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4 votes
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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 ...
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3 votes
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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 \...
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3 votes
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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). ...
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3 votes
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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 ...
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  • 46
3 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 ...
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2 votes
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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 $b >_1 c$ ...
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  • 4,694
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 ...
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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 ...
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  • 51
1 vote
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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", ...
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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 ...
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