5
votes
Accepted
gibbard-satterthwaite theorem and median voting
Gibbard and Satterthwaite insist that the social choice function must be defined over all rational preferences over outcomes. That is, if voters' preferences could be anything (subject to the ...
- 2,156
4
votes
If GOOG shares confer no voting rights, where do their value comes from?
The share value comes from expected discounted cash flows – either from dividends or from share price increases. These can be used for financing consumption from which people derive utility. See ...
- 2,611
3
votes
Accepted
Uncovered set versus top cycle set (voting theory)
This example comes from Miller (1980) (the paper that introduced the uncovered set definition).
Suppose that the majority's preference is defined by:
\begin{aligned}
x \succ y \\
x \succ z \\
y \...
- 353
3
votes
Accepted
Majority Rule and Single Peakedness
Suppose that A={a,b,c,....,z} is a finite set of social alternatives, and let P={>1,>2,....,>N} be a profile of strict preference orders on $A$ (where the set {1,2,...,N} indexes the voters). ...
- 812
2
votes
Accepted
Weighted voting: Vote of representative weighted by number of election votes
You ask an excellent question, as it has been partly but not fully discussed in the scientific literature.
Your exact proposal (weighting representatives by the amount of votes they got in the ...
- 36
2
votes
Accepted
Ranked choice preference with ties - Arrow's Impossibility Theorem
Allowing indifference will not solve the problem of the effect of the independence of irrelevant alternatives (combined with the unanimity and transitivity requirements).
You have said $b >_1 c$ ...
- 4,775
2
votes
Curious definition of ordering in Gibbard's "Manipulation of Voting Schemes: A General Result"
Note that next he defines $x R y$ as $\neg y P x$. If we take the contrapositive of (1b), we get:
$$
(\neg x P y \wedge \neg y P z ) \to \neg x P z,
$$
which then translates to the usual transitivity ...
- 12.8k
2
votes
Arrow’s Impossibility Theorem Proof - Unicity of "dictator"
There cannot be two dictators over all alternatives, what would happen if one wanted alternative 1 and the other alternative 2? So if they prove that Bob is a dictator, they have proven that Bob is ...
- 29.7k
1
vote
(Game Theory) Why is voting for your worst alternative a weakly dominated action?
To see that voting $C$ for a type $A$ voter is weakly dominated you need to find a strategy that results in a weakly better outcome irrespective of the behavior of the other voters. Voting $A$ would ...
1
vote
Part of proof of Gibbard-Satterthwaite Theorem
I solved it; here's my solution:
Let $f:L^n\to A$ be an incentive compatible, non-dictatorial social choice function and let $F:L^n\to L$ be its extension. To show that $F$ is non-dictatorial, then ...
- 51
1
vote
Accepted
Question about the "No Dictator" Criterion in Arrow's Impossibility Theorem
Arrow's Theorem concerns a social preference function ---that is, a function that produces a group preference order for every possible profile of individual preferences. The axioms "Nondictatorship", ...
- 812
1
vote
Weighted voting: Vote of representative weighted by number of election votes
The following recent article might be relevant to your question:
Weighted representative democracy, Marcus Pivato and Arnold Soh, Journal of Mathematical Economics 88, pp.52-63, 2020.
Abstract: We ...
- 812
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