<p>I am looking for axiomatic characterisations of dictatorial social choice/welfare functions; where a dictatorial social choice function is one that always picks the dictator’s favourite outcome, and a dictatorial social welfare function is one whose social preference always coincides with the one of the dictator.</p>
<p>An axiomatic characterisation of a dictatorial social choice/welfare function is a collection of axioms that uniquely identify a dictatorial social choice/welfare function. The three most famous such characterisations I can think of were provided by <a href="https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem" rel="nofollow noreferrer">Arrow (1951, 1963)</a>, <a href="https://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theorem" rel="nofollow noreferrer">Gibbard (1973) &amp; Satterthwaite (1975)</a> and <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/1468-0262.00143?casa_token=VBhAf-_US1YAAAAA:c8f1WATuA-Dwx1uxxeACcZR_mi1zsmTGr4PDeMFX9MB4im2yST_L4FI3oqYLgEYWHIW1jg8LyMbIxGHg" rel="nofollow noreferrer">Koray (2000)</a>:</p>
<ol>
<li>[<a href="https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem" rel="nofollow noreferrer"><strong>Arrow (1951, 1963)</strong></a>] With at least three alternatives, a social welfare function is dictatorial if and only if it satisfies <em>unrestricted domain</em>, <em>Pareto-optimality</em> and <em>independence of irrelevant alternatives</em>.</li>
<li>[<strong><a href="https://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theorem" rel="nofollow noreferrer">Gibbard (1973) &amp; Satterthwaite (1975)</a></strong>] With at least three alternatives, a social choice function is dictatorial if and only if it satisfies <em>unrestricted domain</em> and <em>strategy-proofness</em>.</li>
<li>[<strong><a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/1468-0262.00143?casa_token=VBhAf-_US1YAAAAA:c8f1WATuA-Dwx1uxxeACcZR_mi1zsmTGr4PDeMFX9MB4im2yST_L4FI3oqYLgEYWHIW1jg8LyMbIxGHg" rel="nofollow noreferrer">Koray (2000)</a></strong>] A social choice function satisfying <em>unrestricted domain</em>, <em>unanimity</em> and <em>neutrality</em> is <em>self-selective</em> if and only if it is dictatorial.</li>
</ol>
<p><strong>Can you please direct me to other results in social choice theory that uniquely characterise dictatorships?</strong></p>

CC BY-SA 4.0
2024-05-16T11:08:07.157Z
I am not sure whether this answers your questions so leaving this as a comment, but you can refer to Prof. Arunava Sen's notes on social choice theory. https://www.isid.ac.in/~asen/scdoc/lecarrow_2017.pdf  These notes contains a lot of the major results in social choice, so they might have the sort of results you're seeking.
mynameparv
CC BY-SA 4.0
2024-05-16T13:20:35.883Z
Thank you very much for your comment: these notes are very nice and contain one result I wasn’t aware of (**namely, that unrestricted domain, Maskin monotonicity and unanimity imply dictatorship**). I also saw that the Gibbard & Satterthwaite Theorem is stated in terms of unanimity, unrestricted domain and strategy-proofness. While I see Satterthwaite used unanimity in his paper, I can’t see it in Gibbard’s.
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<microeconomics><reference-request><theory><soft-question><social-choice>
Axiomatic characterisations of dictatorial social choice/welfare functions?
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# Axiomatic characterisations of dictatorial social choice/welfare functions?

(Asked by: username_0 on 2024-05-15)

I am looking for axiomatic characterisations of dictatorial social choice/welfare functions; where a dictatorial social choice function is one that always picks the dictator’s favourite outcome, and a dictatorial social welfare function is one whose social preference always coincides with the one of the dictator.

An axiomatic characterisation of a dictatorial social choice/welfare function is a collection of axioms that uniquely identify a dictatorial social choice/welfare function. The three most famous such characterisations I can think of were provided by [Arrow (1951, 1963)](https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem), [Gibbard (1973) & Satterthwaite (1975)](https://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theorem) and [Koray (2000)](https://onlinelibrary.wiley.com/doi/abs/10.1111/1468-0262.00143?casa_token=VBhAf-_US1YAAAAA:c8f1WATuA-Dwx1uxxeACcZR_mi1zsmTGr4PDeMFX9MB4im2yST_L4FI3oqYLgEYWHIW1jg8LyMbIxGHg):

1. [[**Arrow (1951, 1963)**](https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem)] With at least three alternatives, a social welfare function is dictatorial if and only if it satisfies *unrestricted domain*, *Pareto-optimality* and *independence of irrelevant alternatives*.
2. [**[Gibbard (1973) & Satterthwaite (1975)](https://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theorem)**] With at least three alternatives, a social choice function is dictatorial if and only if it satisfies *unrestricted domain* and *strategy-proofness*.
3. [**[Koray (2000)](https://onlinelibrary.wiley.com/doi/abs/10.1111/1468-0262.00143?casa_token=VBhAf-_US1YAAAAA:c8f1WATuA-Dwx1uxxeACcZR_mi1zsmTGr4PDeMFX9MB4im2yST_L4FI3oqYLgEYWHIW1jg8LyMbIxGHg)**] A social choice function satisfying *unrestricted domain*, *unanimity* and *neutrality* is *self-selective* if and only if it is dictatorial.

**Can you please direct me to other results in social choice theory that uniquely characterise dictatorships?**

**Tags:** microeconomics, reference-request, theory, soft-question, social-choice

> **Comments:**
> **username_1**: I am not sure whether this answers your questions so leaving this as a comment, but you can refer to Prof. Arunava Sen's notes on social choice theory. https://www.isid.ac.in/~asen/scdoc/lecarrow_2017.pdf  These notes contains a lot of the major results in social choice, so they might have the sort of results you're seeking.  
> **username_0**: Thank you very much for your comment: these notes are very nice and contain one result I wasn’t aware of (**namely, that unrestricted domain, Maskin monotonicity and unanimity imply dictatorship**). I also saw that the Gibbard & Satterthwaite Theorem is stated in terms of unanimity, unrestricted domain and strategy-proofness. While I see Satterthwaite used unanimity in his paper, I can’t see it in Gibbard’s.  

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## 0 answers

