For questions regarding the formal analysis of collective decision problems.
Questions tagged [social-choice-theory]
72 questions
3
votes
1 answer
How do I interpret the social choice function noted by Felix Brandt?
How do I read this:
Let $\mathscr{U}$ be a universe of alternatives
Let $\mathcal{F}(\mathscr{U}):\forall\mathscr{A}\in\mathcal{F}(\mathscr{U}),\mathscr{A}\subseteq\mathscr{P}_{\geq1}(\mathscr{U})$
A choice function is a function…
John Moser
- 193
- 4
1
vote
1 answer
Properties of rules of preference
I am working on aggregation of preferences and something is unclear concerning one property of rules of preference namely the monotonicity.
A $\mathcal{W}$ rule of preference is a function $F$ from $\Pi=W(A)^{N}$ to $W(A)$ where $W(A)$ is a set of…
coboy
- 1,339
1
vote
0 answers
Theory of social choice - relation of preference
Let $X =\{ a,b,c,d\}$ be a set a of possible choices. Define a relation of preference $R$ which generates a rule of choice $C'$ such that it generates another relation $R'$ which is different from $R$ (or prove it's impossible).
I would be very…
Pasato
- 269
1
vote
1 answer
Arrow's Impossibility Theorem: example function
I am looking for a social welfare function which satisfies "unrestricted domain", "Pareto efficiency", and "independence of irrelevant alternatives". One of the known proofs for Arrow's theorem argues by assuming the existance of such a function and…
Andreas T
- 197
1
vote
1 answer
Can a Condorcet winner be generally dispreferred on an individual basis?
Suppose that a Condorcet winner exists in an election. Certainly it is possible that an individual voter prefers some other candidates to the Condorcet winner. They might even prefer most, or all, other candidates to the Condorcet winner.
But what…
Colin P. Hill
- 155
0
votes
1 answer
Arrow's impossibility theorem and the independence of irrelevant alternatives
I have a question about the axiom of independence of irrelevant alternatives (IIA). According to the Wikipedia page on IIA, Arrow's formulation of IIA is as in here. I do not quite get this. In particular, what does $R_i \cap \{x,y\}^2$ mean? $R_i$…
Calculon
- 5,725
0
votes
1 answer
Checking choice correspondence satisfy Weak Axiom of Revealed Preferences
I have a question whether the below choice correspondence satisfies WARP or not. I know how to check a choice satisfies WARP when set X is in he form of X={x,y,z} however i cannot figure out when it is in the form given below. Can you help me?
By…
D.S
- 13
0
votes
1 answer
Rational Fuctions, Choice Correspondence, Utility, Path Independence
I'm trying to prove that path independence implies that Sen's alpha holds. Can someone guide me on how i can approach this proof?
Specifically Sen's alpha essentially states, that if for a choice function, I am the champion of the world, then I…
