报告人：丁一峰 （UC Berkeley）

题目：Split Cycle: a New Condorcet Consistent Voting Method and Its Axiomatic Characterization

时间：2021/06/04 09:00-12:00

腾讯会议ID：215 663 425

摘要：In this talk, I will first present a new voting method called Split Cycle proposed recently by Wesley Holliday and Eric Pacuit. The presentation will be based on comparing it with other well-known voting methods and showing that it enjoys various desirable properties that, taken together, no other known voting methods can have. Among these properties are (1) Immunity to Spoilers, (2) Positive Involvement, and (3) Negative Involvement. Roughly, Immunity to Spoilers says that a new candidate who is not winning cannot stop an existing candidate from winning while being majority-dispreferred to her, and Positive (resp. Negative) Involvement says that a new voter cannot stop a candidate from winning (resp. loosing) by placing that candidate in the first (resp. last) place of her ballot. These properties directly rule out `paradoxical' situations in contexts where every voter shall be treated with equal power. However, the above three properties (together with other common properties for voting methods) do not uniquely pin down Split Cycle, as far as we know. In other words, they don't axiomatically characterize Split Cycle. I will then report an ongoing project on axiomatically characterizing Split Cycle, not as a voting method which only outputs a set of winners, but as a collective choice rule which outputs a binary relation we shall call the relation of defeat. The axiomatization uses a new weakening of the famous Independence of Irrelevant Alternatives (IIA) called Locally Coherent IIA, which is stronger than Immunity to Spoilers under a few very weak assumptions, and Positive Involvement in Defeat, which can be seen as Positive Involvement phrased in terms of collective choice rules. Time permitting, I will also discuss the difficulty in axiomatizing Split Cycle as a voting method and our current plan in addressing that.