Questions tagged [social-choice]

The study of how groups of people should make collective decisions. This can involve voting, bargaining, the application of some protocol (e.g. to fairly divide goods), or maximizing some measure of social welfare.

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What does social choice theory say about how to assign different positions to every member in a committee?

Consider the following setting: A committee has $N$ members. There are $m$ types of positions in the committee. For each type of positions $1 \leq i \leq m$, there are $n_i$ identitical positions for ...
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103 views

Definition of direct revelation mechanism

In Algorithmic Game Theory by Noam Nisan, a (general) mechanism for $n$ player is defined as $$ M=(\{T_i\},\{X_i\},A,\{v_i\},a,\{p_i\}),\tag1 $$ where $T_1,\dots,T_n$ are the players' type spaces (...
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53 views

Part of proof of Gibbard-Satterthwaite Theorem

I'm currently working through Nisan's Algorithmic Game Theory, Chapter 9 (Introduction to Mechanism Design). A part of the proof for the Gibbard-Satterthwaite Theorem is given as "obvious," ...
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How *do* NGOs, think tanks, and governments weigh income/consumption tradeoffs/transfers at different income levels?

In considering policies and transfers, how do we (economists, NGOs, governments & think tanks) weigh income (consumption) tradeoffs between the poor & the very poor? E.g., 'is giving 100 USD/...
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Comparing voting methods when there are only two voters

Consider the Schulze, Kemeny-Young, Ranked Pairs and Borda count voting methods. (The last is obviously the odd one out in this list!) Suppose that there are only two voters. Each voter gives a ...
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Axiom of Minimal Liberalism & Sen's Theorem of Paretial Liberal

Suppose that a person believes that all humans are guaranteed a set of rights that cannot be taken from them in any situation or circumstance (for example, the right to marry a person of your choice, ...
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184 views

Question about Social Welfare Function and Social Profile

What are the meanings of a social welfare function and social profile? How are they related?
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106 views

Rawlsian SWF and Arrow Impossibilty Theorem

given Arrow impossibility theorem the only social welfare function that satisfies unrestricted domain, pareto and the independence of irrelevant alternatives is Dictatorship. However I was wondering ...
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Is $(\mathbb{R}^m)^n$ the real coordinate space of dimension $m\cdot n$?

Very simple question here: say that there are n individuals and each individual $i\leq n$ has a consumption bundle $x_i\in \mathbb{R}^m$ (i.e. there are $m$ types of goods). Suppose that social ...
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84 views

Utility representation of single peaked preferences

Is it true that a single-peaked preference (with the peak at some finite point) over the set of real numbers, always has a utility representation ?? If yes, can you please hint towards the proof or ...
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Doesn't the Pareto-extension rule invalidate Eliaz's (2004) unified theorem of social choice?

Eliaz (2004) uses social aggregators to provide a unique "meta-theorem" from which Arrow and Gibbard-Satterthwaite follow as corollaries. He defines social aggregators as follows. Let $\...
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Difference between social choice functions and social decision functions?

A social decision function (SDF) à la Sen (1970) is defined as a collective choice rule whose range is restricted to social preference relations which generate a choice function. From Gaertner (2009), ...
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489 views

Good books to learn social choice theory

I wanted to learn Social Choice Theory and have fine mathematical background. I have read about it as a part of advanced microeconomics (Jehle and Rene)- Arrow's Impossibility Theorem etc. and got ...
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Arrow’s impossibility theorem and voting schemes

Arrow’s impossibility theorem states that there is no procedure for aggregating individual preference orderings into a collective preference ordering that satisfies certain apparently desirable axioms....
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Is single-peaked preferences necessary for majority rule to be transitive and yield non-empty choice set?

I understand that when individuals have single-peaked preferences, majority rule will be transitive and the choice set will be non-empty. So single peaked preferences is a sufficient condition. Is it ...
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209 views

Example of social choice rule that does not satisly the unrestricted domain condition [closed]

Can any social choice rule that is not complete said to be violating the unrestricted domain condition? Could you provide an example of SCR other than Pareto dominance that is not complete or violates ...
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Direct revelation mechanism's sets of strategies and types

Mas-Colell, Whinston and Green in Microeconomic Theory describe the direct revelation mechanism as it follows: The employed notation is the following: $θ_i$: Player i's type $Θ_i$: Set of types for ...
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Difference between social choice function and mechanism outcome function

Mas-Colell, Whinston and Green's Microeconomic Theory (3rd edition) defines the social choice function as the following: Later, the mechanism outcome function is also defined: The relationship ...
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Do any social welfare functionals, other than maximin, meet all of Arrow's conditions plus invariance regarding ordinal level comparability?

In the literature on social welfare functionals, the only example I've seen of a functional which meets all of Arrow's conditions–––or at least utility analogues of Arrow's conditions–––plus ...
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Arrows Theorem: Dictatorship

How does Arrow's Impossible Theorem show that the only aggregation rule that works is Dictatorship. Couldn't we have a Non-dictatorship with IIA or a Non-Dictatorship with Pareto Efficiency?
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If an ordinal-scaled utility function is defined via strictly increasing transformation, how can it represent a case of indifference?

Problem: According to Wulf Gaertner’s (2009, p. 13) A Primer in Social Choice Theory, any strictly increasing transformation of an individual’s ordinal utility function is informationally equivalent. ...
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Meltzer-Richard Model and Single Peaked Preferences

How does the Meltzer-Richard model provide a valid justification for single peaked preferences? It has something to do with the Envelope Theorem and showing that the middle class' preferences over ...
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Feasible approaches to allocate n unique indivisable items among n individuals

Suppose I have n individuals and n unique, indivisible objects of potential value. I want to allocate those objects so as to make total welfare as great as possible, subject to the constraint that no ...
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Question on Finding the Correct Emission Tax $t$

Let there be two companies $U_{1}$ and $U_{2}$ where, initially $U_{1}$ produces and sells $x$ units at $p=18$. Production costs are $C_{U_{1}}(x)=\frac{1}{6}x^3$ and in the process $a$ units of ...
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Majority Rule and Single Peakedness

Majority Rule will induce non empty choice set if individual preferences are single peaked Is this statement true? I have some trouble in understanding the meaning of 'single peakedness' in context ...
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Question about the "No Dictator" Criterion in Arrow's Impossibility Theorem

I have a question about Arrow's impossibility theorem. I'm not sure I understand exactly what is meant by the "no dictator" criterion. Does the presence of a "dictator" mean that across all possible ...
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137 views

Unrestricted domain vs complete

Arrow's impossibility theorem states that no social choice rule satisfies a certain list of desiderata. Amongst these are completeness and unrestricted domain. Could someone please explain the ...
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Weighted voting: Vote of representative weighted by number of election votes

I was wondering if there is any literature on voting systems where voters elect representatives, and in the representatives' assembly the vote of each representative is weighted by the number of votes ...
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160 views

Is a social choice aggregation rule defined for a set of weightings over the set of voters (N)?

In Christian List's Stanford Encyclopaedia entry Social Choice Theory (2013, https://plato.stanford.edu/entries/social-choice) he says that: "an aggregation rule is defined for a fixed set of ...
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Is quadratic voting efficient in multiple winner elections?

Quadratic voting approximates efficiency for a large collective making a sequence of binary decisions. What if a group can take multiple actions? Say, for example, a series of decisions where 2 out of ...
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What is the best example social norm effect economy?

Here is my example. I read the paper called "Social norms and Energy Conservation" (2010) by Hunt Allcott, about the energy conservation of households by providing them with the amount of energy ...
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Social conflicts in economic growth models

I'm highly interested in theories and models which explain how do social conflicts influence economic growth. What papers on the topic can you recommend? I was searching for some seminal and most ...
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Which of Arrow's four desirable properties' is violated in this scenario?

So the scenario is as follows: there are 3 agents and 4 alternatives, $a,b,c,$ and $d$. Society's ranking of the 4 alternatives is such that the highest-ranked alternative is agent 1's highest-...
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Anonymity in social welfare function

Currently reading David Adler's text on distributional weights in benefit-cost analysis (https://scholarship.law.duke.edu/faculty_scholarship/3110/), I cannot manage to fully grasp the definition of ...
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418 views

What is the economic incentive to cheat? How does an experiment capture exogenous deviations?

In my undergraduate career an economic experiment was conducted on my class: one class was the control two classes were the experimental (I was in an experimental class) The basic premise was a ...
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Social choice theory

Is it possible for a social choice rule to simultaneously violate the condition of non dictatorship and weak pareto property? Non dictatorship is when there is no individual such that if he prefers x ...
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289 views

Arrow's impossibility theorem

In social choice theory, Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem stating that when voters have three or more distinct alternatives ...
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107 views

gibbard-satterthwaite theorem and median voting

The gibbard-saterthwatie theorem states that a social choice function where truthfullness is a dominant strategy must be dictatorial. However, in a median voting system, with single peaked preferences ...
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Minimalist example of voter profiles yielding different outcomes

Let the set of alternatives be $\left\{a,b,c,d\right\}$. Let there be $n$ types of voter profiles, each type with a different strict ordering over the set of alternatives. The number of voters ...
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Sen's Liberal Paradox

Economist and philosopher Amartya Sen posited that no social system could guarantee: A minimal sense of freedom in social choice Pareto efficiency His original article can be found here. In his ...
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Social Choice: from Independence axiom to Mixture symmetry axiom

Harsanyi's Utilitarian theorems' has been criticized by Diamond Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utilities and others that, it is the morally unacceptable for ...
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Segal (2000) question about utility opportunity set

I am reading a JPE paper "Let's agree all dictatorship are equally bad" from Uzi Segal (2000). I have a small problem with this paper. We have the following Utility Opportunity Set (UOS): $$ S(w)=\{...
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Removing a degree of freedom from relative utilitarianism

Relative utilitarianism takes utilities as reported by agents, rescales them so that, for each agent, the alternatives have utility values between 0 and 1, and then chooses an alternative to maximize ...
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Gale-Shapley Follow-up Literature and General Questions

The Gale-Shapley Algorithm is a way of matchmaking between two different entities of people. It guarantees that every individual player is matched and that the matches are stable. What sort of ...
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What are good mathematics books to learn decision theory?

I am looking for a set of mathematics books to understand proofs in decision theory. Examples would be proofs of utility representations and social choice (im-)possibility results. I found many ...
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285 views

Nash social welfare function with negative exponential utilities

I got one question about the Nash-SWF. Typically it is defined as the product of individual utilities, ie. $$ NSWF:=u_1(x_1) \cdot u_2(x_2) \cdot u_3(x_3) \cdot ... $$ For this to make sense, ...
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Practical examples of fair division algorithms being used

Consider the problem of fairly sharing a homogeneous cake between two people. It is well-known that a fair division can be achieved through the divide and choose procedure: player 1 cuts the cake into ...
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Is there an economic reason why employees don't share salary information with each other?

In Western society, one's salary is often a taboo topic and people tend to not tell other people what they earn. In China by contrast, I have been told that asking one's salary is fairly normal ...
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Game theory for showing interest and availability when dating

The more cynical (or perhaps realistic) of us would argue that there's a fair amount of game theory going on in the dating game. For example a classic ploy is 'Don't ring for three days, because you ...
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Does vNM rationality depend on the good chosen?

The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...