<p>Compare a) A social planner who prefers the gains to go to one group instead of another, and b) A social planner who equally values a gain regardless of who got it. </p>

<p>In terms of "inequality aversion", consider the specific mathematical definitions. The Gini index, for example, does not correct for whether the identities of the individuals are Mrs. Smith or Mr. Lee.</p>

CC BY-SA 3.0
2018-03-08T19:38:03.693Z
2018-03-08T19:38:03.693Z
nathanwww
<blockquote>
  <p>Anonymous/impartial SWFs focus only on the pattern of well-being,
  and not the identities of the people who end up at particular well-being levels.</p>
</blockquote>

<p><em>Identities</em> here simply means names. When applying an impartial SWF, one only looks at the profile of utilities, not <em>who</em> those utilities are associated with. Consider the following two cases: 
\begin{array}{ccc}
&amp;U_{\text{President}}&amp;U_{\text{CEO}}&amp;U_{\text{Farmer}} \\\hline
\text{Case 1}&amp; 100 &amp; 80 &amp; 10\\
\text{Case 2}&amp; 10 &amp; 100 &amp; 80
\end{array}
The <strong><em>patterns</em></strong> of the distribution of well-being/utility in the two cases are essentially the same, and yet they differ in <strong><em>who</em></strong> is better/worse off. An impartial SWF would generate the same outcome in both cases, since it only focuses on the pattern (i.e. the utility numbers) of the well-being distribution and <em>not</em> on who (i.e. the identity) has which level of utility. In particular, the fact that the President is the happiest person in Case 1 but the most miserable in Case 2 has no impact whatsoever on the outcome of the impartial SWF. </p>

CC BY-SA 3.0
2018-03-04T22:03:27.423Z
2018-03-04T22:03:27.423Z
Herr K.
<p>Currently reading David Adler's text on distributional weights in benefit-cost analysis (<a href="https://scholarship.law.duke.edu/faculty_scholarship/3110/" rel="nofollow noreferrer">https://scholarship.law.duke.edu/faculty_scholarship/3110/</a>), I cannot manage to fully grasp the definition of the anonymity axiom. </p>

<p>The isoelastic/Atkinson social welfare function (SWF) allows for an inequality aversion parameter; greater weight is put on changes affecting worse-off individuals. Adler states that this function satisfies the anonymity/impartiality axiom, defined here as "meaning indifference between any given utility vectora and all rearrangements of component numbers". I understand this, broadly, as meaning that the levels of utility, and not the persons enjoying those levels, are what counts. </p>

<p>I can't manage to reconcile the fact that the "anonymity/impartial SWFs focus only on the patern of well-being, and not on the identities of the people who end up at particular well-being levels" (page 267 of the text) with the use of an inequality aversion parameter, which, by definition, treats individuals differently. Would this not mean focusing "on the identities of the people who end up at particular well-being levels"?</p>

<p>What am I missing ? </p>

<p>Any links towards readings on this subject would be much appreciated as well. </p>

<p>Many thanks.</p>

CC BY-SA 3.0
2018-03-04T18:29:24.263Z
Is it possible if you can cite the specific quote you are having difficulty understanding?
Bensstats
CC BY-SA 3.0
2018-03-04T18:33:30.853Z
"Anonymity/impartial SWFs focus only on the patern of well-being, and not on the identities of the people who end up at particular well-being levels" (page 267, first paragraph); which I cannot reconcile with the fact that the isoelastic SWF puts more weight on changes affecting less well off individuals. I must be missing something but haven't managed to find any documentation that helps... 

Many thanks
Ploit88
CC BY-SA 3.0
2018-03-04T18:34:41.217Z
Is it possible if you can include that in your edited question? Sorry for the bother.
Bensstats
CC BY-SA 3.0
2018-03-04T18:38:10.857Z
No worries, thanks for pointing out that it needed to be clarified.
Ploit88
<social-welfare><social-choice>
Anonymity in social welfare function
Ploit88
# Anonymity in social welfare function

(Asked by: username_0 on 2018-03-04)

Currently reading David Adler's text on distributional weights in benefit-cost analysis (<https://scholarship.law.duke.edu/faculty_scholarship/3110/>), I cannot manage to fully grasp the definition of the anonymity axiom.

The isoelastic/Atkinson social welfare function (SWF) allows for an inequality aversion parameter; greater weight is put on changes affecting worse-off individuals. Adler states that this function satisfies the anonymity/impartiality axiom, defined here as "meaning indifference between any given utility vectora and all rearrangements of component numbers". I understand this, broadly, as meaning that the levels of utility, and not the persons enjoying those levels, are what counts.

I can't manage to reconcile the fact that the "anonymity/impartial SWFs focus only on the patern of well-being, and not on the identities of the people who end up at particular well-being levels" (page 267 of the text) with the use of an inequality aversion parameter, which, by definition, treats individuals differently. Would this not mean focusing "on the identities of the people who end up at particular well-being levels"?

What am I missing ?

Any links towards readings on this subject would be much appreciated as well.

Many thanks.

**Tags:** social-welfare, social-choice

> **Comments:**
> **username_1**: Is it possible if you can cite the specific quote you are having difficulty understanding?  
> **username_0**: "Anonymity/impartial SWFs focus only on the patern of well-being, and not on the identities of the people who end up at particular well-being levels" (page 267, first paragraph); which I cannot reconcile with the fact that the isoelastic SWF puts more weight on changes affecting less well off individuals. I must be missing something but haven't managed to find any documentation that helps...   Many thanks  
> **username_1**: Is it possible if you can include that in your edited question? Sorry for the bother.  
> **username_0**: No worries, thanks for pointing out that it needed to be clarified.  

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## 2 answers

### Answer by username_3 on 2018-03-04. Score: 3 | Accepted answer

> Anonymous/impartial SWFs focus only on the pattern of well-being,
> and not the identities of the people who end up at particular well-being levels.

*Identities* here simply means names. When applying an impartial SWF, one only looks at the profile of utilities, not *who* those utilities are associated with. Consider the following two cases:
\begin{array}{ccc}
&U\_{\text{President}}&U\_{\text{CEO}}&U\_{\text{Farmer}} \\\hline
\text{Case 1}& 100 & 80 & 10\\
\text{Case 2}& 10 & 100 & 80
\end{array}
The ***patterns*** of the distribution of well-being/utility in the two cases are essentially the same, and yet they differ in ***who*** is better/worse off. An impartial SWF would generate the same outcome in both cases, since it only focuses on the pattern (i.e. the utility numbers) of the well-being distribution and *not* on who (i.e. the identity) has which level of utility. In particular, the fact that the President is the happiest person in Case 1 but the most miserable in Case 2 has no impact whatsoever on the outcome of the impartial SWF.


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### Answer by username_2 on 2018-03-08. Score: 0

Compare a) A social planner who prefers the gains to go to one group instead of another, and b) A social planner who equally values a gain regardless of who got it.

In terms of "inequality aversion", consider the specific mathematical definitions. The Gini index, for example, does not correct for whether the identities of the individuals are Mrs. Smith or Mr. Lee.


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