Restricted Domains of Dichotomous Preferences with Possibly Incomplete Information

Abstract

Restricted domains over voter preferences have been extensively studied within the area of computational social choice, initially for preferences that are total orders over the set of alternatives and subsequently for preferences that are dichotomous—i.e., that correspond to approved and disapproved alternatives. This paper contributes to the latter stream of work in a twofold manner. First, we obtain forbidden subprofile characterisations for various important dichotomous domains. Then, we are concerned with incomplete profiles that may arise in many real-world scenarios, where we have partial information about the voters’ preferences. We tackle the problem of determining whether an incomplete profile admits a completion within a certain restricted domain and design constructive, polynomial algorithms to that effect.

Representation with Incomplete Votes

“…In Section 3.2 we adapt a local-search algorithm of Aziz et al (2018) to the case of exact queries and show 5 There is a body of work in computational social choice related to incomplete votes. For instance, some papers aim to find winning committees, given incomplete approval votes, or to fill in the missing votes, given knowledge about the domain of approval profiles (Imber et al 2022;Terzopoulou, Karpov, and Obraztsova 2021;Zhou, Yang, and Guo 2019). However, these papers are primarily concerned with the computational complexity of these problems, while we focus on information-theoretic questions.…”