Metric Distortion of STV on the Line and the Impact of Voter Turnout
摘要
Public interest in ranked choice voting mechanisms such as Single Transferable Vote (STV) has increased in recent years, as a potentially more equitable approach, leading to its adoption for political elections in various cities, states, and countries. A recently-studied measure of interest is metric distortion, which captures how much worse an elected candidate is from the socially optimal choice. Building upon the known lower bound of 3 on the metric distortion of any deterministic voting rule shown by Anshelevich et al. [3], and the known upper bound of 15 on the metric distortion of STV on the line by Anagnostides et al. [2], we improve the gap between these bounds by providing an upper bound of 11 on the metric distortion of STV on the line. In addition, we consider the impact of voter turnout on elections, giving a lower bound on the metric distortion of STV on the line that is a function of the voter turnout percentage; in particular, 50% turnout yields a lower bound of 7. We then run simulations with randomly positioned candidates and voters on the line to show how distortion is impacted by varying percentages of voter turnout. Finally, we empirically study the impact of voter turnout on the 2021 New York City Democratic Primary Election. Despite ranked voting having advantages over non-ranked (plurality) voting, STV appears to provide lower accuracy and higher distortion than other commonly-studied ranked voting rules. However, the accuracy of STV appears to be less sensitive to voter turnout than other voting rules.