Analyzing the Probability of Election Outcomes with Abstentions

Abstract

Earlier analysis considered the coincidence probability for the Condorcet Winners from preference rankings of possible voters and of participating voters when abstention is allowed. The probability of non-coincidence becomes quite high for low voter participation rates with independent voters’ preferences. Pessimistic results were also found under the same conditions for both the Condorcet Efficiency and the probability of observing a Borda Paradox with some common single-stage voting rules. Two options are considered to reverse these negative results. The first adds dependence among voters’ preferences with a commonly used model. The second uses the single-stage voting rules as the basis for two-stage elimination election procedures. Both options are found to make things worse for all voting rules with low voter participation rates. The same negative outcome is also observed for Approval Voting when some voter indifference between candidates is allowed. These preliminary results are valid, but what they are actually found to be showing is that very bad results can be expected for all voting rules when statistical dependence exists among abstaining voters, particularly for low voter participation rates. If a model requires that voters choose to abstain independently, then the addition of dependence among the possible voters’ preferences significantly improves the very negative outcomes that were initially observed.