The Complexity of Control and Bribery in Majority Judgment

We study strategic voting problems for majority judgment, in which each voter assigns to every candidate a grade and the winners are determined by their majority-grades. We first study the constructive/destructive control by adding/deleting votes/candidates problems. Then we study the bribery problem, where an external agent wants to change the result by asking a limited number of voters to change their votes. In addition, we study the variant of the bribery problem where each voter has a price for changing her grade assigned to a candidate and the external agent has a limited budget. Finally, we propose and study the constructive/destructive control by adding & deleting grades problem where an external agent aims to change the result by adding and deleting some grades simultaneously. We show that majority judgment is immune to constructive control by adding candidates and destructive control by deleting candidates. Moreover, for each other problem, we either derive a polynomial-time algorithm or show it is NP-hard.