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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 Economics I Learned from Online Dating that covers some of this ground, including the paper linked above. Another theoretical paper suggests that costly signals ...

11

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 question. Imagine that we live in a world with three people: Person 1, Person 2, and Person 3. Each of these people have preferences over three outcomes $x$, $y$, and ...

9

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: Handbook of Social Choice and Welfare By A. Sen, Kotaro Suzumura Handbook of Social Choice and Voting by Jac C. Heckelman, Nicholas R. Miller Handbook of ...

7

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 Alliprantis and Border. They contain most (if not all) results on convex analysis and functional analysis used by economists.

7

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 assumption is still that the underlying graph is bipartite (and that preferences are transitive). If we allow for members of a given type to propose to each ...

6

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 profiles is the Cartesian product $$\mathcal{P}^n = \times_{i=1}^{n} \mathcal{P}.$$ Let us denote the preference ordering $$a_1 \succ a_2 \succ ... \succ a_k$$ ...

6

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 opinion should be accepted by the whole at the same measure, as number of issues goes to infinity. In other words, current observed acceptance rate should be a ...

6

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 $\succeq$ so that $x\succeq y$ exactly if either $|x|<|y|$ or $|x|=|y|$ and $x\leq y$. Basically, the closer to the peak of $0$ a number is, the better, and in case of ...

5

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 the assumption that every social ranking is possible, one obtains a generalization in which every SCG corresponds to a dictatorship or an anti-dictatorship in ...

5

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 understand the general concepts of open source and how it works. To start of, I would like to say that open source does not mean that you cannot make money on ...

5

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 N, the kth positional dictatorship SWF orders social alternatives in terms of the preferences of the "kth best off" agent. Formally, given any social ...

5

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, $m=2$ and $n=3$. Then $$(\mathbb{R}^m\big)^n=(\mathbb{R}^m\big)^n$$ =\big(\mathbb{R}^2\big)^3=\Big\{\big((x_1,x_2),(x_3,x_4),(x_5,x_6)\big)\mid (x_1,x_2)\in\...

5

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 "benevolent social planner" who makes decisions for the society). Let $X$ be some space of "social outcomes". (Social outcomes could be anything. But ...

4

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: Interdisciplinary and Applied Perhaps one problem is that several assumptions should be addressed, like: Why shouldn't we date many partners in the first place? (so ...

4

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 constraint of completeness and transitivity), then we have the Gibbard–Satterthwaite theorem. On the other hand, if preferences were single-peaked, then the ...

4

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. Indeed, it does not. Independence off irrelevant alternatives is actually the only property that is violated. Here are two profiles, only the preferences of the ...

4

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 arguments of the outcome function are strategies of the players, which are observable, not their preference parameters, which, although indirectly determine the players'...

4

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 $s \in S := \times S_i$. In a direct mechanism, players are simply asked to report their type. Hence, every player $i$ must have a strategy that corresponds to "I am type $... 4 Let$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$has at least one maximum under this relation. A social choice function maps profiles of preference orderings to elements of$X$. Now let$P$be a profile of preferences,$f$a social decision function,... 4 Independence of irrelevant alternatives prevents you from using the information needed to implement a Rawlsian SWF; the information who is society's worst-off cannot be used. Indeed, the relevant information is not even specified in a profile of preferences. 3 You are correct that it is not possible to violate Weak Pareto and Nondictatorship at the same time. But your explanation (second paragraph) is a bit muddled. Here is how I would put it. To prove, "it is not possible to violate Weak Pareto and Nondictatorship at the same time", it suffices to prove: "Any Dictatorship satisfies Weak Pareto." To prove ... 3 First, let me state that this is a beautiful problem! Here is a proof that$n=4$. To prove that$n \leq 4$, consider the following example:$m+4$voters have preference$a \succ d \succ b \succ cm+3$voters have preference$b \succ d \succ c \succ am+2$voters have preference$c \succ d \succ b \succ am$voters have preference$d \succ c \succ a \...

3

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 an impartial SWF, one only looks at the profile of utilities, not who those utilities are associated with. Consider the following two cases: \begin{array}{ccc} ...

3

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 lone piece of dessert. Depending on what you'd accept for "concrete example", Abraham and Lot use this method to divide the land of Canaan. A two-stage fair ...

3

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 of those around them than it does on their absolute level of material wellbeing. If two people share salary information then it will generally be true that one ...

3

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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 mentioned in other answers expected utility is not equipped to handle uncertainty because it deals with taking expectations and expectations cannot be computed when ...

3

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 election) has been discussed on a blog post (in french) by Jean-François Laslier see here. In practice, representatives are often elected on a geographical basis, ...

3

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). We say that the profile P is single-peaked if there is some way to order the alternatives in A (e.g. in alphabetical order) such that, for each of the ...

3

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 society's preferences by $\succ^*$. If the individual rankings are: 1: A $\succ$ B $\succ$ C $\succ$ D 2: B $\succ$ D $\succ$ A $\succ$ C, then B $\succ^*$ A. ...

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