For questions regarding the formal analysis of collective decision problems.

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Game Theory in relation to economics and sociology [closed]

I know some algebra and calculus, and have been reading about Linear Programming/Game Theory. How are the models in this field, even the infinite calculus models, usable in macro economics. Even ...
2
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1answer
46 views

Arrow's Impossibility Theorem Using Boolean Algebra

I am currently working on a research project which involves using Boolean matrices for the proof of Arrow's Impossibility Theorem and various other lemmas and results related to quasi ordered sets. In ...
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0answers
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Game Theory - Voting

In this setup there are 4 candidates running. For a candidate to be eliminated, the candidate needs to receive less than 1/3 of the votes when paired up with another candidate. This process ...
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1answer
33 views

Are the following two definitions of Borda winner equivalent?

The Borda count is a method used to determine the winner object where people rank objects. For instance, imagine each person ranking 3 objects. The highest ranked object gets 2 points, the second gets ...
2
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1answer
75 views

the proof of Arrow's Theorem

I read Philip J. Reny's paper (Arrow’s Theorem and the Gibbard-Satterthwaite Theorem: A Unified Approach) What I cannot understand is step 5 of the proof of arrow's theorem. I think figure 4 is a ...
3
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1answer
118 views

Arrow's Impossibility Theorem and Ultrafilters. References

I need some references (far away from Wikipedia) about the proof using Ultrafilters of Arrow's Impossibility Theorem. Online resources are preferred.
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1answer
148 views

Does risk aversion cause diminishing marginal utility, or vice versa?

Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. ...
2
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1answer
72 views

Counting in Arrow's theorem

I seem to be really confused with the counting system in Arrow's theorem. Can I have a simple explanation how they determine the outcome? I can't determine the outcome using rules from my notes. It ...
2
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2answers
99 views

Why not n=2 in Arrow's theorem

Why in the statement of Arrow's impossibility theorem we omit the case n=2? I will appreciate it if you can explain it in easy words. I'm by no means an expert in the area (I think it's very much ...
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2answers
193 views

Functions minimized at the median of their arguments

I am doing research on problems of location of a public facility on a network which lead me to the following question. Is there an interesting way to characterize the class of functions $f : ...
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2answers
230 views

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

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 ...
2
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1answer
215 views

How can a social welfare function be a linear combination of von Neumann-Morgenstern utility functions?

The von Neumann-Morgenstern axioms were an attempt to characterize rational decision-making in the presence of risk. The von Neumann-Morgenstern utility theorem says that if someone is vNM-rational, ...
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2answers
77 views

Decide the most favorable candidate

Consider an election voting process where people need to elect a representative among n number of candidates. Is there an approach to determine the most favorable option? Voting just a single person ...
3
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1answer
76 views

Stability under supremum of sets of social choice function with single peaked preferences

Here is a question emerging from reading Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35(4), 437–455. The setting is as follows: A non-empty finite set of ...
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1answer
96 views

Using limit argument with non-continuous social-choice functions

This question is related to another question of mine Invariance of strategy-proof social choice function when peaks are made close from solution, and it revolves around the use of limit arguments with ...
6
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1answer
122 views

Invariance of strategy-proof social choice function when peaks are made close from solution

A question emerging from reading Schummer, J., & Vohra, R. V. (2002). Strategy-proof Location on a Network. Journal of Economic Theory, 104(2), 405–428. The setting is as follows: A finite set ...
4
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2answers
106 views

Does Arrow's Theorem apply when choosing a single best candidate?

According to Wiki, Arrow's Impossibility Theorem proves that we cannot create a social welfare function that obeys unanimity, non-dictatorship, and IIA. However, in real elections, we want to choose ...
2
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1answer
124 views

What is the general formula for electoral districts tying.

I apologize if this question is a bit of a read. (You might want to get a frosty beverage.) Professor Alan Natapoff of MIT demonstrated, if 9 Voters are districted into 3 electoral districts of 3 ...
4
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1answer
494 views

Gibbard–Satterthwaite Theorem versus Arrow Theorem

Arrow Theorem is a very classical result in social choice theory, stating very roughly that any reasonable voting procedure is either dictatorial or subject to tactical voting. More precisely, there ...
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0answers
89 views

Can the Nash bargaining solution be applied in repeated game?

I am trying to develop a model involving two agents who interact strategically to set an optimal time for a joint work. These agents will have to meet repeatedly. I want to derive the optimal time for ...
8
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2answers
168 views

Is there a voting method with a sane strategy?

Is there a voting method where the best strategy for strategic voters can be explained in a sane way? According to Gibbard–Satterthwaite, there is no "strategy-free" (and reasonable) voting ...
7
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1answer
104 views

Does it make sense to run Meek STV with more choices than seats?

During the current batch of moderator elections at Gaming, it has been argued that since only 2 seats are up for grabs in this round of elections, it only makes sense to cast ballots by only ranking ...
3
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1answer
149 views

Bayesian analysis of the Venice Doge elections

Does anyone know of a Bayesian (or a classical) analysis of the Venetian Doge election system? I am looking mainly for chances of subversion, chances for a candidate to be elected at each stage, or ...
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1answer
81 views

$N\setminus S$ is not $\beta$-effective for $A\setminus B$, and $S$ is not $\beta$-effective for $B$

Given a social choice function $F$, a subset $B\subset A$ of the candidates and a coalition $S\subset N$ of the voters, $\beta$-effectiveness of $S$ for $B$ is equivalent to $N\setminus S$ not being ...
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0answers
114 views

Question on social choice functions

We showed in class that every strongly, exactly consistent s.c.f is strongly firm (I don't know if this is the right translation - we defined strong firmness as the equivalence of $*,\alpha,\beta$ ...