# Tag Info

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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 ...
• 1,105
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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 ...
• 1,573
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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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### 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 ...
• 3,202
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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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### 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 ...
• 26.6k
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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 ...
• 31.9k
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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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### 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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### 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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### 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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• 5,090
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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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### 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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