Costly Voting with Sequential Participation

This paper examines the property of the m votes to win mechanism. Voting is an effective way to make a collective decision but voting behaviors, e.g., monitoring the voting process, may incur a cost, that is, voting is often costly. In this case, compulsory voting incurs a larger cost. Random decision making can reduce the cost for voting but is skeptical in the quality of decision making. That is, we face the problem of how to balance the quality of collective decision making with the reduction of the cost for voting. To solve this problem, this paper focuses on the m votes to win mechanism, in which voters sequentially vote and if an alternative receives m votes, the voting process immediately terminates and the alternative received m votes wins. The similar voting mechanism is actually used in the Apache projects. However, the property of the m votes to win mechanism has not sufficiently studied. The questions include how to find a desirable value of m and what situation this mechanism is superior to other mechanisms. To answer these question, we create the discussion model where two alternatives is included, and analyze what voting strategy is rational. Based on the analysis, we examine what factors affects the social surplus, i.e., to what extent the quality of collective decision making and the reduction of the cost for voting are well balanced, and clarify whether the m votes to win mechanism is superior to the compulsory voting or the random decision making in terms of social surplus.