Solving the social choice problem under equality constraints

TL;DR

This paper reformulates the social choice problem with equality constraints as a constrained optimization problem, providing an elementary language-based solution and insights into the rationality of alternative sets.

Contribution

It introduces a novel approach to social choice under equality constraints, reducing it to a standard optimization problem with a new interpretative framework.

Findings

Social choice problem can be expressed as a constrained optimization problem.

Elementary language simplifies the analysis of social choice under constraints.

Interpretation focuses on the rationality of the set of alternatives.

Abstract

In a context where a decision has to be taken collectively by several agents, the social choice problem consists in deciding whether there exists a socially acceptable rule that aggregates the individual preferences of the agents into a social one. We analyze this problem for sets of alternatives defined by equality constraints and obtain a solution that, in sharp contrast to the classical ones, is expressed in an elementary language and ultimately reduces the social choice problem to a standard constrained optimization problem. By considering a toy example we shall be able to interpret this general result in terms of the rationality (in the sense of Economics) of the design of the set of alternatives rather than, surprisingly, that of the agents involved in the actual social choice problem.