Questions tagged [social-choice]

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6 votes
0 answers
215 views

Recursive runoff voting schemes

Background: I will below describe a generalization of the following voting systems (what is meant by “voting system” will be defined formally below) which are occasionally used in the real world: “...
  • 23.9k
2 votes
1 answer
175 views

Is there a version of Arrow's theorem without unrestricted domain?

To recall Arrow's theorem: Suppose we have a finite set $X$ of voters and a finite set $Y$ of candidates. An election is a map $\phi: X \rightarrow T$ where $T$ is the space of total orderings of $Y$. ...
  • 3,934
4 votes
0 answers
215 views

Necessary and sufficient conditions for affine maps to coincide on their respective domains

Let $\mathcal{A}$ be a set of convex subsets of $\mathbb{R}^n$ and for each $A\in\mathcal{A}$ let there be an affine linear map $f_A\colon \mathbb{R}^n\rightarrow\mathbb{R}$. Moreover, assume that for ...
19 votes
3 answers
1k views

What is the fairest order for stage-striking (and is it the Thue-Morse sequence)?

Here's a fair-sequencing problem that doesn't quite match the usual fair-division problems. I think that, like those, the answer should also be the Thue-Morse sequence ("balanced alternation"), ...
  • 2,535
2 votes
0 answers
1k views

The Rise and Fall of Dictators & How it Depends on Our Choice

This question is loosely inspired by the following paper of Shelah on Arrow property in which he answered a question of Gil Kalai affirmatively. Shelah, Saharon, On the Arrow property. Adv. in Appl. ...
38 votes
8 answers
3k views

Is there a truly general voting impossibility theorem that applies to real elections?

The purpose of most political elections is to select from the set of candidates a predetermined number $n$ of successful candidates. (Often $n = 1$.) In brief, my question is: Has it been proved ...
  • 26.1k
1 vote
2 answers
472 views

What does Arrow's theorem say about Kaldor-Hicks social welfare functions with von Neumann-Morgenstern utility? [closed]

Let $A$ be the set of all possible states of the world, let $G(A)$ be the set of all "lotteries" or "gambles", i.e. the set of all probability distributions over $A$. Now consider an individual with ...
4 votes
2 answers
9k views

Seeking a solution algorithm to the 3-partition problem

I need to divide 48 pieces of jewelry between 3 inheritors so as to give equal, or nearly equal value, to each. I have learned that this is called the 3-partition problem. I solved it for 9 pieces of ...
2 votes
0 answers
191 views

Forcing the existence of a Condorcet Winner

Suppose that there is an election with three candidate and an infinite number of voters whose opinion lie in a two-dimensional issue space according to some distribution, and that voter's candidate ...
8 votes
3 answers
1k views

Mathematicians working on social choice theory

Can someone tell me which mathematicians are actively working on social choice theory, or point to a place where they may be listed?