14 votes
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Game theory for showing interest and availability when dating

Sending costly signals may work, at least when the recipient is less attractive than the sender. There's also a nice popular science book by Paul Oyer called Everything I Ever Needed to Know About ...
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  • 1,105
11 votes
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Condorcet's paradox: Is the majority rule transitive?

As you stated, transitivity is that overall $x \succeq y$ and $y \succeq z$ implies $x \succeq z$. I will show an example where majority rule isn't transitive and hopefully it will answer your ...
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  • 1,573
9 votes
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Good books to learn social choice theory

Start with: A primer in Social Choice Theory, by Wulf Gaertner. If you want more, have a look at: Welfare Economics and Social Choice Theory by Allan Feldman and Roberto Serrano To dig deeper: ...
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7 votes
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What are good mathematics books to learn decision theory?

I do not know about social choice, but for utility representations I think the two most cited books are "Convex analysis" by Rockafellar and "Infinite Dimensional Analysis: A Hitchhiker's Guide" by ...
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  • 3,202
7 votes
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Gale-Shapley Follow-up Literature and General Questions

How does social welfare change when the two entities do not have the same number of individuals in them, so that not everyone can be matched? The algorithm works fine in this case. The important ...
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  • 1,216
6 votes

Arrow's impossibility theorem

Let the set of alternatives be $A = \left\{a_1,a_2,...,a_k\right\}$. Let the number of players be $n$. Let the set of preference orderings over $A$ be $\mathcal{P}$. Then the set of preference ...
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  • 26.6k
6 votes
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Fair voting procedure when there are many issues

That's interesting: the flavor of the frequentist approach to probability used for a socio-political fairness criterion: if my measure as a population group is $0<p<1$, and known, then my ...
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6 votes
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Utility representation of single peaked preferences

No. Basically, you can encode a form of lexicographic preferences, probably the most familiar example of non-representable preferences, as single-peaked preferences on $\mathbb{R}$. Define $\succeq$ ...
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5 votes

Arrow's impossibility theorem

The Pareto criterion has two effects: It guarantees that every ranking can occur as a social ranking and it connects social rankings to individual rankings. If one drops the Pareto criterion but keeps ...
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5 votes

How does GNU software development sustain economically?

I would like to start by saying that I'm not a programmer and I have never contributed to any open source project. However, I have been interested in open source for a long time and I believe that I ...
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  • 340
5 votes
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Do any social welfare functionals, other than maximin, meet all of Arrow's conditions plus invariance regarding ordinal level comparability?

There are at least two other examples of SWFs that satisfy these conditions. The first is a positional dictatorship. Let N be the number of individuals (assume it is fixed). For any k between 1 and ...
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5 votes
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Is $(\mathbb{R}^m)^n$ the real coordinate space of dimension $m\cdot n$?

No. And yes. For any set $X$ we have (by definition) $$X^k=\underbrace{X\times\cdots\times X}_{k\text{-times}}=\{(x_1,x_2,\ldots,x_k)\mid x_i\in X\text{ for }i=1,\ldots,k\}.$$ Now let, for example, $m=...
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5 votes

Question about Social Welfare Function and Social Profile

In its most general formulation, a social welfare function is just a utility function representing the preferences of "society as a whole" (or the preferences of a hypothetical "...
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4 votes

Game theory for showing interest and availability when dating

In serious economics journals, no, as far as I know of. In other areas there has been done something, but it concerns availability and communication with God: The Journal of Psychology: ...
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4 votes

Question about the Ellsberg Paradox in Expected Utility Theory

The short answer seems to be yes your example violates expected utility... It mostly seems to me like a simple transformation of the first example you gave (but you got rid of the red balls). As ...
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  • 1,573
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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4 votes
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Which of Arrow's four desirable properties' is violated in this scenario?

Note that an alternative being highest-ranked by an agent involves comparisons with all other alternatives, which raises doubts that your method satisfies independence of irrelevant alternatives. ...
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4 votes
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Difference between social choice function and mechanism outcome function

A social choice function presumes the individuals' preference parameters $\theta_i$'s are observable, whereas in a mechanism, such knowledge is not presupposed. Therefore, in a mechanism, the ...
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  • 14.6k
4 votes
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Direct revelation mechanism's sets of strategies and types

In mechanism design you are free to choose the rules of the game. The designer can determine $(S, g)$, i.e., what players can do and what happens when players played some strategy profile $s \in S := \...
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  • 5,090
4 votes
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Difference between social choice functions and social decision functions?

Let $X$ be the set of alternatives. A social decision function maps profiles of preference orderings to relations on $X$ such that every nonempty subset of $X$ has at least one maximum under this ...
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4 votes

Rawlsian SWF and Arrow Impossibilty Theorem

Independence of irrelevant alternatives prevents you from using the information needed to implement a Rawlsian SWF; the information who is society's worst-off cannot be used. Indeed, the relevant ...
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3 votes

Social choice theory

You are correct that it is not possible to violate Weak Pareto and Nondictatorship at the same time. But your explanation (second paragraph) is a bit muddled. Here is how I would put it. To prove, "...
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3 votes

Minimalist example of voter profiles yielding different outcomes

First, let me state that this is a beautiful problem! Here is a proof that $n=4$. To prove that $n \leq 4$, consider the following example: $m+4$ voters have preference $a \succ d \succ b \succ c$ $...
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  • 3,202
3 votes
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Anonymity in social welfare function

Anonymous/impartial SWFs focus only on the pattern of well-being, and not the identities of the people who end up at particular well-being levels. Identities here simply means names. When applying ...
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  • 14.6k
3 votes
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Practical examples of fair division algorithms being used

The easiest generalization, of envy free sharing of a heterogeneous cake between two cake eaters is quite common. My family growing up frequently used the you divide and I choose method for sharing a ...
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  • 15.9k
3 votes

Is there an economic reason why employees don't share salary information with each other?

Two remarks: Firstly, there is some research on subjective wellbeing, where a common theme is that people's happiness seems to depend more on a relative comparison of their material wellbeing to that ...
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  • 16.6k
3 votes

Is there an economic reason why employees don't share salary information with each other?

dwjohnston, To answer your question briefly: no, because it is rather a social or psychological matter than it is an economic matter. There is already asked a good question about this subject in The ...
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3 votes

Question about the Ellsberg Paradox in Expected Utility Theory

"...one of the major challenges for expected-value theory is the Ellsberg Paradox." Hmm, but in what way? Elsberg paradox is not like other related paradoxes surrounding Expected Utility theory, (...
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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
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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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