# Tag Info

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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: ...

### 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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### 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 $\succeq$ ...
• 13.3k
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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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### 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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### 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 ...
• 13.3k
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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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### 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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### 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 ...
• 13.3k
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### Arrow's Dictator

The object of Arrow's theorem are social welfare functions, which maps profiles of strict preference relations to to preference relations, $f:\mathcal{P}^n\to\mathcal{R}$. There are some variations in ...
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### White Flight from Asian Immigration: Evidence from California Public Schools - is the methodology robust?

is the methodology robust? They used panel fixed effects to control for unobservable and IV for potential reverse causality, which is decent methodology for their research question. They follow ...
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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). ...

### 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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### 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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### 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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### Rawlsian SWF and Arrow Impossibilty Theorem

Let's say there are individuals 1 and 2, and alternatives A, B, C, and D. Society uses the Rawlsian SWF and thus ranks alternatives according to their maximal rank within individuals' rankings. Denote ...
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### Axiom of Minimal Liberalism & Sen's Theorem of Paretial Liberal

Your question is a bit confused, because it mixes together several different things. For example, in the title, you mention Sen's Minimal Liberalism, but in the actual question, you don't mention Sen ...
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### Possibilities in social choice: number of possible collective decision function?

I can't think of any theorems which specifically focus on the number of social aggregation rules (of some type) satisfying axioms X, Y, and Z. However, aside from impossibility theorems, most of the ...

### White Flight from Asian Immigration: Evidence from California Public Schools - is the methodology robust?

Here's an analysis of that paper... Link to Marginal Revolution blog. A quote... However, I don’t think the headline result in this paper is particularly credible. First, there isn’t a well-...
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### Gale-Shapley Follow-up Literature and General Questions

This is a very old question but I just want to add a few notes not covered in ml0105's great answer. What sort of literature has been done building off of this? ... What sort of applications does the ...
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### What are good mathematics books to learn decision theory?

For decision theory: Gilboa, I. (2009). Theory of decision under uncertainty. Cambridge University Press. Parmigiani, G., & Inoue, L. (2009). Decision theory: Principles and approaches. John ...

### What are good mathematics books to learn decision theory?

Decisions with Multiple Objectives: Preferences and Value Tradeoffs by Ralph L Keeney

### How does GNU software development sustain economically?

Open-source software development is done for diverse reasons, but it's a common misunderstanding that it's done primarily by hobbyists or professionally but as a side-project. I'm answering this ...
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### Minimalist example of voter profiles yielding different outcomes

This is not mathematically rigorous but I believe the reasoning is correct. We assume that the allocation of votes between voter types is such that ties are not allowed, where it matters. Also, ...
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