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 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 ...
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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 & ...
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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 ...
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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?
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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 ...
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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 $\...
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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 ...
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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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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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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 ...
user17900
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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 ...
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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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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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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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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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