Social choice theory

Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Empirical methods Prescriptive and policy Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making.

[5][6][7] It is closely related to mechanism design, which uses game theory to model social choice with imperfect information and self-interested citizens.

The earliest work on social choice theory comes from the writings of the Marquis de Condorcet, who formulated several key results including his jury theorem and his example showing the impossibility of majority rule.

His work was prefigured by Ramon Llull's 1299 manuscript Ars Electionis (The Art of Elections), which discussed many of the same concepts, but was lost in the Late Middle Ages and only rediscovered in the early 21st century.

[11][12][13] Arrow's impossibility theorem is a key result showing that social choice functions based only on ordinal comparisons, rather than cardinal utility, will behave incoherently (unless they are dictatorial).

Condorcet's example demonstrates that democracy cannot be thought of as being the same as simple majority rule or majoritarianism; otherwise, it will be self-contradictory when three or more options are available.

This contrasts with May's theorem, which shows that simple majority is the optimal voting mechanism when there are only two outcomes, and only ordinal preferences are allowed.

This lends some support to the viewpoint expressed of John Stuart Mill, who identified democracy with the ideal of maximizing the common good (or utility) of society as a whole, under an equal consideration of interests.

The field of mechanism design, a subset of social choice theory, deals with the identification of rules that preserve while incentivizing agents to honestly reveal their preferences.

But much of the research in the field assumes that those utility functions are internal to humans, lack a meaningful unit of measure and cannot be compared across different individuals.

Following arguments similar to those espoused by behaviorists in psychology, Robbins argued concepts of utility were unscientific and unfalsifiable.

It has been used to defend transfers of wealth from the "rich" to the "poor" on the premise that the former do not derive as much utility as the latter from an extra unit of income.

Amartya Sen argues that even if interpersonal comparisons of utility are imperfect, we can still say that (despite being positive for Nero) the Great Fire of Rome had a negative overall value.

Harsanyi and Sen thus argue that at least partial comparability of utility is possible, and social choice theory should proceed under that assumption.

Public choice deals with the modeling of political systems as they actually exist in the real world, and is primarily limited to positive economics (predicting how politicians and other stakeholders will act).

By contrast, social choice has a much more normative bent, and deals with the abstract study of decision procedures and their properties.

We can think of this subset as the winners of an election, and compare different social choice functions based on which axioms or mathematical properties they fulfill.

The Gibbard–Satterthwaite theorem implies that the only rule satisfying non-imposition (every alternative can be chosen) and strategyproofness when there are more than two candidates is the dictatorship mechanism.