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?

Policy preferences among individuals can often conflict. Signup and view all the answers

What is the goal when examining institutions in social choice?

To assess and potentially improve decision-making institutions Signup and view all the answers

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

Individual savings plans Signup and view all the answers

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

Using an institution-free approach starting from fundamental situations Signup and view all the answers

Which aspect is considered fundamental in discussions about social choice?

The ways people express their policy preferences Signup and view all the answers

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

It generates a social ranking for every preference profile. Signup and view all the answers

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

It leads to the Condorcet paradox. Signup and view all the answers

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

It must output a social ranking in cases where all prefer one alternative over another. Signup and view all the answers

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

In school choice scenarios. Signup and view all the answers

What characterizes a complete and transitive social ranking?

Every alternative is ranked in relation to every other alternative. Signup and view all the answers

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

By constructing specific preference profiles and analyzing the outcomes. Signup and view all the answers

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

It may lead to dissatisfaction among individuals whose preferences are ignored. Signup and view all the answers

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

It helps in establishing the criteria for a good SWF. Signup and view all the answers

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

Unanimity Signup and view all the answers

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

Unanimity, Liberalism, and Universal Domain Signup and view all the answers

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

They should determine societal rankings for alternatives. Signup and view all the answers

Which example best illustrates Sen's liberalism principle?

Prude deciding whether to read a controversial book. Signup and view all the answers

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

Detailed socio-economic conditions. 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?

The two alternatives only differ in a personal preference dimension. Signup and view all the answers

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

Liberalism Signup and view all the answers

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

The social ranking is c ≻∗ a. Signup and view all the answers

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

The social ordering only depends on individual orderings of the alternatives. Signup and view all the answers

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

It should output the same ordering of a versus b. 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?

The output will remain unchanged. Signup and view all the answers

Which statement best reflects a common misconception about IIA?

IIA allows irrelevant alternatives to influence decisions. Signup and view all the answers

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

Consistency in the output when individual preferences relative to a pair are unchanged. Signup and view all the answers

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

The comparison between the chosen alternatives. Signup and view all the answers

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

The social ordering remains unaffected. Signup and view all the answers

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

The ranking between a and b remains unchanged despite preferences for c. Signup and view all the answers

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

The reliability of the SWF is compromised. Signup and view all the answers

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

It reinforces consistency in preference-based decisions. Signup and view all the answers

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

It always produces a social ranking based on an individual’s preferences. Signup and view all the answers

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

Non-Dictatorship (ND) Signup and view all the answers

What does the Borda Rule primarily involve?

Summing the ranks given to each candidate across all voters. Signup and view all the answers

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

At least three alternatives must be present. Signup and view all the answers

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

It ideally should satisfy more criteria than just UD, U, and IIA. Signup and view all the answers

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

The dictator will also prefer 'a' over 'b' as per Unanimity. Signup and view all the answers

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

It states that social ordering of a pair only depends on preferences within that pair. Signup and view all the answers

What does the Borda score of a candidate reflect?

The cumulative rank total from all individual rankings. Signup and view all the answers

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

It provides a fair representation of all individual preferences. Signup and view all the answers

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

If all individuals prefer one option over another, it must be chosen. Signup and view all the answers

What main factors can influence strategic manipulation in algorithms?

Type of decision procedures used Signup and view all the answers

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

Social choice theory and welfare economics Signup and view all the answers

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

It offers insights on the potential for manipulation Signup and view all the answers

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

Muller-Satterthwaite Theorem Signup and view all the answers

How does institutional design relate to mathematical algorithms?

It influences the framework for algorithm creation Signup and view all the answers

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

It examines the social implications of decision-making procedures Signup and view all the answers

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

Vulnerability to strategic manipulation Signup and view all the answers

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

Enhancement of systems for evaluating choices Signup and view all the answers

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

The empirical study of algorithm effectiveness in decision processes Signup and view all the answers

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

Speed of algorithm processing Signup and view all the answers

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

The foundational properties of social choice theory Signup and view all the answers

How might school choice algorithms impact social outcomes?

By potentially disadvantaging certain groups Signup and view all the answers

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

Collective or group decision-making Signup and view all the answers

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

Economic principles do not apply to algorithm evaluation Signup and view all the answers

Study Notes

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.

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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Description

Test your understanding of social choice theory and welfare economics. This quiz explores how individual preferences and group decisions shape public policies. Dive into examples such as elections and public goods to see the real-world applications of these concepts.