}+\frac{3}{4}\frac{n-2}{n-1} & 0 \\ \\ 2
            & \frac{1}{2}& \frac{1}{2} & \frac{3}{4} & \cdots &
            \frac{3}{4} &
            \frac{\frac{1}{2}}{n-1}+\frac{3}{4}\frac{n-2}{n-1} & \frac{\epsilon}{n-1} \\ \\ 3 &
            \frac{1}{4} & \frac{1}{4} & \frac{1}{2} & \cdots & \frac{1}{2}  &
            \frac{1}{2}\frac{n-2}{n-1} &  \frac{\frac{1}{2}+\epsilon}{n-1}+\frac{1}{4}\frac{n-2}{n-1}  \\ \\ \vdots & \vdots & \vdots & \vdots &
            \ddots & \vdots & \vdots & \vdots \\ \\ n & \frac{1}{4}-\epsilon & \frac{1}{4} &
            \frac{1}{2} & \cdots & \frac{1}{2} &
            -\frac{\epsilon}{n-1}+\frac{1}{2}\frac{n-2}{n-1} &
            \frac{\frac{1}{2}+2\epsilon}{n-1}+\frac{1}{4}\frac{n-2}{n-1} \\
        \end{block}
    \end{blockarray}
    \label{badP1matrix}
\end{equation}
\begin{equation}
    P_2 =
    \begin{blockarray}{cccccccc}
        & 1 & 2 & 3 & \cdots & n & s_i & s_1-s_i\\
        \begin{block}{c(ccccc)cc} 1 & \frac{1}{2} &
            \frac{1}{2}+\frac{\epsilon}{n-1} & \frac{3}{4}+\frac{\epsilon}{n-1}
            & \cdots & \frac{3}{4}+\frac{\epsilon}{n-1} &
            \frac{\frac{1}{2}+\epsilon}{n-1}+\frac{3}{4}\frac{n-2}{n-1} & 0 \\
            \\
            2 & \frac{1}{2}-\frac{\epsilon}{n-1} & \frac{1}{2} & \frac{3}{4} &
            \cdots & \frac{3}{4} &
            \frac{\frac{1}{2}-\frac{\epsilon}{n-1}}{n-1}+\frac{3}{4}\frac{n-2}{n-1} &
            \frac{\epsilon}{n-1} + \frac{\epsilon}{(n-1)^2} \\ \\
            3 & \frac{1}{4}-\frac{\epsilon}{n-1} & \frac{1}{4} & \frac{1}{2} &
            \cdots & \frac{1}{2} & \frac{-\frac{\epsilon}{n-1}}{n-1}+
            \frac{1}{2}\frac{n-2}{n-1} &
            \frac{\frac{1}{2}+\epsilon+\frac{\epsilon}{n-1}}{n-1}+
            \frac{1}{4}\frac{n-2}{n-1}  \\ \\
            \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots &
            \vdots \\ \\ n & \frac{1}{4} -\frac{\epsilon}{n-1} & \frac{1}{4} &
            \frac{1}{2} & \cdots & \frac{1}{2} &
            \frac{-\frac{\epsilon}{n-1}}{n-1} + \frac{1}{2}\frac{n-2}{n-1} &
            \frac{\frac{1}{2}+\epsilon+\frac{\epsilon}{n-1}}{n-1}+
            \frac{1}{4}\frac{n-2}{n-1}  \\
        \end{block}
    \end{blockarray}
    \label{badP2matrix}
\end{equation}
\end{table*}

We define the \textit{Borda score} of an arm $i$ to be the probability of the
$i^{\text{th}}$ arm winning a duel with another arm chosen uniformly at random:
\begin{equation*} s_i = \tfrac{1}{n-1}\sum\limits_{j\neq i}p_{i,j} \, .
\end{equation*} Without loss of generality, we assume that $s_1 > s_2 \geq \dots
\geq s_n$ but that this ordering is unknown to the algorithm. As mentioned
above, if the Borda reduction is used then the dueling bandit problem becomes a
regular multi-armed bandit problem and lower bounds for the multi-armed bandit problem
\citep{kaufmann2014complexity,mannortsitsiklis} suggest that the number of samples
required should scale like $\Omega \left( \sum_{i\neq 1}\frac{1}{(s_1-s_i)^2}
\log \frac{1}{\delta} \right)$, which depends only on the Borda scores, and not
the individual entries of the preference matrix. This would imply that  any preference
matrix $P$ with Borda scores $s_i$ is just as hard as another matrix $P'$ with
Borda scores $s_i'$ as long as $(s_1-s_i) = (s_1'-s_i')$. Of course, this lower bound only applies to algorithms using the Borda reduction, and not any algorithm for identifying the Borda winner that may, for instance, collect the duels in a more deliberate way. Next we consider  specific $P$ matrices that exhibit two very different kinds of structure but have the same differences in Borda scores which motivates the structure considered in this paper.

\subsection{Preference Matrix $P$ known up to permutation of indices}
Shown below in equations (\ref{badP1matrix}) and (\ref{badP2matrix}) are two preference matrices $P_1$ and $P_2$ indexed by the number of arms $n$ that essentially have
the same Borda gaps -- $(s_1-s_i)$ is either like $\frac{\epsilon}{n}$ or
approximately $1/4$ -- but we will argue that $P_1$ is much ``easier'' than $P_2$ in a
certain sense (assume $\epsilon$ is an unknown constant, like $\epsilon =1/5$). Specifically,
if given $P_1$ and $P_2$ up to a permutation of the labels of their indices (i.e. given $\Lambda P_1 \Lambda^T$ for some unknown permutation matrix $\Lambda$), how many comparisons does it take to find the Borda winner in each case for different values of $n$?

Recall from above that if we ignore the fact that we know the matrices up to a
permutation and use the Borda reduction technique, we can use a
multi-armed bandit algorithm (e.g. \citet{karnin2013almost,lilucb}) and find the best arm for both
$P_1$ and $P_2$ using  $O \left( {n^2} \log(\log(n)) \right)$ samples. We next
argue that given $P_1$ and $P_2$ up to a permutation, there exists an algorithm
that can identify the Borda winner of $P_1$ with just $O(n \log(n))$ samples
while the identification of the Borda winner for $P_2$ requires at least
$\Omega(n^2)$ samples. This shows that given the probability matrices up to a permutation, the sample complexity of identifying the Borda winner does not rely just on the Borda differences, but on the particular structure of the probability matrix.

Consider $P_1$. We claim that there exists a procedure that exploits the
structure of the matrix to find the best arm of $P_1$ using just $O(n
\log(n))$ samples. Here's how: For each arm, duel it with $32\log
\frac{n}{\delta}$ other arms chosen uniformly at random. By Hoeffding's
inequality, with probability at least $1-\delta$ our empirical estimate of the
Borda score will be within $1/8$ of its true value for all $n$ arms and we can
remove the bottom $(n-2)$ arms due to the fact that their Borda gaps exceed $1/4$.
Having reduced the possible winners to just two arms, we can identify which rows
in the matrix they correspond to and duel each of these two arms against all of the
remaining $(n-2)$ arms $O(\frac{1}{\epsilon^2})$ times to find out which one
has the larger Borda score using just $O\left(
\frac{2(n-2)}{\epsilon^2} \right)$ samples, giving an overall sample complexity
of $O\left( n \log n \right)$. We have improved the sample complexity from $O(n^2 \log(\log(n)))$ using the Borda
reduction to just $O(n \log(n))$.

Consider $P_2$. We claim that given this matrix up to a permutation of its indices, no algorithm can determine the winner of $P_2$ without
requesting $\Omega(n^2)$ samples.  To see this, suppose an oracle has made the
problem easier by reducing the problem down to just the top two rows of the
$P_2$ matrix. This is a binary hypothesis test for which Fano's inequality implies that to guarantee that the probability of error is not above some constant level, the number of samples to identify the Borda winner must scale like  $\min_{j \in [n] \setminus \{1,2\}} \frac{1}{KL(p_{1,j},p_{2,j})} \geq \min_{j \in [n] \setminus \{1,2\}} \frac{c}{(p_{1,j}-p_{2,j})^2} = \Omega(  (n/\epsilon)^2 )$ where the inequality holds for some $c$ by Lemma~\ref{klbernoulliupperbound} in the Appendix.

We just argued that the
structure of the $P$ matrix, and not just the Borda gaps, can dramatically
influence the sample complexity of finding the Borda winner. This leads us to
ask the question: if we don't know anything about the $P$ matrix beforehand (i.e. do not know the matrix up to a permutation of its indices), can
we learn and exploit this kind of structural information in an online fashion
and improve over the Borda reduction scheme? The answer is no, as we
argue next.

\subsection{Distribution-Dependent Lower Bound}
\label{lowerboundsection}
We prove a distribution-dependent lower bound on the complexity of finding the
best Borda arm for a general $P$ matrix. This is a result important in its own
right as it shows that the lower bound obtained for an algorithm using the Borda reduction is tight, that is, this result implies that barring any structural assumptions, the Borda reduction is optimal.
\begin{definition}
{\em $\delta$-PAC dueling bandits algorithm}: A $\delta$-PAC dueling
bandits algorithm is an algorithm that selects duels between arms and based on the outcomes finds the Borda winner with probability
greater than or equal to $1-\delta$.
\end{definition}
The techniques used to prove the following result are inspired from Lemma 1 in
\citet{kaufmann2014complexity} and Theorem 1 in \citet{mannortsitsiklis}.

\begin{theorem}
    (Distribution-Dependent Lower Bound)
    Consider a matrix $P$ such that $\frac{3}{8} \leq p_{i,j} \leq \frac{5}{8},
    \forall i,j \in [n]$ with $n \geq 4$. Let $\tau$ be the total number of duels. Then for
    $\delta \leq 0.15$, any $\delta$-PAC dueling bandits algorithm to find the
    Borda winner has $$\mathbb{E}_P[\tau] \geq C \log
    \frac{1}{2\delta}
    \sum\limits_{i \neq 1}^{} \frac{1}{(s_1-s_i)^2} $$ where $s_i = \frac{1}{n-1}\sum_{j \neq
    i} p_{i,j}$ denotes the Borda score of arm $i$. Furthermore, $C$ can be chosen to be
    $1/90$.\\
\end{theorem}

The proof can be found in the supplementary material.

In particular, this implies that for the preference matrix $P_1$ in
\eqref{badP1matrix}, any algorithm that makes no assumption about the structure
of the $P$ matrix requires $\Omega \left( n^2 \right)$ samples.  Next we argue that the particular structure found in $P_1$ is an extreme case of a more general structural phenomenon found in real datasets and that it is a natural structure to assume and design algorithms to exploit.

\subsection{Motivation from Real-World Data}
The matrices $P_1$ and $P_2$ above illustrate a key structural aspect that can
make it easier to find the Borda winner.  If the arms with the top Borda scores
are distinguished by duels with a small subset of the arms (as exemplified in
$P_1$), then finding the Borda winner may be easier than in the general case.
Before formalizing a model for this sort of structure, let us look at two
real-world datasets, which motivate the model.

We consider the Microsoft Learning to Rank web search datasets MSLR-WEB10k
\citep{letor} and MQ2008-list \citep{letor2} (see the experimental section for a
descrptions).  Each dataset is used to construct a corresponding probability
matrix $P$.  We use these datasets to test the hypothesis that comparisons with
a small subset of the arms may suffice to determine which of two arms has a
greater Borda score.

Specifically, we will consider the Borda score of the best arm (arm $1$) and
every other arm.
 For any other arm $i>1$ and any positive integer $k
\in [n-2]$,
let $\Omega_{i,k}$ be a set of cardinality $k$ containing the indices $j \in [n]\setminus \{1,i\}$ with the $k$ largest
discrepancies $|p_{1,j}-p_{i,j}|$. These are the duels that, individually,
display the greatest differences between arm $1$ and $i$.  For each $k$, define
$\alpha_i(k)=2(p_{1,i}-\tfrac{1}{2}) + \sum_{j\in \Omega_{i,k}} (p_{1,j}-p_{i,j})$.  If the hypothesis
holds, then the duels with a small number of (appropriately chosen) arms should
indicate that arm $1$ is better than arm $i$.  In other words, $\alpha_i(k)$
should become and stay positive as soon as $k$ reaches a relatively small
value.
 Plots of these $\alpha_i$ curves for two datasets are presented in
Figures~\ref{modelFit}, and indicate that the Borda winner is apparent for small
$k$.  This behavior is explained by the fact that the individual discrepancies
$|p_{1,j}-p_{i,j}|$, decay quickly when ordered from largest to smallest, as
shown in Figure~\ref{des}.

The take away message is that it is unnecessary to estimate the difference  or
gap between the Borda scores of two arms. It suffices to compute the {\em
partial} Borda gap based on duels with a small subset of the arms.  An
appropriately chosen subset of the duels will correctly indicate which arm has a
larger Borda score. The algorithm proposed in the next section automatically
exploits this structure.

\begin{figure}[h]
\centering
\includegraphics[width=8cm]{alpha2}
\caption{Plots of $\alpha_i(k)=2(p_{1,i}-\tfrac{1}{2}) + \sum_{j\in \Omega_{i,k}} (p_{1,j}-p_{1,j})$ vs.
$k$ for $30$ randomly chosen arms (for visualization purposes); MSLR-WEB10k on
left, MQ2008-list on right. The curves are strictly positive after a small
number of duels.}
\label{modelFit}
\end{figure}

\begin{figure}[h]
\centering
\includegraphics[width=8cm]{d1}
\caption{Plots of discrepancies $|p_{1,j}-p_{i,j}|$ in descending order for $30$
randomly chosen arms (for visualization purposes); MSLR-WEB10k on left,
MQ2008-list on right.}
\label{des}
\end{figure}

\section{ALGORITHM AND ANALYSIS}

\begin{algorithm*}
Input sparsity level $k \in [n-2]$, time gate $T_0 \geq 0$ \\
Start with active set $A_1 = \{1,2,\cdots,n \}$, $t=1$\\
Let $C_t = \sqrt{ \frac{2\log(4 n^2 t^2 / \delta)}{t/n} } + \frac{ 2 \log(4n^2t^2/\delta)}{3t/n}$\\
\While{$|A_t|>1$}{
Choose $I_t$ uniformly at random $[n]$.\\
\For{$j \in A_t$}{
Observe $Z_{j,I_t}^{(t)}$ and update $\widehat{p}_{j,I_t,t} = \frac{n}{t}
\sum_{\ell=1}^t  Z_{j,I_\ell}^{(\ell)} \mathbf{1}_{I_\ell = I_t}$, $\widehat{s}_{j,t} =
\frac{   n/(n-1)  }{t} \sum_{\ell=1}^t Z_{j,I_\ell}^{(\ell)}$.\\
}
$\displaystyle A_{t+1} = A_t \setminus \bigg\{ j \in A_t : \exists i \in A_t \text{ with }\ \ $\\ \quad\, \hspace{.4in} $ \, 1) \ \ \ \mathbf{1}_{\{t > T_0\}} \, \widehat{\Delta}_{i,j,t}\left(  \arg\max_{\Omega \subset [n] : |\Omega| = k} \widehat{\nabla}_{i,j,t}(\Omega)  \right) ~> ~6 (k+1) C_t$ \\ \indent\hspace{.3in}$\text{  \textbf{OR}  } \ \ \ 2) \ \  \ \widehat{s}_{i,t} > \widehat{s}_{j,t} + \frac{n}{n-1}\sqrt{ \frac{2 \log(4 n t^2/\delta)}{t}  } \bigg\}$\\
$t \leftarrow t+1$\\
}
\caption{Sparse Borda Algorithm}
\end{algorithm*}

In this section we propose a new algorithm that exploits the kind of structure just described above and prove a sample complexity bound. The algorithm is inspired by the Successive Elimination (SE) algorithm of \citet{even2006action} for standard multi-armed bandit problems. Essentially, the proposed algorithm below implements SE with the Borda reduction and an additional elimination criterion that exploits sparsity (condition 1 in the algorithm). We call the algorithm Successive Elimination with Comparison Sparsity (SECS).

We will use $\mathbf{1}_E$ to denote the indicator of the event $E$ and $[n] = \{1,2,\dots,n\}$. The algorithm maintains an active set of arms $A_t$ such that if $j \notin A_t$ then the algorithm has concluded that arm $j$ is not the Borda winner. At each time $t$, the algorithm chooses an arm $I_t$ uniformly at random from $[n]$ and compares it with all the arms in $A_t$. Note that $A_{k} \subseteq A_{\ell}$ for all $k \geq \ell$. Let $Z_{i,j}^{(t)} \in \{0,1\}$ be independent Bernoulli random variables with $\mathbb{E}[Z_{i,j}^{(t)}] = p_{i,j}$, each denoting the outcome of ``dueling'' $i,j \in [n]$ at time $t$ (define $Z_{i,j}^{(t)}=0$ for $i=j$). For any $t \geq 1$, $i \in [n]$, and $j \in A_t$ define
\begin{align*}
\widehat{p}_{j,i,t} = \frac{n}{t}
\sum_{\ell=1}^t  Z_{j,I_\ell}^{(\ell)} \mathbf{1}_{I_\ell = i}
\end{align*}
so that $\mathbb{E}\left[ \widehat{p}_{j,i,t} \right] = p_{j,i}$. Furthermore, for any $t \geq1$, $j \in A_t$ define
\begin{align*}
\widehat{s}_{j,t} =
\frac{ n/(n-1) }{t} \sum_{\ell=1}^t Z_{j,I_\ell}^{(\ell)}
\end{align*}
so that $\mathbb{E}\left[ \widehat{s}_{j,t} \right] = s_{j}$.
For any $\Omega \subset [n]$ and $i,j \in [n]$ define
\begin{align*}
\Delta_{i,j}(\Omega) &= 2(p_{i,j}-\tfrac{1}{2}) + \sum_{\omega \in \Omega: \omega \neq i \neq j} ( p_{i,\omega} - p_{j,\omega} )\\
\widehat{\Delta}_{i,j,t}(\Omega) &=  2( \widehat{p}_{i,j,t} -\tfrac{1}{2})  + \sum_{\omega \in \Omega: \omega \neq i \neq j} ( \widehat{p}_{i,\omega,t} - \widehat{p}_{j,\omega,t} ) \\
{\nabla}_{i,j}(\Omega) &=   \sum_{\omega \in \Omega: \omega \neq i \neq j} | {p}_{i,\omega} - {p}_{j,\omega} | \\
\widehat{\nabla}_{i,j}(\Omega) &=  \sum_{\omega \in \Omega: \omega \neq i \neq j} | \widehat{p}_{i,\omega,t} - \widehat{p}_{j,\omega,t} | \ .
\end{align*}
The quantity $\Delta_{i,j}(\Omega)$ is the {\em partial} gap between the Borda scores for $i$ and $j$, based on only the comparisons with the arms in $\Omega$.  Note that $\frac{1}{n-1}\Delta_{i,j}([n]) = s_i - s_j$.
The quantity $ \arg\max_{\Omega \subset [n] : |\Omega| = k} {\nabla}_{i,j}(\Omega) $ selects the indices $\omega$ yielding the largest discrepancies $|p_{i,\omega} -p_{j,\omega}|$. $\widehat{\Delta}$ and $\widehat{\nabla}$ are empirical analogs of these quantities.

\begin{definition}
For any $i \in [n] \setminus 1$ we say the set $\{ (p_{1,\omega}-p_{i,\omega}) \}_{\omega \neq 1 \neq i}$ is $(\gamma,k)$-approximately sparse if
\begin{align*}
\displaystyle \max_{\Omega \in [n] : |\Omega| \leq k}\nabla_{1,i}(\Omega \setminus \Omega_i)  \ \leq \ \gamma \Delta_{1,i}(\Omega_i)
\end{align*}
where $\displaystyle\Omega_i =  \arg\max_{\Omega \subset[n] : |\Omega|=k} \nabla_{1,i}( \Omega )$.
\end{definition}
Instead of the strong assumption that the set $\{ (p_{1,\omega}-p_{i,\omega}) \}_{\omega \neq 1 \neq i}$ has no more than $k$ non-zero coefficients, the above definition relaxes this idea and just assumes that the absolute value of the coefficients outside the largest $k$ are small relative to the partial Borda gap. This definition is inspired by the structure described in previous sections and will allow us to find the Borda winner faster.

The parameter $T_0$ is specified (see Theorem~\ref{sparseTheorem}) to guarantee that all arms with sufficiently large gaps $s_1-s_i$ are eliminated by time step $T_0$ (condition 2). Once $t > T_0$, condition 1 also becomes active and the algorithm starts removing arms with large partial Borda gaps, exploiting the assumption that the top arms can be distinguished by comparisons with a sparse set of other arms. The algorithm terminates when only one arm remains.

\begin{theorem} \label{sparseTheorem}
Let $k \geq 0$ and $T_0>0$ be inputs to the above algorithm and let $R$ be the solution to $\frac{32 }{R^2} \log\left( \frac{32 n/ \delta}{R^2 }  \right) = T_0$. If for all $i \in [n] \setminus 1$, at least one of the following holds:
\begin{enumerate}
\item$\{ (p_{1,\omega}-p_{i,\omega}) \}_{\omega \neq 1 \neq i}$ is $(\tfrac{1}{3},k)$-approximately sparse,
\item $(s_1-s_i) \geq R$,
\end{enumerate}
then with probability at least $1- 3\delta$, the algorithm returns the best arm after no more than
\begin{align*}
c \sum_{j > 1} \min\Big\{  \max\left\{  \tfrac{1 }{R^2} \log\left( \tfrac{ n/
\delta}{R^2 }  \right), \tfrac{ (k+1)^2 / n }{ \Delta_{j}^2} \log\left(  \tfrac{
n / \delta }{ \Delta_{j}^{2} } \right)  \right\} ,\\
\tfrac{ 1 }{ \Delta_{j}^{2}}
\log\left(  \tfrac{ n / \delta }{ \Delta_{j}^{2} } \right)  \Big\}
\end{align*}
samples where $\Delta_{j}:= s_{1} - s_j$ and $c>0$ is an absolute constant.
\end{theorem}

The second argument of the $\min$ is precisely the result one would obtain by running Successive Elimination with the Borda reduction \citep{even2006action}. Thus, under the stated assumptions, the algorithm never does worse than the Borda reduction scheme.  The first argument of the $\min$ indicates the potential improvement gained by exploiting the sparsity assumption.  The first argument of the $\max$ is the result of throwing out the arms with large Borda differences and the second argument is the result of throwing out arms where a {\em partial} Borda difference was observed to be large.

To illustrate the potential improvements, consider the $P_1$ matrix discussed above, the theorem implies that by setting $T_0 = \frac{32 }{R^2} \log\left( \frac{32 n/ \delta}{R^2 }  \right) $ with $R = \frac{1/2 + \epsilon}{n-1} + \frac{1}{4} \frac{n-2}{n-1} \approx \frac{1}{4}$ and $k=1$ we obtain a sample complexity of $O( \epsilon^{-2} n \log(n))$ for the proposed algorithm compared to the standard Borda reduction sample complexity of $\Omega(n^2)$.

In practice it is difficult optimize the choice of  $T_0$ and $k$, but motivated by the results shown in the experiments section, we recommend setting $T_0=0$ and $k=5$ for typical problems.

\section{EXPERIMENTS}
The goal of this section is not to obtain the best possible sample complexity results for the specified datasets, but to show the {\em relative} performance gain of exploiting structure using the proposed SECS algorithm with respect to the Borda reduction. That is, we just want to measure the effect of exploiting sparsity while keeping all other parts of the algorithms constant. Thus, the algorithm we compare to that uses the simple Borda reduction is simply the SECS algorithm described above but with $T_0 = \infty$ so that the sparse condition never becomes activated. Running the algorithm in this way, it is very closely related to the Successive Elimination algorithm of \citet{even2006action}. In what follows, our proposed algorithm will be called SECS and the benchmark algorithm will be denoted as just the Borda reduction (BR) algorithm.

We experiment on both simulated data and two real-world datasets. During all experiments, both the BR and SECS algorithms were run with $\delta=0.1$. For the SECS algorithm we set $T_0=0$ to enable condition 1 from the very beginning (recall for BR we set $T_0 = \infty$). Also, while the algorithm has a constant factor of 6 multiplying $(k+1)C_t$, we feel that the analysis that led to this constant is very loose so in practice we recommend the use of a constant of $1/2$ which was used in our experiments. While the change of this constant invalidates the guarantee of Theorem~\ref{sparseTheorem}, we note that in all of the experiments to be presented here, neither algorithm ever failed to return the best arm. This observation also suggests that the SECS algorithm is robust to possible inconsistencies of the model assumptions.

\subsection{Synthetic Preference matrix}
\label{synth}
Both algorithms were tasked with finding the best arm using the $P_1$ matrix of \eqref{badP1matrix} with $\epsilon = 1/5$ for problem sizes equal to  $n=10,20,30,40,50,60,70,80$ arms. Inspecting the $P_1$ matrix, we see that a value of $k=1$ in the SECS algorithm suffices so this is used for all problem sizes. The entries of the preference matrix $P_{i,j}$ are used to simulate comparisons between the respective arms and each experiment was repeated 75 times.

\begin{figure}
\centering
\includegraphics[trim=0cm 0cm 0cm 0cm, clip=true, scale = 0.4]{P1.png}
\caption{Comparison of the Borda reduction algorithm and the proposed SECS algorithm ran on the $P_1$ matrix for different values of $n$. Plot is on log-log scale so that the sample complexity grows like $n^s$ where $s$ is the slope of the line.}
\label{SyntheticResults}
\end{figure}

Recall from Section~\ref{motivationSection} that any algorithm using the Borda reduction on the $P_1$ matrix has a sample complexity of $\Omega(n^2)$. Moreover, inspecting the proof of Theorem~\ref{sparseTheorem} one concludes that the BR algorithm has a sample complexity of $O(n^2 \log(n))$ for the $P_1$ matrix. On the other hand, Theorem~\ref{sparseTheorem} states that the SECS algorithm should have a sample complexity no worse than $O( n \log(n) )$ for the $P_1$ matrix. Figure \ref{SyntheticResults} plots the sample complexities of SECS and BR on a log-log plot. On this scale, to match our sample complexity hypotheses, the slope of the BR line should be about $2$ while the slope of the SECS line should be about $1$, which is exactly what we observe.

\subsection{Web search data}
We consider two web search data sets. The first is the MSLR-WEB10k Microsoft Learning to Rank data set \citep{letor} that is characterized by approximately 30,000 search queries over a number of documents from search results. The data also contains the values of 136 features and corresponding user labelled relevance factors with respect to each query-document pair. We use the training set of Fold 1, which comprises of about 2,000 queries. The second data set is the MQ2008-list from the Microsoft Learning to Rank 4.0 (MQ2008) data set \citep{letor2}. We use the training set of Fold 1, which has about 550 queries. Each query has a list of documents with 46 features and corresponding user labelled relevance factors.

For each data set, we create a set of rankers, each corresponding to a feature from the feature list. The aim of this task is be to determine the feature whose ranking of query-document pairs is the most relevant. To compare two rankers, we randomly choose a pair of documents and compare their relevance rankings with those of the features. Whenever a mismatch occurs between the rankings returned by the two features, the feature whose ranking matches that of the relevance factors of the two documents ``wins the duel''. If both features rank the documents similarly, the duel is deemed to have resulted in a tie and we flip a fair coin. We run a Monte Carlo simulation on both data sets to obtain a preference matrix $P$ corresponding to their respective feature sets. As with the previous setup, the entries of the preference matrices ($[P]_{i,j}=p_{i,j}$) are used to simulate comparisons between the respective arms and each experiment was repeated 75 times.

From the MSLR-WEB10k data set, a single arm was removed for our experiments as its Borda score was unreasonably close to the arm with the best Borda score and behaved unlike any other arm in the dataset with respect to its $\alpha_i$ curves, confounding our model.
For these real datasets, we consider a range of different $k$ values for the SECS algorithm. As noted above, while there is no guarantee that the SECS algorithm will return the true Borda winner, in all of our trials for all values of $k$ reported we never observed a single error. This is remarkable as it shows that the correctness of the algorithm is insensitive to the value of $k$ on at least these two real datasets. The sample complexities of BR and SECS on both datasets are reported in Figure~\ref{realData}. We observe that the SECS algorithm, for small values of $k$, can identify the Borda winner using as few as {\em half} the number required using the Borda reduction method. As $k$ grows, the performance of the SECS algorithm becomes that of the BR algorithm, as predicted by Theorem~\ref{sparseTheorem}.

\begin{figure}
\centering
\begin{subfloat}[MSLR-WEB10k]{
\centering
\includegraphics[trim=0cm 0cm 0cm 0cm, clip=true, scale = 0.4]{P135.png}
}
\begin{subfloat}[MQ2008]{
\centering
\includegraphics[trim=.25cm 0cm 0cm 0cm, clip=true, scale = 0.4]{P46.png}
}
\end{subfloat}%
\end{subfloat}
\caption{Comparison of an action elimination-style algorithm using the Borda reduction (denoted as BR) and the proposed SECS algorithm with different values of $k$ on the two datasets.}
\label{realData}
\end{figure}

Lastly, the preference matrices of the two data
sets support the argument for finding the Borda winner over the Condorcet
winner. The MSLR-WEB10k data set has no Condorcet winner arm. However, while the MQ2008 data set has a Condorcet winner,  when we consider the Borda scores of the arms, it ranks second.

redpajama_set_name: RedPajamaArXiv


text:
Pollution from cars is harmful to children
Air pollution from motor vehicles is harmful to humans but especially harmful to children. We know it can damage the growth of their lungs, raise the risk of asthma and allergies, affect brain development and intelligence, raise the risk of heart disease and cancer, and it even affects unborn children in their mother's womb. But whenever I dare to suggest we avoid driving our children right up to the school gate I receive an indignant glare and a "But I love my car!" response.
Let's say the average primary school has 400 children (I have no idea if this is accurate but it's about the number of kids at the school my children attend) and assume about half of them have a sibling in the school, which makes 200 parents wanting to get children to school each day. Imagine if all 200 of those parents drove their kids to the school gate every morning? It would be mayhem! When we lived in York parents couldn't park in the streets right next to the primary school. No one seemed to mind this rule and as far as I could tell it was mostly obeyed.
I feel particularly emotionally invested in air pollution because I have a theory that it affected my pregnancy with Daniel. I had gestational diabetes during my pregnancy, something which was not repeated with Elizabeth when I was pregnant with her a few years later and this in itself is very unusual because it typically gets worse with subsequent pregnancies. There's a probable link between diabetes and air pollution and it's my theory that air pollution in the Christchurch winter that I was pregnant with Daniel, which was horrendous, led to my diabetes which led to his autism. We also know air pollution can cross the placenta and there's a link between maternal diabetes and autism in offspring. I realise, of course, that I can never prove this just like a smoker can never definitively say his smoking directly caused his lung cancer. He may have got lung cancer anyway. But the link between air pollution and health problems is very real.
You might be surprised to hear that air pollution is a problem in Christchurch. It is but it's not cars that is the main source. It's smoke from wood burning fires. Christchurch has a peculiar inversion layer over the city which traps all the smog near the ground. I breathed a lot of it during the winter of my first trimester with Daniel because it was worse in the evening and that's when I walked my dogs. I worked during the day and so I used to walk them in the evening but the smoke was at its worst then. I can remember thinking how much my hair stank of smoke after taking the dogs out for a walk. But what was I to do? Not walk them for 6 months? When Elizabeth came along I was a stay-at-home mum and able to walk the dogs during the day when the pollution wasn't so bad. This is my theory for why I didn't have any complications during my pregnancy with her.
Fortunately we don't have to worry about winter smoke here but toxic fumes from cars are a problem. The solution is a combination of things: invest in active travel (it should be 10% of the transport budget), ban cars from parking on school streets, replace petrol/diesel cars with electric cars, invest in public transport, and plant trees.
air pollution, cars, fumes, pollution, pregnancy, toxic, traffic
7 responses to "Pollution from cars is harmful to children"
fossilcyclist says:
Another way of doing things? https://www.theguardian.com/cities/2018/sep/18/paradise-life-spanish-city-banned-cars-pontevedra
That's amazing! What a huge transformation. It just shows any city can do it.
sevencyclist says:
I have an idea … how about riding bikes to school? I know, times have changed a lot since I went to school. I can count the number of times I was driven to school, or drove to school, and it's definitely < 20. I cringe when I see all the car traffic, in the 1 or 2 blocks near a school. It becomes a hazard when I try to ride my bike past the school, having parents cars dodging in and out of the parking entrance/exit from the school. It's not a stretch, when I say it is the most dangerous part of my commute.
I absolutely agree. It's not just the pollution but the danger of having so many cars around children crossing roads to get to school. It's a catch 22 because there are too many cars which makes cycling unsafe so everyone drives.
We have a Green group at school now! One of the other teachers suggested it and I don't have the energy to do it by myself but there's a group of three of us leading it now. The students choose their own topics to campaign on, but I am hoping that sustainable transport and air pollution will be one of the things that we can educate the school's population about, including getting the adults to change their ways. If they do choose that topic, I will suggest that they research how pollution particularly affects children.
That sounds fantastic! What a great idea. Having the pupils themselves campaign is a much more effective way to change parental behaviour.
Aileen says:
I've read my fair share of air pollution and it's affects on people who are exposed to it and it is honestly very sad. If enough people made a change to help lessen the amount of air pollution that develops, we would all be at a much better place.

redpajama_set_name: RedPajamaCommonCrawl


Ullswater is holding its annual Outdoor Festival from Sat 24 September through to Sun 2 October. The launch is held at Glenridding at the top end of Ullswater which is handy for anyone staying in our Ullswater Cottages, and is just half an hour for anyone staying in our Keswick cottages.
The launch at Glenridding will include Taffy Thomas (a local Lake District legend) telling his stories to people of all ages, children's entertainment with Laura J, and displays from the Lake District Bird of Prey Centre. There will be various arts & crafts activities and a small farmers' market. The Lake District Mountain Rescue will be there to answer any questions you may have and there will also be a fire engine on display.
The week will consist of various activities from guided walks to learning basic map and compass skills to kayaking, canoeing and dingy sailing to a variety of scrambles up the fells to illustrated talks. Most of the activities are free and the Ullswater valley is a beautiful one – breathtaking and not too busy despite the fact that Ullswater is the nearest lake in the Lake District to the M6 (just a ten minute drive).
Guided walks include a walk to Red Tarn (below Helvellyn), High Hartsop Dodd, Place Fell (via Fusedale, Martindale and Boredale), Maiden Castle Settlement (via Dalemain), Deepdale Valley, Aira Force, Glencoyne, the Fusedale Valley at Ullswater, Hallin Fell circuit, Kirkstone, and a trip to Greenside and Keppel Cove (to view the remains of Greenside mining activities). Most of the walks take around 6 hours so bring a packed lunch! Well behaved dogs are welcome on many of the walks.
Please call Ullswater Tourist Information Centre on 017684 82414 to book or find out further information. This will be a well worthwhile event if you have booked to stay in one of our Lake District Cottages at the end of September this year.


User A created a shopping cart and send it. User B gets the shopping cart and have a question. User B set the position on "Rückfragen(inquire)" and sent it back to User A. User A answers and sent it back to User B. The preselection of the radiobutton is still on "Rückfragen (inquire)".
We want to controll the preselection of the radio button. The preselection should always be "Genehmigen(approve)". Is there a way to do it?
This could probably be achieved by doing webdynpro enhancement or though implementation of BADI WD_BADI_DOMODIFYVIEW which gets called for every webdynpro view method WDDOMODIFYVIEW. You have to provide right filter values to this BADI implementation corresponding to the webdynpro component and view where radio button exists.
Here you could access the radio button and then set the default to "approve".


I started knitting after seing this model in an old Phildar book. It was last year but I didn't dare to knit it.
The pattern is easy (basic points), the wool is not expensive (2 yarns of Phildar's Aurore, approximatly 6 dollars or 4.2 euros) but it took ages!!!
I had to knit 450 stich for the bust.
This is totally going on my wist! Its GORGEOUS!!!!
haha on mines too, I adore the sweather and the color, I love the way you wear it in the first picture!
Absolutely Beautiful- The colour is just gorgeous, I want this!
It's amazing!! This is exactly the sort of thing that makes me want to learn to knit... Doubt I could ever produce something as beautiful as this though THIS ROCKS!
Gorgeous!! LOVE IT! It looks so pretty and delicate.
This is gorgeous! It looks so soft.
This is BUUU- T- FUL. I knit a little but nothing that needs a real shape, you must have great skills and patients. Any comment I could leave wouldn't be sufficient. I would love to see a close up of the knitting to see how small it must be!


text:
Geek Related
A place to get some role-playing game goodness.
Rules You Can Use
Carrion Crown
Chapter 1 – The Haunting of Harrowstone
Chapter 2 – Trial of the Beast
Chapter 3 – Broken Moon
Chapter 4 – Wake of the Watcher
Chapter 5 – Ashes at Dawn
Chapter 6 – Shadows of Gallowspire
City of Sigil
Dakani Night Scream
Curse of the Crimson Throne
Chapter 1 – Edge of Anarchy
Chapter 2 – Seven Days to the Grave
Chapter 3 – Escape From Old Korvosa
Chapter 4 – A History of Ashes
Chapter 5 – Skeletons of Scarwall
Chapter 6 – Crown of Fangs
Empire of Ashes
Freak Watch
Jade Regent
Chapter 1 – The Brinewall Legacy
Chapter 2 – Night of Frozen Shadows
Chapter 3 – The Hungry Storm
Chapter 4 – Forest of Spirits
Chapter 5 – Tide of Honor
Chapter 6 – The Empty Throne
Legends of Steel
Mummy Rustlers
Chapter 1 – The Half-Dead City
Chapter 2 – Empty Graves
Reavers on the Seas of Fate
Meet the Reavers
Reavers NPCs and Monsters
Reavers Session Summaries
Reavers Sources
Chapter 1 – Burnt Offerings
Chapter 2 – The Skinsaw Murders
Chapter 3 – The Hook Mountain Massacre
Chapter 4 – Fortress of the Stone Giants
Chapter 5 – Sins of the Saviors
Chapter 6 – Spires of Xin-Shalast
Runelords Skill Rules
Valgrim the Summoner
Lighthouse Session Summaries
The Redeemers
Chapter 1 – The Worldwound Incursion
Chapter 2 – Sword of Valor
Chapter 3 – Demon's Heresy
Chapter 4 – The Midnight Isles
Chapter 5 – Herald of the Ivory Labyrinth
Chapter 6 – City of Locusts
Tag Archives: discretion
Rule Zero Over The Years
Posted on October 12, 2013 | 10 comments
A recent question on RPG Stack Exchange had me researching the attitudes of Dungeons & Dragons towards rule interpretation over the years and I thought I'd expand it into a post here.
The allowed scope of DM rulings has absolutely changed over time in D&D. The balance between Dungeon Master's discretion versus reign of the rules versus player empowerment has always been debated in D&D circles but there's a clear evolution of thinking across the span of versions. The attitude towards rulings vs. rules in the game shows up
directly and explicitly in the rules text
implicitly in the text and detectable via textual analysis
in the surrounding publications considered semi-canonical (Dragon magazine, nowadays forums and designer blogs), and
the culture of gamers surrounding it.
Let's stick mostly to the first two in the interest of space.
Original Dungeons & Dragons (0e, OD&D)
In the origins of the game, Chainmail, there was no concept of straying from the rules – it was a wargame. You could (and often did) mod the rules prior to play, but the whole thing about wargaming is that, like board gaming, the rules are considered inviolate during an instance of play as a core assumption. Some wargames didn't have a "referee" role, and those that did, the role was very much like a sports referee – to determine if some violation of the rules had occurred.
But in the very first version of Dungeons & Dragons, Gary Gygax and Dave Arneson open the OD&D Men & Magic book with this admonishment to the "referee":
These rules are as complete as possible within the limitations imposed by the space of three booklets. That is, they cover the major aspects of fantasy campaigns but still remain flexible. As with any other set of miniatures rules they are guidelines to follow in designing your own fantastic-medieval campaign. They provide the framework around which you will build a game of simplicity or tremendous complexity — your time and imagination are about the only limiting factors, and the fact that you have purchased these rules tends to indicate that there is no lack of imagination — the fascination of the game will tend to make participants find more and more time. We advise, however, that a campaign be begun slowly, following the steps outlined herein, so as to avoid becoming too bogged down with unfamiliar details at first. That way your campaign will build naturally, at the pace best suited to the referee and players, smoothing the way for all concerned. New details can be added and old "laws" altered so as to provide continually new and different situations. In addition, the players themselves will interact in such a way as to make the campaign variable and unique, and this is quite desirable.
– Gary Gygax and Dave Arneson, Dungeons & Dragons Volume 1, Men & Magic (1974), p.4
This is supported by textual analysis as well – the game rules' intent (medieval people having adventures!) versus the relative paucity of the rules basically required large degrees of interpolation and discretion just to run a game. The gap between the mode of play and the written rules is so wide that reading the rules as an all-encompassing legal text on how to play is infeasible. Still, the metaphor is of the referee changing the rules as you proceed, with little discussion about ad hoc rulings.
Later supplements continued this theme. In Swords & Spells, the mass combat add-on, they note:
The second thing to remember is that these rules deal with fantasy. If something is unclear as to how or why it works that way, remember that it is all fantasy. Fantasy is not bound to rigid rules and rationales. Fantasy is imaginative. If you feel that your fantasy is better that this in some aspect, that's fine. After all, it's your fantasy. Be warned, however, that unless certain balances are maintained, the game soon becomes very lopsided and very little fun. BALANCE is to be maintained at all times."
– Tim Kask, Dungeons & Dragons Swords & Spells (1976), Foreword.
In any case fantasy is a growing and flexible form of gaming, and referees must feel at home modifying and expanding upon rules as the situation dictates.
– Gary Gygax, Dungeons & Dragons Swords & Spells (1976), Introduction.
The terminology – "referee," "modifying the rules," still hew close to the wargaming metaphor. Also in Kask's quote, you see the first time balance, or as he states it, "BALANCE", is mentioned. You'll see it again…
Basic Dungeons & Dragons – Moldvay/Cook (B/X)
The 1977 version of Dungeons & Dragons births one of three major strains of thought on the issue of DM rulings.
Moldvay p.B2 (Foreword) on changing the rules: "In a sense, the D&D game has no rules, only rule suggestions. No rule is inviolate, particularly if a new or altered rule will encourage creativity and imagination." Paragraph 3 of the second column p.B3 also discusses how the rules are good as-is but should be changed if desired by the group and with the DM's permission. Also notable for using the term "rules as written", but only as normal descriptive English rather than a technical term.
Moldvay also has most of a page (B60) devoted to telling the DM that they're the boss, not the players or the rules. Notably, it has explicit guidance on making rulings when there aren't obvious applications of the rules. It also notes that though a good DM will discuss rulings with players after the game, a player who still disagrees is welcome to quit as their only recourse.
As you can see Basic moves well away from D&D's wargaming roots, gives the players a voice but puts the DM in the predominant place. I would venture to say that regardless of what the text of each game says, this became the predominant model of operation for the vast amount of the history of D&D.
Advanced Dungeons & Dragons (1e)
In first edition AD&D, you see further development of ambivalence between the role of the Dungeon Master and the beauty and balance of the rules, though the DM is still considered the apex. It departs from B/X in that players are pretty much actively denigrated. In the opening pages of the 1e Dungeon Master's Guide, Gary Gygax rambles on at some length on this exact topic.
What follows herein is strictly for the eyes of you, the campaign referee. As the creator and ultimate authority in your respective game, this work is written as one Dungeon Master equal to another. Pronouncements there may be, but they are not from "on high" as respects your game. Dictums are given for the sake of the game only, for if ADVANCED DUNGEONS & DRAGONS is to survive and grow, it must have some degree of uniformity, a familiarity of method and procedure from campaign to campaign within the whole.[…] In this lies a great danger, however. The systems and parameters contained in the whole of ADVANCED DUNGEONS & DRAGONS are based on a great deal of knowledge, experience gained through discussion, play, testing, questioning, and (hopefully) personal insight. Limitations, checks, balances, and all the rest are placed into the system in order to assure that what is based thereon will be a superior campaign, a campaign which offers the most interesting play possibilities to the greatest number of participants for the longest period of time possible.[…] Naturally, everything possible cannot be included in the whole of this work. As a participant in the game, I would not care to have anyone telling me exactly what must go into a campaign and how it must be handled; if so, why not play some game like chess? As the author I also realize that there are limits to my creativity and imagination. Others will think of things I didn't, and devise things beyond my capability.[…] The danger of a mutable system is that you or your players will go too far in some undesirable direction and end up with a short-lived campaign. Participants will always be pushing for a game which allows them to become strong and powerful far desire is to issue a death warrant to a campaign.[…] As this book is the exclusive precinct of the DM, you must view any non-DM player possessing it as something less than worthy of honorable death.
– Gary Gygax, Advanced Dungeons & Dragons Dungeon Master's Guide (1979), Preface pp.6-7.
You can see that player empowerment definitely isn't on the menu in the seventies, but there is a stronger strain inserted of the wisdom of the rules and how while the DM is still above the rules, they should tread lightly and wisely in changing them. After apparently sucking down some whip-its, he goes on to say:
Know the game systems, and you will know how and when to take upon yourself the ultimate power. To become the final arbiter, rather than the interpreter of the rules, can be a difficult and demanding task, and it cannot be undertaken lightly, for your players expect to play this game, not one made up on the spot. By the same token, they are playing the game the way you, their DM, imagines and creates it. Remembering that the game is greater than its parts, and knowing all of the parts, you will have overcome the greater part of the challenge of being a referee. Being a true DM requires cleverness and imagination which no set of rules books can bestow. Seeing that you were clever enough to buy this volume, and you have enough imagination to desire to become the maker of a fantasy world, you are almost there already! Read and become familiar with the contents of this work and the one written for players, learn your monsters, and spice things up with some pantheons of super-powerful beings. Then put your judging and refereeing ability into the creation of your own personal milieu, and you have donned the mantle of Dungeon Master. Welcome to the exalted ranks of the overworked and harrassed, whose cleverness and imagination are all too often unappreciated by cloddish characters whose only thought in life is to loot, pillage, slay, and who fail to appreciate the hours of preparation which went into the creation of what they aim to destroy as cheaply and quickly as possible. As a DM you must live by the immortal words of the sage who said: "Never give a sucker an even break." Also, don't be a sucker for your players, for you'd better be sure they follow sage advice too. As the DM, you have to prove in every game that you are still the best. This book is dedicated to helping to assure that you are.
– Gary Gygax, Advanced Dungeons & Dragons Dungeon Master's Guide (1979), Introduction pp. 9.
This would certainly excite comment if written today in a RPG.
And then in closing out the pages of this hallowed tome, Gygax writes:
It is the spirit of the game, not the letter of the rules, which is important. NEVER hold to the letter written, nor allow some barracks room lawyer to force quotations from the rule book upon you, IF it goes against the obvious intent of the game. As you hew the line with respect to conformity to major systems and uniformity of play in general, also be certain the game is mastered by you and not by your players. Within the broad parameters give in the Advanced Dungeons and Dragons Volumes, YOU are creator and final arbiter. By ordering things as they should be, the game as a WHOLE first, your CAMPAIGN next, and your participants thereafter, you will be playing Advanced Dungeons and Dragons as it was meant to be. May you find as much pleasure in so doing as the rest of us do."
– Gary Gygax, AD&D Dungeon Masters Guide (1979), Afterword.
This marks an interesting change. In Chainmail and OD&D the referee is just there to facilitate play between players. In Advanced D&D the DM has a predominant role and, while he is expected to become a master of the rules, reigns over the rules and players alike and can essentially extrapolate and make rulings according to his sovereign will.
Also notable here is the extensive (if mildly mental) discussion of the subject – many later editions barely spare a couple sentences on it.
Basic Dungeons & Dragons – Mentzer (BECMI)
Ah, my first Dungeons & Dragons – the Red Box. In the Basic Player's Manual, it briefly describes the DM as "the person who plays the parts of the monsters and runs the game" (p.23). I think it's so interesting that all the player books over time don't really expand on the DM role to players beyond one sentence of "this person's gonna run the game."
The Dungeon Masters Rulebook makes a dramatic break with all that has come before.
The Most Important Rule
There is one rule which applies to everything you will do as a Dungeon Master. It is the most important of all the rules! It is simply this: BE FAIR. A Dungeon Master must not take sides. You will play the roles of the creatures encountered, but do so fairly, without favoring the monsters or the characters. Play the monsters as they would actually behave, at least as you imagine them. The players are not fighting the DM! The characters may be fighting the monsters, but everyone is playing the game to have fun. The players have fun exploring and earning more powerful characters, and the DM has fun playing the monsters and entertaining players. For example, it's not fair to change the rules unless everyone agrees to the change. When you add optional rules, apply them evenly to everyone, players and monsters. Do not make exceptions; stick to the rules, and be fair.
– Frank Menzer, Basic Dungeons & Dragons Dungeon Masters Rulebook p. 2 (1983)
The DM's role as described is exceptionally limited when you compare the parallel AD&D. Heck, the DM can't even change the rules without group consensus! All the advice in the first section harps on the fairness aspect. "…so should the DM keep the "monster knowledge" completely separated from the "DM information."" It tends to assume the rules are complete and impartial application of the rules is all that is required in the game.
There is no explicit discussion of the GM using their judgment or making rulings at all. The rules section just says briefly that if the DM has questions they should 1) read the rules, 2) read some more rules, 3) ask an experienced DM, 4) send mail to TSR to get an answer (no, seriously). The only other mention is under the "Complaints" section that talks about listening to player complaints and admitting to your mistakes. The subsequent sets (Expert, Companion…) have exactly zero to say on the topic of the DM's dilemma of making rulings using their judgment except inasmuch as constructing the adventure and choosing monsters is within the DM's purview.
As you can see, BECMI takes the ideas from B/X and then apparently reacts against the strong strain of competition and DM entitlement in AD&D and swings way over in the other direction. Basic's decline came when 2e came out but its concepts get picked up much later by 4e.
Advanced Dungeons & Dragons Second Edition (2e)
The Second Edition DMG kicks in with a significantly different attitude towards rules, picking back up some of the B/X thread. Rulings are discussed explicitly and rules are put in the back seat in terms of primacy.
Choice is what the AD&D game is all about. We've tried to offer you what we think are the best choices for your AD&D campaign, but each of us has different likes and dislikes. The game that I enjoy may be quite different from your own campaign. But it is not for me to say what is right or wrong for your game. True, I and everyone working on the AD&D game have had to make fundamental decisions, but we've tried to avoid being dogmatic and inflexible. The AD&D game is yours, it's mine, it's every player's game.
So is there an "official" AD&D game? Yes, but only when there needs to be. Although I don't have a crystal ball, it's likely that tournaments and other official events will use all of the core rules in these books.[…] Take the time to have fun with the AD&D rules. Add, create, expand, and extrapolate. Don't just let the game sit there, and don't become a rules lawyer worrying about each piddly little detail. If you can't figure out the answer, MAKE IT UP! And whatever you do, don't fall into the trap of believing these rules are complete. They are not. You cannot sit back and let the rule book do everything for you. Take the time and effort to become not just a good DM, but a brilliant one.
At conventions, in letters, and over the phone I'm often asked for the instant answer to a fine point of the game rules. More often than not, I come back with a question—what do you feel is right? And the people asking the questions discover that not only can they create an answer, but that their answer is as good as anyone else's. The rules are only guidelines.
– David "Zeb" Cook, Dungeons & Dragons Second Edition Dungeon Master's Guide, Foreword (1989).
This is very notable – the rules are super flexible, both the rules as written (RAW) and even the rules as intended (RAI) are completely at your discretion, is the messaging. The DMG then talks a lot more about the players' role in creating the story and in the DM's role in entertaining them.
A mailing list debate from 2000 highlighting the difference in attitudes – 2e was more about freedom with less specific prescription, and some folks liked that and some didn't:
1st edition was very personal and idiosyncratic, and not to everyone's taste.[…] The second edition represents a shift in paradigm from this model (the shift began, of course, right away, as the D&D rules quickly mutated in the hands of individuals, but 2nd Edition was the first time it became evident in the products produced by TSR). Where once there was a complete game found in a few canonical books, now there is a nebulous web of possibilities spun through any number of sources.
In reply:
There are some good ideas in 2nd edition[…] Other than that, my opinion is that it's a mish-mash of rules that nobody ever took the time to playtest in conjunction with each other. Put the burden on the DM? Like I need to have more burdens placed on me!
Some folks are more comfortable with a more constrained and prescriptive ruleset; 2e (along with a lot of the storytelling focus of that decade with Vampire and the like) sets the rules aside for the focus on story and DM discretion.
Dungeons & Dragons Third Edition (3e)
In the Dungeons & Dragons Third Edition Player's Handbook is the source of the term "Rule Zero" which is often used as shorthand for "DM discretion."
0. CHECK WITH YOUR DUNGEON MASTER
Your Dungeon Master (DM) may have house rules or campaign standards that vary from the standard rules. You might also want to know what character types the other players are playing so that you
can create a character that fits in well with the group.
– Character Creation, Dungeons & Dragons Player's Handbook (2000).
Since then, Rule Zero has been expanded in the popular mindset to be "The DM Is Always Right/Can Do What He Wants" or, alternately, "Having Fun Is The Most Important Thing." It caught on as a term to describe judiciously breaking the rules – and the very fact that it emerged as an explicit term shows that there was discussion of the concept going on.
In the 3e PHB, it is pretty matter of fact about "Here's the rules. You'll be using them." Except for Rule Zero there's no mention of possible variation and no real discussion of the DM's role beyond:
One person in the game, the Dungeon Master (DM), controls the monsters and people that live in the fantasy world. You and your friends face the dangers and explore the mysteries your Dungeon Master sets before you.
– Dungeons & Dragons Player's Handbook, Introduction p.6 (2000).
The 3e DMG starts out with a whole chapter on the Dungeon Master's role. This edition talks a lot about the player role – "The players and the DM work together to create the game as a whole" (p.8). The DM provides the adventure and the world and adjudicates, but the book provides a whole checklist to guide adjudication and creating house rules. For adjudication, check the rules, check similar rules, if you make something up it's a house rule and you should be consistent with it for the campaign because "Consistency keeps players satisfied and gives them the feeling that they adventure in a stable, predictable universe and not in some random, nonsensical place subject only to the DM's whims" (p.9). Any ruling made effectively should become a consistent, permanent house rule.
For house ruling, there's a section discussing it, and the overall gist is to read the rules, understand why the rules exist, be careful about changing the rules – but still do it. "Given the creativity of gamers, almost every campaign will, in time, develop its own house rules."
I have extensive RPG mailing list email archives going back to 1997, and as I search for incidences of the phrase "rules as written," there's occasional uses of the phrase all the way back but it comes into heavy use as a gaming jargon phrase on D&D lists in 2000-2001 with the advent of Third Edition.
My experience is that since 3e didn't really explicitly say a lot about the DM's role, 2e attitudes mostly carried over into 3e until 3.5e, when new players without previous edition experience and the more tactical rules focus enhanced in 3.5e caused a shift in attitudes not strictly prescribed by the difference between 3e and 3.5e text.
Over the course of 3e/3.5e, there was a significant culture change around rules adherence. WotC put a lot of work into their RPGA/Organized Play campaigns, and especially the Living campaigns had to, due to their format, enforce strict "rules as written" adherence (as predicted by Zeb Cook in the 2e preface, you'll note!). This generated debate, and as time went on, altered more of the default mode of players towards the rules being fixed above the individual DM's discretion.
A quote from a Living Greyhawk organizer list email in December 1999:
Last I heard, the rule from on high was: Greyhawk will be the flagship campaign. It WILL follow core rules, period. I suspect we both agree this means we will be playing some silly rules, tho not necessarily which ones actually are bad. However, until we hear otherwise, we had best be prepared to accept Core rules as written in stone.
And an immediate counterpoint:
I would be very…disappointed…if this were true. If this is the case then another Fate of Istus type thing seems inevitable – weird things springing up in the setting just cos they changed the rules again. The mechanics of the game should poke through the skin of the setting as little as possible IMO. Setting over rules – other wise you make things a complete homogeneous sludge.
Dungeons & Dragons Third Edition, Revised (3.5e)
The 3.5e Player's Handbook still cites Rule Zero (though without the "0," so it's just a sentence in the Character Creation section). Its description of the DM role is:
The DM controls the monsters and enemies, narrates the action, referees the game, and sets up the adventures.
The DMG is largely the same as 3e with some slight shading of language couching the DM's role and authority in more limited terms. "you control the pacing, and the types of adventures and encounters, the whole tenor of the game is in your hands" (p.4). Collaboration with the players is called out explicitly more. Also, the sheer magnitude of the rules and their attempt to cover all conditions makes the book more inherently readable as a self-contained guide to the game.
Gary Gygax had some harsh words for D&D 3.5 on this topic:
The new D&D is too rule intensive. It's relegated the Dungeon Master to being an entertainer rather than master of the game. It's done away with the archetypes, focused on nothing but combat and character power, lost the group cooperative aspect, bastardized the class-based system, and resembles a comic-book superheroes game more than a fantasy RPG where a player can play any alignment desired, not just lawful good.
– Gary Gygax, GameSpy interview, Pt. 2 (16 August 2004)
At the end of 3.5e's reign, the Rules Compendium had this to say, in departure from what had become the mainstream, about this essential assumption behind the rules:
Essential to the D&D game is the Dungeon Master (DM). The DM is the referee and storyteller for the game, as well as the judge when the rules don't cover a particular topic.
Let's face it: No set of rules can cover every possible circumstance in a game meant to mimic life in a fantasy world. The rules clear up as much as possible, assuming the DM can make a judgment in a situation that the rules don't cover or that they don't cover adequately. DMs are expected to use knowledge of existing rules, common sense, realworld knowledge, and a sense of fun when dealing with such special cases. Knowledge of the existing rules is key, because the rules often do cover similar cases or combine to make such judgment calls unnecessary. It's not always true, but you often can do or at least try something the rules fail to directly forbid, as long as the DM thinks doing so is reasonable. For example, the rules don't come out and say that a Medium creature threatens all squares within 10 feet while wielding a reach weapon and wearing spiked gauntlets. However, it's appropriate to assume the creature does just that.
The DM is also there to keep the game moving. Doing so might require expedient rulings that later prove troublesome or just plain incorrect. That's okay. Players and DMs make mistakes, and these mistakes tend to average out over time. It's better for everyone's fun if the game just keeps going rather than devolving into a rules argument or going back to revisit the round in which a mistake was made.
– D&D Rules Compendium p.5
This statement, while still backing the rules, tries to cut beleaguered DMs some slack in the rulings department, even saying "let's not go back and hash it over again" as some of the other advice gives on this subject.. James Wyatt writes a full page essay called "Rules and Fun" in the Rules Compendium (p. 63) that explains why we have rules and how they are important for balance and for introducing new possibilities, as opposed to their function as limits. He argues that the rules aren't as restrictive as say a computer game's, and says the D&D rules "limit your options without too narrowly defining them. The beauty of D&D is that your character can try anything you can imagine. The rules are there as a yardstick to measure your chance of success."
The problem with this from a textual interpretation standpoint is that it's hard to not interpret the raft of "possibility" options in the 3e branch of D&D as being restriction of options. I can try to throw my opponent in a grapple – until a feat comes out that says "In a grapple, you can now throw your opponent." Thus despite mitigating statements by the designers, their design itself passively promulgates an approach to the rules as written.
Dungeons & Dragons Fourth Edition – 4e
The 4e DMG does a lot of recasting of the role of the DM. He is described "one of the players," a turn of phrase never used before in D&D, albeit a player with a special role (p.6) – "The DM is the rules moderator, the narrator, a player of many different characters, and the primary creator of the game's world, the campaign, and the adventure." He "stands as a mediator between the rules and the players." If he makes a rules call during the session, it should be re-discussed later and he should "admit his mistake" and "make it up to the players." The tenor of this couldn't be more different from that of Gygax in AD&D, but you can see callbacks to BECMI in the wording.
4e does have a section on house rules (DMG p.189) as something "some DMs" might like to do, and allows that changing the rules is within your rights.
The word "judgment" in reference to the DM using their judgment or making judgment calls is used only 4 times in the 4e DMG, as opposed to 10 in 3e and 15 in 2e. In general it is stressed less in the text as a concept; implying that the rules handle most situations without that being necessary or desirable.
Another significant change here is the formal introduction of dissociated mechanics. In later 3.5e the concept had definitely emerged of "RAW, right or wrong" and that attempting to use game world simulation or physics was undesirable and you should just do what the rules say whether it makes sense or not. 4e codified that and formally dissociated the character powers into "rules first" mechanisms that can be skinned into the world however you want, but that have entirely deterministic effects not beholden to game world simulation. This mode of play places story above world/fiction and thus eliminates a lot of the motivation for rulings calls beyond pure "the rules aren't clear here" in the game.
(Yes, Pathfinder is a version of D&D, duh.) Much of the Pathfinder Core Rulebook's GM advice is cribbed from 3e, with slightly stronger statements echoing earlier editions about "All the rulebooks, including this one, are his [the GM's] tools, but his word is the law" "GM Fiat: The GM is the law of the game."
When complications involving rules interpretations occur, listen to the player and make the decision as quickly as you can on how to resolve the situation. If the rule in question isn't one you're familiar with, you can go with the player's interpretation but with the knowledge that after the game you'll read up on the rules and, with the next session, will have an official ruling in play. Alternatively, you can simply rule that something works in a way that helps the story move on, despite the most logical or impassioned arguments from the players. Even then, you owe it to your players to spend time after the game researching the rule to make sure your ruling was fair— and if not, make amends the next game as necessary.
Cheating and Fudging: We all know that cheating is bad. But sometimes, as a GM, you might find yourself in a situation where cheating might improve the game. We prefer to call this "fudging" rather than cheating, and while you should try to avoid it when you can, you are the law in your world, and you shouldn't feel bound by the dice. […]
Likewise, don't feel bound to the predetermined plot of an encounter or the rules as written. Feel free to adjust the results or interpret things creatively—especially in cases where you as the GM made a poor assumption to begin with.
So they come out on the side of GM rulings, fiat, and fudging (all forms of primacy over the rules), with a bit of the "make amends if you weren't fair" flavor.
The Gamemastery Guide has lengthy and detailed advice on running a game including a section called "Winging It," "GM Subterfuge," "The Illusion Of Free Choice," and other related topics. Most of it tiptoes around the topic of ruling in addition to/overriding the rules. It talks about the GM having the final say and not wasting too much time in game with rules disputes but still comes strongly from the rules-fairness viewpoint. It does talk about dealing with "Rules Lawyers," and says
Even if you follow these rules, you may still have trouble with rules lawyers. Not everyone views rules the same way. The important thing is to stand behind your rulings, and when certain things break the rules—for good reason— don't feel like you have to reveal world secrets just because the rules lawyer demands answers. GMs work in mysterious ways, and with any luck history will vindicate your choice.
There's also an "advanced" section on "Customizing Your Game" and it talks about making some non-rules-supported rulings – as long as it's carefully concealed from the players. "And with some shuffling of notes
and hidden dice roles, no player should be the wiser tosuch an improvised ruling."
This is an interesting and ambivalent approach – sure, the DM should be ruling, but it's somewhat shameful and if the players find out then you will be somehow compromised. It's like being a closeted 1e DM posing as a 4e GM.
It's worth noting the Old School Renaissance movement to bring back older versions of D&D, with its seminal A Quick Primer For Old School Gaming using the phrase "rulings, not rules" to try to describe the spirit of older editions as compared to newer editions. It cites these four pillars:
Rulings, Not Rules
Player Skill, not Character Abilities
Heroic, not Superhero
Forget "Game Balance"
Most of the time in old-style gaming, you don't use a rule; you make a ruling. It's easy to understand that sentence, but it takes a flash of insight to really "get it." The players can describe any action, without needing to look at a character sheet to see if they "can" do it. The referee, in turn, uses common sense to decide what happens or rolls a die if he thinks there's some random element involved, and then the game moves on. This is why characters have so few numbers on the character sheet, and why they have so few specified abilities.
Some, however, consider this to be a bit of a retcon of how old school gaming actually worked. As you can see from this research, it is and it isn't – the "rulings vs. rules" concept was very strong especially in B/X and 2e, somewhat less so in 0e/1e, and actively militated against in BECMI. Hackmaster and the Knights of the Dinner Table comic prominently parody the not uncommon rules-adherence mode of play in AD&D. As all nostalgia does, the Quick Primer picks certain elements out of the past to bring back and leaves aside some other elements.
Dungeons & Dragons Fifth Edition (5e)
The 5e playtest, when it was called "D&D Next," had some very retro things to say about the interaction of DM and rules. "The rules are a tool that you and the players use to have a good time," "The rules aren't in charge. You, the DM, are…" "the DM's power comes with responsibility. Be fair and impartial with the players." This last quote directly hearkens back to a quote from Zeb Cook's 2e introduction – "As a Dungeon Master, you have great power, and 'with great power comes great responsibility.' Use it wisely." It even goes on to discuss ignoring the dice – "The dice don't run the game. You do." This sweeps aside a lot of the underlying play assumptions of later 3.5e/4e and brings back a lot of B/X and 2e concepts.
In the final 5e books, it definitely takes a step back from the "rules are God" approach that 3.5e and 4e had been heading towards. In the Player's Handbook, it says in the Introduction:
Because there is so much diversity among the worlds of D&D, you should check with your DM about any house rules that will affect your play of the game. Ultimately, the Dungeon Master is the authority on the campaign and itssetting, even if the setting is a published world.
It also appears to take a hint from the OSR's formulation of "rulings, not rules" as well as the prominent fiction-first modern indie games like Apocalypse World when it describes the basic pattern of play –
The DM describes the environment
The players describe what they want to do (and the DM decides how to resolve those actions – importantly, the PCs don't decide what rules they use)
The DM narrates the results
In the Dungeon Master's Guide, the DM is described as the "creative force behind a D&D game," and it goes into their multiple hats (designer, actor, etc.). And in its Introduction it's very clear that
The D&D rules help you and the other players have a good time, but the rules aren't in charge. You're the DM, and you are in charge of the game.
Emphasis is in the original. The three parts of the DMG are "Master of Worlds," "Master of Adventures," and "Master of Rules". As "Master of Rules" the DM is described as the mediator between the players and the rules.
As you read through the 5e DMG, I get a very 2e feel off of it, down to the art direction, and its approach to the game is very similar too.
In Part 3: Master of Rules, it's very straightforward about presenting the GM with pros and cons of approaches including rolling dice in the open vs rolling behind a screen and fudging (changing rolls) if you want to. It offers options about the role of dice including using them a lot to mostly ignoring or not using them, OSR style. In the early stages of 5e development they had some discussions about "5e being compatible with all the versions!" which of course was impossible and left by the wayside, but they've tried to preserve some of that in terms of saying you can take as rigid or loose a playstyle as you want regarding the rules – but in the end, it's the DM's call.
And in Chapter 9, you are encouraged to "let your imagination run wild" and use optional rules or make up your own, with pages of advice on how to do that well.
Now, this is how the text reads – but the designers have done a very good job of continuing this. Games live on past their pages, and now in the age of the Internet, you can reach out to the designers in realtime. 5e designer Jeremy Crawford gives official rulings via Twitter. But the tone of his and Mike Mearls' responses is usually "here's how I'd rule", not saying "this is what's right you have to do it" like Sage Advice columns of old.
Though in each edition you had some elements of each approach, there's a clear move in philosophy over time from
0e – the referee is an aribter and fills in the gaps
1e – the DM is large and in charge, the rules are pretty good, your players are at both's behest
B/X and 2e – the DM and players are both important, the rules are super mutable
3e/early 3.5e – the rules and players and DM are leveled out in importance, meaning rulings are minimized and a negotiation with players
BECMI/late 3.5e/4e – the rules are pretty fixed and players and DM are equal and subject to the rules as law; RAW is an option
OSR and Pathfinder – splitting off in their own directions in reaction to 4e, OSR back to a mix of 0e and B/X flavored attitudes and Pathfinder to a hybrid of 1e/2e/3e attitudes
5e – The DM is clearly in charge and can ignore/change rules and rolls as they deem wise, with the goal of everyone having fun (as opposed to the sometimes-stated 1e goal of "keeping the players in their place".) It reincorporated a lot of the 1e and 2e thinking into the game to an even greater degree than Pathfinder.
At the same time, prominent "D&D Offramp" games like 13th Age and Numenera have a large portion of their pitch not just new setting/rules but explicit attitudes towards the running of the game – in Numenera, Monte Cook has a very large section about GM empowerment that, while not written in Grand High Gygaxian, still recalls much of the AD&D 1e and 2e advice about the GM being in charge and doing what they darn well please. 13th Age is a little more 4e-ey but both with rules-crafting and rules advice tries to take D&D in more of a storygaming direction. Dungeon World, a D&D-style game build on the Apocalypse World engine, is interestingly picky about the rules but the rules are kept to a minimum and it's always the DM's decision what rule is getting invoked at any time.
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Tagged 1e, 2e, 3e, 4e, advanced, basic, D&D, discretion, dungeons and dragons, fiat, next, RPG, RPGs, rule 0, rule zero, rules, rulings
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The Columbus Blue Jackets look to sweep the Blues this season with a win in their final meet-up tonight. However, the Jackets were up late last night battling the Pittsburgh Penguins in overtime while the Blues had two days off.
The Blues have won 5/5 games when leading after the first period. They look to come out aggressive tonight.
Defensemen Joel Edmundson will be back in the lineup tonight, taking the place of Robert Bortuzzo. Edmundson has been a healthy scratch for the last two games.


text:
Q: Global variable inside a function cant be access outside If I understood it correctly, declaring a variable without using the keyword var inside a function will create a global scoped variable.
But I am getting this "ReferenceError: oopsGlobal is not defined" when accessing the variable from outside its container function.
,,,
 // Declare the myGlobal variable below this line
var myGlobal = 10

function fun1() {
  // Assign 5 to oopsGlobal Here
  oopsGlobal = 5
}

// Only change code above this line

function fun2() {
  var output = "";
  if (typeof myGlobal != "undefined") {
    output += "myGlobal: " + myGlobal;
  }
  if (typeof oopsGlobal != "undefined") {
    output += " oopsGlobal: " + oopsGlobal;
  }
  console.log(output);
}

console.log(oopsGlobal) // ReferenceError: oopsGlobal is not defined
,,,

A: That is happening because you are never actually running fun1(). If you don't call a function, the code inside will never be executed.

ReferenceError:

 // Declare the myGlobal variable below this line
var myGlobal = 10

function fun1() {
  // Assign 5 to oopsGlobal Here
  oopsGlobal = 5
}

// Only change code above this line

function fun2() {
  var output = "";
  if (typeof myGlobal != "undefined") {
    output += "myGlobal: " + myGlobal;
  }
  if (typeof oopsGlobal != "undefined") {
    output += " oopsGlobal: " + oopsGlobal;
  }
  console.log(output);
}

console.log(oopsGlobal) // ReferenceError: oopsGlobal is not defined

No ReferenceError (note that fun1() is called before console.log())

 // Declare the myGlobal variable below this line
var myGlobal = 10

function fun1() {
  // Assign 5 to oopsGlobal Here
  oopsGlobal = 5
}

// Only change code above this line

function fun2() {
  var output = "";
  if (typeof myGlobal != "undefined") {
    output += "myGlobal: " + myGlobal;
  }
  if (typeof oopsGlobal != "undefined") {
    output += " oopsGlobal: " + oopsGlobal;
  }
  console.log(output);
}

fun1()
console.log(oopsGlobal)

A: You have written code, but never INVOKED it. fun1 and fun2 are never run. I added one line below that invokes the fun1() function which causes the assignment to happen.
This is more of an answer to provide a demonstration -- more than likely you do NOT want to actually write code that has global variables or side-effects like this. If you are writing software for the browser, using window or globalThis to store you global state also may make it more clear as well.

// Declare the myGlobal variable below this line
var myGlobal = 10

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Home Brussels Member states falling behind in meeting EU fisheries policy targets
Member states falling behind in meeting EU fisheries policy targets
by editor December 12, 2018
EU Member States have had five years to implement measures within the Common Fisheries Policy (CFP), but are still lagging behind and are likely to miss important 2020 deadlines on biodiversity conservation and sustainable fisheries management.
This according to a new report published by the Brussels-based office of the World Wide Fund for Nature (WWF) yesterday (11 December), presenting European and Member State decision-makers with an evaluation on the implementation of key articles of the CFP.
"EU Member States have had ample time to implement the provisions of the reformed CFP, but have demonstrated an unacceptable lack of political will towards sustainable fisheries management," commented Samantha Burgess, Head of Marine Policy at WWF European Policy Office.
"European fisheries are facing unprecedented challenges, with high levels of overfishing, destruction of marine habitats, impacts of climate change, with continued illegal activities and poor management of the fisheries sector," she added.
The report includes individual data for each EU Member State. Only one out of 46 CFP actions assessed by WWF was accomplished by all Member States (establishing an administrative system for registering fishing vessels). About half of the actions have only been partially accomplished, whilst the others have not been tackled to date.
On a number of key actions, the implementation score was in particular low for Latvia, Rumania, Cyprus, Bulgaria, Finland, Greece and Lithuania. Belgium has a score above average.
WWF also rated actions undertaken by the European Commission, and these findings show more encouraging efforts. The Commission has achieved nearly half of the implementation actions for the CFP, earning 47% of the maximum score possible.
1 January 2019 is the deadline for full implementation of the landing obligation by all EU Member States, whereby fishing vessels are required to retain and bring to port all seafood catches and count them against quota to eliminate discarding (returning unwanted catches to the sea).
Analyses by WWF have found that exemptions (derogations), allowing operators to discard up to 7% of their catches, have increased by 300% between 2017 and 2018. Phasing-in implementation of the landing obligation to January's fast approaching deadline has not reduced discarding, nor brought the much-needed changes to make fishing practices more sustainable.
WWF analysed 46 articles with measurable actions and deadlines. Asked by – about the most important fisheries policies goals, the Fund replied that all CFP articles should be seen as a whole and as part of a system intended to help achieve sustainable fisheries in Europe.
"However, the challenge with this complex piece of legislation is that many of the articles aren't measurable or don't have specific deadlines," WWF explained. "That said, the most critical actions include the discard ban and the landing obligation."
Overfishing
How do you explain that the goal for discarding fish has not been achieved? "The landing obligation is viewed as a major challenge by many fishers across the EU and lack of the European Maritime and Fisheries Fund (EMFF), which has resources dedicated to supporting fishers in the transition, demonstrates why the transition has been difficult," replied WWF.
Some species are currently overfished, says WWF. "The risks are different to various species dependent on the seas basin they are located in. In the Adriatic Sea, anchovies are heavily overfished, in the Western Mediterranean Sea, hake is overfished, while eel in the Baltic Sea is included in a list of critically endangered species."
"There is still significant conflict between targeting commercial fish species and endangered species which are caught as bycatch or unintended catch in the course of commercial fishing activities."
Enrico Brivio, European Commission spokesperson for maritime affairs and fisheries, told the Brussels Times that the Commission welcomes the WWF report. The report was also discussed at a hearing in the European Parliament last week.
"The Common Fisheries Policies has been in force for only five years and some of its provisions, such as the landing obligation, will enter into full force only next year," he says. "The report is an opportunity to assess the progress. Good progress is reported for certain fisheries and sea basins. In the North East Atlantic, biomass increased by 40 % since 2013."
"Even if Member States have fallen short on individual targets, fishing in some sea basins has on average fallen close to maximum sustainable yield. Of course, lack of progress in the Mediterranean is a major concern."
"A three pillars approach (economic, social and environmental) to achieve sustainability is working but there is still more work to do," Brivio summarises. The Commission urges Member States to improve the low take up of the funding available under the fisheries fund to help implementing the landing obligations.
He explains that the use of derogations increased substantially because the obligation, following a gradual introduction, starts to be fully applied only next year and thus now covers more fisheries. In some cases, temporary exemptions were granted on condition that Member States will produce the necessary data.
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