The nature of individual choice: a formalism for utility function based on set theory

TL;DR

This paper introduces a formal set-theoretic model for individual utility functions, considering individuals and alternatives as composed entities, and defines evaluation processes based on these utilities in social choice theory.

Contribution

It proposes a novel set-theoretic formalism for utility functions that models individuals and alternatives as composite entities, enhancing the understanding of preference evaluation.

Findings

A formal set-theoretic model of utility functions is developed.

Evaluation processes based on utilities are formally defined.

The model offers a new perspective on individual and social preferences.

Abstract

In the theory of social choice the research is focused around the projection of individual preference orders to the social preference order. Also, the justification of the preference order formalism begins with the concept of utility i.e. an alternative is preferred to another one if the utility over the first is higher then the utility over the second. In this paper is proposed an ideal model of measuring utilities by considering individuals and alternatives no more as atomic concepts but as being composed by other entities. Furthermore is proposed a formal definition of evaluation processes based on utilities.