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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Preference aggregation rules that satisfy the property that the most frequent best alternative is the collective best alternative?

Let $X$ be the set of alternatives, and $(R_i)_{i\in N}$ a profile of partial orders for $n= \#N$ individuals. I make the assumption that those partial orders are so that they all give rise to one ...
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Arrow’s Impossibility Theorem Proof - Unicity of "dictator"

I have a hard time understanding completely Arrow’s Impossibility Theorem proof, even the very pedagogical one by Geanakoplos, that can be found for instance here : https://users.ssc.wisc.edu/~dquint/...
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Can you prove a social choice function satisfies non-dictatorship using an example?

My question is whether using an example is enough to show that a social choice function satisfies the non-dictatorship property. There are 3 alternatives ($a,b,c$) and 5 individuals ($1,2,3,4,5$). ...
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A question in social choice and preference aggregation

Let $I = \{1, 2, 3\}$ denote the set of individuals and $X = [a, b]\subset \mathbb{R}^+$ with $a, b \in \mathbb{R}^+$ and $a < b$, be the set of alternatives. For each $i\in I$ and some $p_i\in X$ ...
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Why is the preference relation based on the pareto criterion used as the social choice rule not complete?

Let $\mathbb{R}$ be the set of all possible preference relations. Let $\mathbb{R}^n=\{(R_1,\dots,R_n)|R_i \in \mathbb{R} \}$ be the set of all possible profiles. A social choice rule (SCR) is a ...
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Does a social preference relation with unrestricted domain have to necessarily be complete?

I understand that the social preference relation need not be an ordering. But is it also not necessary that it be complete? I have read conflicting viewpoints on this. We haven't been taught what the ...
thecountofmontecristo's user avatar
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Who is a personal computer buyer in 80s?

There are many materials devoted to the rise of the personal computer industry. Some of them focus on technic aspects. Like "IBM PC was cheap and has open arcitecture. So it won Atari, Commodore ...
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How do I derive a SWF from mean income and an inequality index?

If one makes welfarist assumptions about the general good, and further assumes that SWFs can be fully characterized by the mean income and an inequality index, then it is possible to recover the ...
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Choice Theory Book Reccomendations

I am a post-graduate economics student in India, currently taking a core course in Choice Theory. Unfortunately, there is no standardized text which we are following for the course. The course ...
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What does the empirical literature tell us about the relative merits of alternative functional forms describing the marginal utility of income?

Among the various functional forms that have been used on model the marginal utility of income in, e.g., in making decisions under uncertainty, and perhaps intertemporal choice as well, is the ...
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McKelvey-Schofield Chaos Theorem Without Agenda Setter

The McKelvey-Schofield Chaos Theorem states that in a multidimensional preference space, it is almost always possible to reverse engineer the implementation of your desired policy by constructing an ...
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White Flight from Asian Immigration: Evidence from California Public Schools - is the methodology robust?

White Flight from Asian Immigration: Evidence from California Public Schools https://www.nber.org/papers/w31434 suggests that "as Asian students arrive, white student enrollment declines in ...
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Truthful assignment for facility allocation problems

We have the following congestion game. $n$ agents and $m$ facilities are positioned on the real line $\mathbb{R}$. The position of agent $i$ is denoted by $x_i\in \mathbb{R}$ and the location of ...
Mengfan Ma's user avatar
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What does social/public-choice theory have to say about plural v. unitary executive?

There are many state-level offices in the US that are elected by the people other than the legislature and the Governor, in the executive (Treasurer, Controller, Attorney General, Secretary, oil & ...
TheReal_Skywalker's user avatar
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Possibilities in social choice: number of possible collective decision function?

I know many papers about showing the existence (or the impossibility) of a social choice rule satisfying a set of properties. However, I was wondering whether there were some references trying to ...
MiKiDe's user avatar
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Arrow's Dictator

Arrow's Impossibility Theorem is often presented as a negative result in graduate classes. I wonder if the 'dictator' is taken too literally. If the assumptions of the theorem hold, there exists an ...
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What social aggregators are complete?

I am reading Eliaz (2004) for a general treatment of social-choice impossibilities. I am confused by the fact that it seems that we should get completeness even in situations where we should not have ...
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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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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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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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Question about Social Welfare Function and Social Profile

What are the meanings of a social welfare function and social profile? How are they related?
Satish Rao's user avatar
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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 ...
Hustler885's user avatar
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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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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 $\...
decisionsdecisions's user avatar
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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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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 ...
Ishan Kashyap Hazarika's user avatar
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2 answers
169 views

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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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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1 answer
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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 ...
Nikelmouse Dylar's user avatar
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1 answer
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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?
Maths's user avatar
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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. ...
Nikelmouse Dylar's user avatar
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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 ...
PhysicsEnthu's user avatar
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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 ...
andrewH's user avatar
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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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2 votes
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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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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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5 votes
3 answers
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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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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 ...
Nikelmouse Dylar's user avatar
1 vote
0 answers
51 views

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 ...
Jorge's user avatar
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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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3 votes
1 answer
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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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