Optimal ballot-length in approval balloting-based multi-winner elections.

As a common task for choosing a group of representatives, the problem of approval voting has been studied in contexts varying from democratic elections, to sports, to products marketing, and to multi-criteria decision making. In these applications, the length of individual ballots is often enforced, but how many candidates should be approved in an individual ballot is still a puzzling question. The experimental framework we present here endeavors to understand the impact of ballot-length in the effectiveness of election outcomes. Our results suggest that: (1) given the number of voters and candidates, the effectiveness of election outcome is U-shaped in the variance of individual ballot-length; (2) the determination of the optimal ballot-length critically depends on the accuracy of ballots; (3) more voters bring more effective election outcomes. Our study of how ballot length affects the effectiveness of election outcome provides new insights into an understudied area, and it can serve as a starting point for future studies of the approval balloting-based elections in other retail contexts.