# The distortion of distributed voting

## TL;DR

This paper investigates how dividing voters into districts affects the efficiency of voting rules, revealing that distributed voting can significantly increase distortion compared to centralized voting, supported by theoretical bounds and real-world data.

## Contribution

It introduces a formal analysis of distortion in distributed voting systems, providing tight bounds and highlighting the impact of district partitioning on societal welfare.

## Key findings

- Distributed voting increases distortion compared to centralized voting.
- Tight bounds on distortion are established for various voting rules.
- Real-world data confirms higher distortion in distributed elections.

## Abstract

Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the voting process on the societal welfare for the outcome, by bounding the distortion of voting rules. Even though there has been significant progress towards this goal, all previous works have so far neglected the fact that in many scenarios (like presidential elections) voting is actually a distributed procedure. In this paper, we consider a setting in which the voters are partitioned into disjoint districts and vote locally therein to elect local winning alternatives using a voting rule; the final outcome is then chosen from the set of these alternatives. We prove tight bounds on the distortion of well-known voting rules for such distributed elections both from a worst-case perspective as well as from a best-case one. Our results indicate that the partition of voters into districts leads to considerably higher distortion, a phenomenon which we also experimentally showcase using real-world data.