Questions tagged [social-choice]
The study of how groups of people should make collective decisions. This can involve voting, bargaining, the application of some protocol (e.g. to fairly divide goods), or maximizing some measure of social welfare.
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What is the “Reinforcement Axiom” for a social choice function?
I recently came across this Computational Social Choice lecture note from Stanford, where an axiom for social choice functions called “Reinforcement” is introduced as a desirable axiom. I am trying to ...
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Question on neutral and stochastic voting rules of variable size
I have a question regarding neutral and stochastic voting rules with domain of variable size.
THE SETUP
Let $N=\{1,2\}$ be a two player set, let $A_\tau=\{a_1,\dots,a_\tau\}$ be a finite alternative ...
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Proof of the Gibbard-Satterthwaite theorem in Osborne and Rubinstein
I'm self-studying Osborne and Rubinstein's Models in Microeconomic Theory and I'm struggling to understand a step in their proof of the Gibbard-Satterthwaite theorem. I won't provide the full proof, ...
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Collections of axioms that imply monotonicity?
I am currently searching for collections of axioms that imply monotonicity.
Let $N$ be a finite set of players, let $A$ be a finite set of alternatives, let $\mathcal{P}$ be the set of all linear ...
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Are all subcorrespondences of the weak Pareto correspondence monotonic at the unrestricted domain of linear orders?
I have a doubt regarding the well-known concepts of weak Pareto optimality and monotonicity.
Let $N$ be a finite set of players, let $A$ be a finite set of alternatives, let $\mathcal{P}$ be the set ...
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Where does Arrow’s Impossibility Theorem standard proof rely on the existence of at least three alternatives?
I am trying to understand the proof of the world-famous Arrow’s Impossibility Theorem. To do that, I have been relying on Wikipedia’s proof by decisive coalition, as well as on the proof provided by ...
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Axiomatic characterisations of dictatorial social choice/welfare functions?
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 ...
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Preference aggregation rules that satisfy the property that the most frequent best alternative is the collective best alternative?
Let $X$ be the set of alternatives, and $(R_i)_{i\in N}$ a profile of partial orders for $n= \#N$ individuals. I make the assumption that those partial orders are so that they all give rise to one ...
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Arrow’s Impossibility Theorem Proof - Unicity of "dictator"
I have a hard time understanding completely Arrow’s Impossibility Theorem proof, even the very pedagogical one by Geanakoplos, that can be found for instance here : https://users.ssc.wisc.edu/~dquint/...
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Can you prove a social choice function satisfies non-dictatorship using an example?
My question is whether using an example is enough to show that a social choice function satisfies the non-dictatorship property.
There are 3 alternatives ($a,b,c$) and 5 individuals ($1,2,3,4,5$).
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A question in social choice and preference aggregation
Let $I = \{1, 2, 3\}$ denote the set of individuals and $X = [a, b]\subset \mathbb{R}^+$ with $a, b \in \mathbb{R}^+$ and $a < b$, be the set of alternatives. For each $i\in I$ and some $p_i\in X$ ...
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Why is the preference relation based on the pareto criterion used as the social choice rule not complete?
Let $\mathbb{R}$ be the set of all possible preference relations. Let $\mathbb{R}^n=\{(R_1,\dots,R_n)|R_i \in \mathbb{R} \}$ be the set of all possible profiles. A social choice rule (SCR) is a ...
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Does a social preference relation with unrestricted domain have to necessarily be complete?
I understand that the social preference relation need not be an ordering. But is it also not necessary that it be complete? I have read conflicting viewpoints on this.
We haven't been taught what the ...
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Who is a personal computer buyer in 80s?
There are many materials devoted to the rise of the personal computer industry. Some of them focus on technic aspects. Like "IBM PC was cheap and has open arcitecture. So it won Atari, Commodore ...
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How do I derive a SWF from mean income and an inequality index?
If one makes welfarist assumptions about the general good, and further assumes that SWFs can be fully characterized by the mean income and an inequality index, then it is possible to recover the ...
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