Who Is in Your Top Three? Optimizing Learning in Elections with Many Candidates

Abstract

Elections and opinion polls often have many candidates, with the aim to either rank the candidates or identify a small set of winners according to voters’ preferences. In practice, voters do not provide a full ranking; instead, each voter provides their favorite K candidates, potentially in ranked order. The election organizer must choose K and an aggregation rule.
 We provide a theoretical framework to make these choices. Each K-Approval or K-partial ranking mechanism (with a corresponding positional scoring rule) induces a learning rate for the speed at which the election recovers the asymptotic outcome. Given the voter choice distribution, the election planner can thus identify the rate optimal mechanism. Earlier work in this area provides coarse order-of-magnitude guaranties which are not sufficient to make such choices. Our framework further resolves questions of when randomizing between multiple mechanisms may improve learning for arbitrary voter noise models.
 Finally, we use data from 5 large participatory budgeting elections that we organized across several US cities, along with other ranking data, to demonstrate the utility of our methods. In particular, we find that historically such elections have set K too low and that picking the right mechanism can be the difference between identifying the ultimate winner with only a 80% probability or a 99.9% probability after 400 voters.

Rank, Pack, or Approve: Voting Methods in Participatory Budgeting

“…However, (Goel et al 2019) suggests that knapsack voting was less burdensome in practice and desirables strategic properties. In (Garg et al 2019) learning rates were proposed to identify optimal ballot design, concluding that the threshold K was historically set too low in Kapproval voting for optimal learning. A study into the effect of K-approval, threshold-approval, K-ranking (in two variations), knapsack and K-token voting with recruited crowdworkers evaluated the effect on cognitive load and voters' ability to recall their stated preferences (Fairstein, Benade, and Gal 2023), suggesting Value-for-Money ranking as cognitively the hardest on voters.…”

Ballot Length in Instant Runoff Voting

“…Ballot length has been considered in con- texts other than IRV-for instance, research on the Boston school choice mechanism found that limiting the number of schools parents could rank to five resulted in undesirable strategic behavior (Abdulkadiroglu et al 2006). There has also been research on ballot length in approval voting from a learning theory angle, seeking to recover a population's preferences efficiently (Garg et al 2019).…”