Study On Methods Of Multi-stage Voting Under Different Individual Preference Representation

In the voting, because of difference of voters'knowledge structures, individual preferences and understanding for candidates, it is difficult to aggregate individual preferences effectively into group preference through a unique voting stage. Therefore, multi-stage voting is selected to deal with these voting questions. Multi-stage voting allows voters to vote for many times for selecting the final winners from candidates with the method of round-by-way-out. That is, the final voting results are produced by multiple related voting stages. The purposes of voting methods are to aggregate different individual preferences into group preference. In multi-stage voting processes, individual preferences of voters may change with the different voting phases. There are different individual preference representations according to different voting rules. Therefore, the purpose of this paper is to find more valuable information from dynamic individual preferences under different individual preference representations, reduce the strategic voting, reflect true preferences of voters, and provide more fair and reasonable methods for voting selection.This paper focuses on the processes and information aggregation of multi-stage voting based on three different individual preference representation( ranked preference, "one vote" preference and preference with uncertain information ), and put forward to the corresponding multi-stage voting methods.Firstly, as for the ranked individual preferences, based on the relation of individual preferences and group preference, this paper designs two models for dynamically determining weights of voters and voting stages, and provides two multi-stage weighted voting methods based on weights of voters and voting stages, respectively. The dynamic weights of voters are determined by the proximity of individual preferences and the group preference. The weights of different voting stages are determined by the group preferences concentration of each voting stage. The results show that the voting model with weights of voters can quickly aggregate individual preferences into group preference, and enhance the efficiency of voting. The voting model with weights of voting stages can show how polling information of each stages impact on the impact of the election results.Secondly, as for the "one person, one vote" preference representations, this paper focuses on aggregation of preference under two different rules. One is the alternating rule which means status of candidates are variable, and the other is the non-alternating rule which means status of candidates are invariable. In the process of non-alternating multi-stage voting, based on the analysis of the voting process for selecting Olympic game city, the bad questions in multi-stage voting are founded. So, the approach based on the force index of voting is provided. This approach can not only reduce the negative influence of strategic voting to a certain extent, but also more naturally reflect the preferences sequence of voters. In the alternating multi-stage voting, in order to embody the impacts of different voting stages, this paper provides a new method for determining weights of voting stages based on soft set and operators.Finally, as for preference representations with uncertain information, this paper focuses on valid votes with abstaining information. An analyzing model for dealing with abstaining information are provided under the "one person, multiple votes" rules, based on incomplete soft sets and Vague set. This model can give the quantitative estimation of the uncertain information which plays an important role for determining if candidates are eliminated in multi-stage voting. The results show that analyses and estimation for uncertain information can translate uncertain status of candidates into certain status, and provide important basis for determining group preference and the rank of candidates.