Partially Informed Elections -- Analyzing the Impact of Forced Ballot Truncation on Bucklin, Coombs, Plurality with Runoff, and Schulze

Elections employ various voting systems to determine winners based on voters' preferences. However, many recent ranked-choice elections have forced voters to truncate their ballots by only ranking a subset of the candidates. This study analyzes how forced ballot truncation affects the Bucklin, Coombs, plurality with runoff, and Schulze voting systems' abilities to output their true winning sets. Using computer simulations, thousands of preference profiles were generated with the Mallows model using different numbers of candidates, voters, and dispersion values. The true winning set was determined for each system using complete preferences, then compared to winning sets derived from repeatedly truncated preferences within the same preference profile. Results show that plurality with runoff was the most resistant to forced truncation, followed by Schulze, Bucklin, and Coombs. Additionally, elections with fewer voters and higher dispersion values were found to decrease the probability of selecting the true winning set across all systems. The findings provide insights into how forced truncation impacts voting systems, aiding election designers in their work.