An Evaluation of Borda Count Variations Using Ranked Choice Voting Data

TL;DR

This paper evaluates various Borda count variations in ranked choice voting, analyzing their susceptibility to voting failures through empirical data from 421 U.S. elections, highlighting trade-offs between different voting flaws.

Contribution

It introduces and empirically assesses Borda count variations that avoid monotonicity paradoxes, providing insights into their failure modes in real elections.

Findings

Majority failures are rare or nonexistent with certain Borda variations.

Truncation and compromise failures occur more frequently than in instant runoff voting.

Some Borda variations effectively avoid monotonicity paradoxes but at the cost of other failures.

Abstract

The standard voting methods in the United States, plurality and ranked choice (or instant runoff) voting, are susceptible to significant voting failures. These flaws include Condorcet and majority failures as well as monotonicity and no-show paradoxes. We investigate alternative ranked choice voting systems using variations of the points-based Borda count which avoid monotonicity paradoxes. These variations are based on the way partial ballots are counted and on extending the values of the points assigned to each rank in the ballot. In particular, we demonstrate which voting failures are possible for each variation and then empirically study 421 U.S. ranked choice elections conducted from 2004 to 2023 to determine the frequency of voting failures when using five Borda variations. Our analysis demonstrates that the primary vulnerability of majority failures is rare or nonexistent depending on the variation. Other voting failures such as truncation or compromise failures occur more frequently compared to instant runoff voting as a trade-off for avoiding monotonicity paradoxes.