The character of non-manipulable collective choices between two alternatives

TL;DR

This paper characterizes classes of non-manipulable social choice functions with at most two choices, providing explicit functional forms and a unified framework using the concept of 'character' to describe their selection mechanisms.

Contribution

It introduces a novel unified characterization of non-manipulable social choice functions with limited range, using the concept of 'character' to explicitly define their functional forms.

Findings

Provides explicit functional forms for each class of non-manipulable social choice functions.

Introduces the concept of 'character' for unified characterization.

Offers a comprehensive framework for understanding two-alternative social choice functions.

Abstract

We consider classes of non-manipulable social choice functions with range of cardinality at most two within a set of at least two alternatives. We provide the functional form for each of the classes we consider. This functional form is a characterization that explicitly describes how a social choice function of that particular class selects the collective choice corresponding to a profile. We provide a unified formulation of these characterizations using the new concept of "character". The choice of the character, depending on the class of social choice functions, gives the functional form of all social choice functions of the class.