It follows from Arrow's impossibility theorem that social...

Name: Problem 2, Chapter 13: An Introduction to Decision Theory
Uploaded: 2019-08-24T15:25:44-08:00
Duration: 1 min 13 s
Channel: Srikar Katta
Description: It follows from Arrow's impossibility theorem that social decisions cannot be based on majority voting procedures. (a) Exactly what is Arrow's criticism of majority voting? (b) Do you find his criticism convincing?

It follows from Arrow's impossibility theorem that social decisions cannot be based on majority voting procedures. (a) Exactly what is Arrow's criticism of majority voting? (b) Do you find his criticism convincing?

Key Concepts

Arrow’s Impossibility Theorem

Arrow’s theorem is a foundational result in social choice theory which shows that no rank-order voting system can transform individual preferences into a collective decision while simultaneously satisfying a set of fair and reasonable criteria. These criteria typically include unrestricted domain, unanimity (or Pareto efficiency), independence of irrelevant alternatives, and non-dictatorship, among others. The theorem implies that any voting procedure which aims to aggregate diverse individual preferences must compromise on at least one of these desirable conditions.

Majority Voting and the Condorcet Paradox

Majority voting is a procedure where an option is chosen based on most but not necessarily all opinions, and it is vulnerable to cyclical majorities when there are three or more options—a phenomenon known as the Condorcet paradox. This paradox shows that even if individual preferences are transitive, the collective preference order determined by majority voting can be non-transitive, leading to inconsistencies in social choices and undermining the reliability and rationality of the outcome.

Independence of Irrelevant Alternatives (IIA)

The independence of irrelevant alternatives is a crucial condition in Arrow’s framework, stating that the social preference between any two alternatives should depend solely on the individual preferences between those two options and not be influenced by the presence or ranking of additional alternatives. Majority voting procedures can violate this condition, as the introduction or removal of a seemingly irrelevant option can change the outcome of a vote between two specific choices, thereby calling into question the fairness and consistency of the procedure.

Social Choice Aggregation

Social choice aggregation concerns the methods and challenges of combining individual opinions or preferences into a collective decision. Arrow’s theorem highlights the intrinsic difficulties in designing a perfect aggregation mechanism that fulfills all intuitive fairness conditions. It exposes the theoretical limitations of majority voting and similar procedures, showing that trade-offs are inevitable when trying to reconcile individual rationality with collective rationality.

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