Recognizing distributed approval voting forms and correspondences

TL;DR

This paper develops polynomial algorithms to recognize distributed approval voting forms and correspondences, especially for cases with two candidates or voters, and characterizes voting forms with unique row structures.

Contribution

It introduces polynomial recognition algorithms for distributed approval voting forms and correspondences in specific cases, and characterizes voting forms with distinct rows.

Findings

Polynomial algorithms for recognition in special cases

Unique voting correspondence with distinct rows under certain conditions

Characterization of voting forms with distinct rows

Abstract

Each voter $i \in I$ has $\alpha_i$ cards that (s)he distributes among the candidates $a \in A$ as a measure of approval. One (or several) candidate(s) who received the maximum number of cards is (are) elected. We provide polynomial algorithms to recognize voting forms and voting correspondences generated by such voting schemes in cases when either the number of candidates or the number of voters is equal to $2$. We prove that for two voters, if $\alpha_2 \geq \alpha_1-2\geq 0$ then the unique voting correspondence has distinct rows. We also characterize voting forms with distinct rows.