Social Choice and Welfare Quiz

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Questions and Answers

What is a primary focus of the social choice theory discussed?

  • Collective decision-making and preferences (correct)
  • The economic impact of individual choices
  • How best to produce goods for society
  • Distribution of private wealth among individuals

Which of the following is NOT listed as a type of institution for making social decisions?

  • Public speaking forums (correct)
  • Voting systems
  • Delegation methods
  • Market-like institutions

What is the 'Fundamental Economic Problem (Normative version)' related to?

  • Making collective choices regarding production and distribution (correct)
  • Analyzing market demand for products
  • Maximizing individual profits
  • Allocating resources efficiently

In the context of social choices, which of the following statements is true?

<p>Policy preferences among individuals can often conflict. (D)</p> Signup and view all the answers

What is the goal when examining institutions in social choice?

<p>To assess and potentially improve decision-making institutions (A)</p> Signup and view all the answers

Which of the following examples is NOT related to social choices?

<p>Individual savings plans (A)</p> Signup and view all the answers

How does the chapter suggest approaching the study of social institutions?

<p>Using an institution-free approach starting from fundamental situations (C)</p> Signup and view all the answers

Which aspect is considered fundamental in discussions about social choice?

<p>The ways people express their policy preferences (C)</p> Signup and view all the answers

What does it mean for a social welfare function (SWF) to satisfy universal domain?

<p>It generates a social ranking for every preference profile. (D)</p> Signup and view all the answers

Why does majority voting fail to satisfy the universal domain criterion?

<p>It leads to the Condorcet paradox. (B)</p> Signup and view all the answers

What does a SWF need to satisfy in order to be considered to have the Pareto property?

<p>It must output a social ranking in cases where all prefer one alternative over another. (D)</p> Signup and view all the answers

In which context might it be reasonable to relax the universal domain requirement?

<p>In school choice scenarios. (D)</p> Signup and view all the answers

What characterizes a complete and transitive social ranking?

<p>Every alternative is ranked in relation to every other alternative. (C)</p> Signup and view all the answers

How can one determine whether a specific social welfare function satisfies universal domain?

<p>By constructing specific preference profiles and analyzing the outcomes. (A)</p> Signup and view all the answers

What is a potential consequence of failing to meet the Pareto property in a social welfare function?

<p>It may lead to dissatisfaction among individuals whose preferences are ignored. (D)</p> Signup and view all the answers

Which of the following best describes the role of normative reflection in examining social welfare functions?

<p>It helps in establishing the criteria for a good SWF. (B)</p> Signup and view all the answers

What is the least contentious principle identified for a social welfare function (SWF) to be desirable?

<p>Unanimity (C)</p> Signup and view all the answers

According to Sen's Impossibility Theorem, which combination of principles cannot be satisfied simultaneously?

<p>Unanimity, Liberalism, and Universal Domain (C)</p> Signup and view all the answers

What does Sen's principle of liberalism assert about individual preferences?

<p>They should determine societal rankings for alternatives. (D)</p> Signup and view all the answers

Which example best illustrates Sen's liberalism principle?

<p>Prude deciding whether to read a controversial book. (B)</p> Signup and view all the answers

In the context provided, what does 'richly specified state of society' refer to?

<p>Detailed socio-economic conditions. (C)</p> Signup and view all the answers

Which situation would lead to a decisive ranking according to Sen's liberalism for the alternatives a and b?

<p>The two alternatives only differ in a personal preference dimension. (C)</p> Signup and view all the answers

Which principle defines that an individual's preferences are only considered for alternatives they care about?

<p>Liberalism (A)</p> Signup and view all the answers

If Prude prefers c to a, what does this imply about the social ranking of these alternatives?

<p>The social ranking is c ≻∗ a. (A)</p> Signup and view all the answers

What does the Independence of Irrelevant Alternatives (IIA) state about social welfare functions (SWF)?

<p>The social ordering only depends on individual orderings of the alternatives. (D)</p> Signup and view all the answers

Under IIA, how should the SWF respond to two identical preference profiles concerning alternatives a and b?

<p>It should output the same ordering of a versus b. (B)</p> Signup and view all the answers

If two individuals have the same preference for alternatives a and b, what impact does this have on the SWF's output concerning those alternatives?

<p>The output will remain unchanged. (B)</p> Signup and view all the answers

Which statement best reflects a common misconception about IIA?

<p>IIA allows irrelevant alternatives to influence decisions. (A)</p> Signup and view all the answers

What key characteristic does a good SWF exhibit according to IIA?

<p>Consistency in the output when individual preferences relative to a pair are unchanged. (A)</p> Signup and view all the answers

In practical terms, IIA ensures that which aspect of voting or choice behavior remains unchanged?

<p>The comparison between the chosen alternatives. (A)</p> Signup and view all the answers

When applying IIA, what happens to the social ordering if preferences for unrelated alternatives shift?

<p>The social ordering remains unaffected. (D)</p> Signup and view all the answers

Which of the following illustrates the principle of IIA with the given SWF outcomes?

<p>The ranking between a and b remains unchanged despite preferences for c. (B)</p> Signup and view all the answers

What is the consequence of violating the IIA principle in a SWF?

<p>The reliability of the SWF is compromised. (C)</p> Signup and view all the answers

Why is the concept of IIA critical in social choice theory?

<p>It reinforces consistency in preference-based decisions. (A)</p> Signup and view all the answers

What is a defining characteristic of a dictatorship in the context of a social welfare function (SWF)?

<p>It always produces a social ranking based on an individual’s preferences. (C)</p> Signup and view all the answers

Which criterion indicates that a SWF should not lead to dictatorial outcomes?

<p>Non-Dictatorship (ND) (C)</p> Signup and view all the answers

What does the Borda Rule primarily involve?

<p>Summing the ranks given to each candidate across all voters. (C)</p> Signup and view all the answers

In the context of Arrow's Impossibility Theorem, what is required among alternatives considered?

<p>At least three alternatives must be present. (B)</p> Signup and view all the answers

Which statement about the social welfare function (SWF) is true?

<p>It ideally should satisfy more criteria than just UD, U, and IIA. (A)</p> Signup and view all the answers

What happens if all individuals prefer option 'a' over 'b' in a dictatorship?

<p>The dictator will also prefer 'a' over 'b' as per Unanimity. (A)</p> Signup and view all the answers

What is the primary function of the Independence of Irrelevant Alternatives (IIA) criterion?

<p>It states that social ordering of a pair only depends on preferences within that pair. (D)</p> Signup and view all the answers

What does the Borda score of a candidate reflect?

<p>The cumulative rank total from all individual rankings. (A)</p> Signup and view all the answers

Which condition does not apply to a dictatorship according to SWF criteria?

<p>It provides a fair representation of all individual preferences. (D)</p> Signup and view all the answers

In a social welfare function, the Unanimity (U) condition implies that:

<p>If all individuals prefer one option over another, it must be chosen. (A)</p> Signup and view all the answers

What main factors can influence strategic manipulation in algorithms?

<p>Type of decision procedures used (B), Context of application (C)</p> Signup and view all the answers

Which areas of application are highlighted as utilizing collective decision procedures?

<p>Social choice theory and welfare economics (A)</p> Signup and view all the answers

What role does empirical literature play in the understanding of school choice algorithms?

<p>It offers insights on the potential for manipulation (A)</p> Signup and view all the answers

What is a major theorem related to social choice mentioned in the content?

<p>Muller-Satterthwaite Theorem (D)</p> Signup and view all the answers

How does institutional design relate to mathematical algorithms?

<p>It influences the framework for algorithm creation (C)</p> Signup and view all the answers

What is the importance of social epistemology in the study of algorithms?

<p>It examines the social implications of decision-making procedures (A)</p> Signup and view all the answers

Which factor is considered a common issue with school allocation algorithms?

<p>Vulnerability to strategic manipulation (A)</p> Signup and view all the answers

What consequence can arise from the application of social choice theory in economic theory?

<p>Enhancement of systems for evaluating choices (C)</p> Signup and view all the answers

What is a potential research focus indicated by the content regarding algorithms?

<p>The empirical study of algorithm effectiveness in decision processes (C)</p> Signup and view all the answers

Which characteristic is NOT mentioned as a concern regarding the performance of algorithms?

<p>Speed of algorithm processing (B)</p> Signup and view all the answers

What does the proof by Reny (2000) primarily address?

<p>The foundational properties of social choice theory (B)</p> Signup and view all the answers

How might school choice algorithms impact social outcomes?

<p>By potentially disadvantaging certain groups (D)</p> Signup and view all the answers

What type of decision-making process might require the application of social choice theory?

<p>Collective or group decision-making (C)</p> Signup and view all the answers

Which assertion about the relationship between algorithms and economics is incorrect?

<p>Economic principles do not apply to algorithm evaluation (A)</p> Signup and view all the answers

Flashcards

Social Choice

The process by which groups of individuals make collective decisions about public policies.

Public Policies

Possible courses of action chosen by a society.

Group of People

Individuals involved in collective decision-making.

Economic Problem (Normative)

The question of how a society should organize itself to produce and distribute resources.

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Policy Preferences

Individuals' different viewpoints on public policies.

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Presidential Elections

Example of a social choice process.

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Referenda

Example of a social choice process using public votes.

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Market-like Institutions

Allocation methods similar to markets.

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Voting

A method for making social choices.

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Delegation

Assigning decision-making to a smaller group or individual.

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Universal Domain (UD)

A SWF satisfies UD if any combination of individual preferences results in a complete and transitive social ranking.

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Condorcet Paradox

An example showing that majority voting might not satisfy UD by not producing a clear social ranking.

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Pareto property/Unanimity

A SWF satisfies this if, when everyone prefers one alternative (a) to another (b), the social ranking also puts a above b.

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Social Welfare Function (SWF)

A function that takes individual preferences as input and produces a social ranking of alternatives.

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Complete Social Ranking

A ranking that orders all alternatives. Every pair of alternatives is compared and ranked.

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Transitive Social Ranking

A ranking where if a is preferred to b, and b is preferred to c, then a must be preferred to c.

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IIA

Independence of Irrelevant Alternatives; a social welfare function (SWF) satisfies IIA if the social ordering of two alternatives (e.g., a versus b) depends only on how individuals order those two alternatives, ignoring other options.

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Social Welfare Function (SWF)

A rule that aggregates individual preferences into a social preference ordering. It determines the best social choice given individual preferences.

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Preference Profile

A collection of individual preference orderings (e.g., rankings of alternatives) for a set of individuals.

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Social Ordering (of two alternatives)

The outcome of a SWF; which of the two alternatives is socially preferred (better) according to the SWF.

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Individual Preferences

An individual's ordering of different alternatives.

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Sen's Principle of Liberalism

Individual preferences should be decisive in matters concerning only themselves.

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Unanimity

A decision where everyone agrees on a particular choice.

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Universal Domain

A social choice function must be able to handle any possible distribution of individual preferences.

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Social Welfare Function (SWF)

A way to decide what society as a whole should do given individual preferences.

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Sen's Impossibility Theorem

There is no social welfare function that can satisfy Universal Domain, Unanimity and Liberalism simultaneously.

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Richly Specified Alternative

A detailed description of a possible state of society, covering many aspects.

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Lady Chatterley's Lover

A controversial book used as an example in Sen's argument about liberalism.

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School Allocation Algorithms

Methods used to assign students to schools.

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Strategic Manipulation (School Choice)

Students or parents deceptively altering their preferences to get a better school placement.

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Social Choice Theory

Study of collective decision-making procedures and their outcomes.

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Institutional Design

Creation and structuring of rules and guidelines of an organization.

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Welfare Economics

Study of economic policies and their possible benefits on society.

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Social Epistemology

Examines knowledge and belief formation within social contexts.

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Muller-Satterthwaite Theorem

Social choice result proving impossibility of fair and rational voting systems.

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Proof (Reny, 2000)

Mathematical demonstration of the Muller-Satterthwaite Theorem by Reny in 2000.

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Pivotal Voter

Voter whose choice can change the outcome of an election.

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Dictatorship (SWF)

A social welfare function (SWF) where one individual's preferences always determine the social ranking, regardless of others' preferences.

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Social Welfare Function (SWF)

A function that aggregates individual preferences to create a collective social ranking. It takes individual preferences and outputs a social ranking of alternatives.

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UD (in SWF)

The social preference ordering should respect individual preferences — if an individual prefers A to B, the social ordering must also prefer A to B.

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U (in SWF)

The social ranking must never worsen an individual's preference (monotonicity).

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IIA (in SWF)

The social ranking between two alternatives should not change if a third alternative is added or removed and the preferences of all individuals are unchanged for choices between the original two.

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ND (in SWF)

A social welfare function that is not a dictatorship.

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Borda Rule

A specific way to aggregate individual preferences, where each individual ranks candidates and candidates are ranked based on their summed rank.

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Arrow's Impossibility Theorem

A theorem demonstrating that it's impossible to create a social welfare function that satisfies all 4 criteria (UD, U, IIA, and ND) with more than two options.

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Alternative

A choice or option that can be evaluated or ranked.

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Study Notes

Social Choice and Welfare

  • Every human society faces the fundamental economic problem of how to organize to produce and distribute needed resources.
  • Social choices involve a group of people, a set of public policies (alternatives), and individual preferences for these policies.

Introduction

  • Key concern: how individual and social choices are organized.
  • Addresses fundamental economic problems regarding resource production and distribution.
  • Purpose is to understand how groups of individuals can/should make collective decisions.

Social Choices

  • Includes a group of people, a set of potential public policies, and the impact each policy has on all members of the group.
  • Individuals typically have differing preferences regarding the policies.

Many Examples

  • Presidential elections, referendums, public goods provision, school choice, and spectrum allocation fall under the umbrella of social choices. This applies to a wide array of situations impacting society.

Institutions

  • In liberal democracies, social choices are frequently made through market-like institutions, alternative allocation methods, voting systems, and delegation.
  • Market-like institutions, such as stock markets and fish markets, can handle resource allocation problems.
  • Alternative methods involve non-monetary approaches to allocation, like kidney exchanges or course allocation.
  • Voting systems, like presidential elections, are used for political decision-making.
  • Delegation mechanisms, such as those related to the Delta Works flood control project, are another method.

Formalizing the Problem

  • A social choice problem involves a group of individuals (indexed by i = 1,..., N), a set of possible choices (alternatives), individual preferences over these alternatives, and the aggregation of these preferences into a collective choice.

Our Working Example

  • A movie club needs to decide which movie to screen.
  • The club has three choices: Pulp Fiction, Inside Out, and Parasite.
  • The three members have specific preferences.
  • This example demonstrates a social choice problem in practice.

What are we assuming about people?

  • Individuals have complete and coherent preferences.
  • For any two alternatives, individuals can compare them and express a preference.
  • Preferences are complete and transitive (if an individual prefers A to B and B to C, then they prefer A to C).

Aggregating Preferences

  • How individual preferences are combined to form a collective preference is a crucial element in social choice theory.
  • Social welfare function (SWF) is a set of rules that takes individual preferences as input to produce a collective ranking of the options.

Voting

  • Common mechanism for preference aggregation.
  • Several voting systems exist (e.g., majority voting, plurality).

Majority Voting

  • A decision or candidate wins if they receive more than half of the votes.
  • Can lead to cycles/paradoxes if there are more than two alternatives.

Plurality

  • The candidate with the most votes wins, irrespective of the actual vote split.
  • Can also be problematic if there are more than two alternatives and votes are not spread evenly.

Arrow's Impossibility Theorem

  • Arrow's theorem asserts that no ranked voting system can satisfy all the desired criteria simultaneously if there are 3 or more alternatives in the absence of dictatorship.

Impossibility for Choices

  • Arrow's impossibility theorem indicates that finding a social welfare function (SWF) that satisfies all the desired properties (universal domain, Pareto efficiency, independence of irrelevant alternatives) and is not a dictatorship is impossible when there are three or more choices.

Dictatorship

  • In a dictatorship, the SWF always reflects the preferences of a single individual.

Sen's Critique

  • Sen argued that unanimity, a seemingly uncontroversial principle in social choice, can conflict with other values.
  • A society's decision regarding matters that are purely personal, e.g., an individual's sleeping position, should be made by the individual.
  • This exemplifies the tension between majority rule and individual preferences.

Conclusion

  • Social choice theory demonstrates complexities and limitations of social decision-making processes.
  • Finding optimal systems or procedures that satisfy diverse values and preferences is challenging.
  • Many considerations are crucial such as voter preferences, fairness, and the impact of institutions.

Strategy-Proof Voting Methods

  • Ideal method where individuals have incentive to express their true preferences.
  • Individual preferences are aggregated into a collective outcome.

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