Recent Article on the Manipulability of a Class of Social Choice Functions: Plurality kth RulesAn article written by Dezső Bednay and Attila Tasnádi from the Department of Mathematics jointly with Sonal Yadav from the UMEA University (Sweden) was recently published in Review of Economic Design (Aip: 59).
The plurality rule is the most widely applied voting rule selecting the alternative receiving the highest number of votes, where each voter can just vote for one person. As an extension we introduce and investigate the plurality kth voting rule selecting an alternative, which is ranked kth based on the received number of votes. This might seem as a purely theoretical extension; however, when electing a committee of k members, the so-called single nontransferable vote (SNTV) rule chooses the top k members based on the received number of votes. Therefore, the plurality kth rule selects the member just getting into the committee, that is it is concerned about the marginal winning member. The paper investigates the manipulability of the plurality kth rule and establishes a link to the manipulability of the SNTV rule. Furthermore, we propose a decomposition of social choice functions based on plurality kth rules, which we apply for determining non-manipulable subdomains for arbitrary social choice functions.