基于不同个体偏好表现形式的多阶段投票选择方法研究
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摘要
在投票选择活动中,由于投票者知识结构、个人偏好和对候选人信息了解程度等方面的差异,仅仅通过一次投票过程可能难以从多位候选人中选出让多数人满意的获胜者。因此,很多社会选择活动采用多阶段投票方式。多阶段投票规则允许投票人进行多次投票,采用逐轮淘汰方式选出最后的优胜者,最终投票结果是通过多个相互关联的投票阶段产生的。投票选择方法的实质是将投票人的个体偏好集结为群体偏好。在多阶段投票过程中,投票人个体偏好可能会随着投票阶段的改变而发生变化,而根据投票规则的不同,投票人个体偏好也会有不同的表现形式。因此,本文研究的主要目的就是从这些不同形式的、动态变化的个体偏好中挖掘出更多有用的信息,减少策略投票的可能,更真实地反映出投票人的意愿,为民主选择提供更公平合理的、可供借鉴的选择方法。
本论文的主要工作:根据动态群体决策的特点和方法,针对三类不同的个体偏好表现形式,即排序形式的个体偏好、“单票制”形式的个体偏好和带有不确定信息的个体偏好,对多阶段投票过程及信息集结方式进行分析和研究,并提出了相应的投票选择方法。
首先,针对排序式个体偏好,本文通过研究个体偏好和群体偏好之间的关系,构建了投票人动态权重确定模型和投票阶段动态权重确定模型,在此基础上提出了分别基于这两类权重的多阶段投票选择方法。投票人动态权重主要是通过个体偏好和群体偏好的接近程度,即个体偏好偏离量指标来动态调整和确定的。而投票阶段权重则根据每一轮投票中的个体偏好集中程度来进行分析和确定。分析结果表明,考虑投票人权重的投票选择方法能够提高群体偏好认同度,提高投票选择效率,降低决策成本;而考虑了投票阶段权重的投票方法能够充分考虑每一阶段投票信息对最终选举结果所产生的影响,使选举结果更合理。
其次,针对“单票制”个体偏好,本文研究了投票者在交替式投票和非交替式投票两种模式下的个体偏好集结过程,并提出不同的投票选择方法。在非交替式投票模式下,我们首先以奥运会主办城市的投票表决问题为例,分析了真实投票和策略投票过程及存在的问题。基于存在的问题,提出了基于投票效力指数的多阶段投票选择方法。在交替式投票模式下,提出了基于双射软集合和集结算子的投票阶段权重确定方法,为不同投票阶段偏好信息的集结提供了一种可供借鉴的新方法。分析结果说明,基于投票效力指数的投票选择方法能够更真实地反映出投票人的偏好顺序,也能在一定程度上防止投票人的策略性投票行为。
最后,针对不确定个体偏好,本文以“多票制”规则下有效票中的弃权信息为分析对象,通过建立基于不完备软集合和Vague集的不确定信息分析模型,对有效选票中的弃权信息进行估算,并分析了不确定状态下单一投票阶段的选择过程,在此基础上提出了多阶段投票选择方法。分析结果表明,对不确定信息的分析和估算可以将候选人之间的不确定状态转化为确定状态或可忽略的不确定状态,这对于确定群体偏好和候选人排名具有重要的参考价值。
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.
本论文的主要工作:根据动态群体决策的特点和方法,针对三类不同的个体偏好表现形式,即排序形式的个体偏好、“单票制”形式的个体偏好和带有不确定信息的个体偏好,对多阶段投票过程及信息集结方式进行分析和研究,并提出了相应的投票选择方法。
首先,针对排序式个体偏好,本文通过研究个体偏好和群体偏好之间的关系,构建了投票人动态权重确定模型和投票阶段动态权重确定模型,在此基础上提出了分别基于这两类权重的多阶段投票选择方法。投票人动态权重主要是通过个体偏好和群体偏好的接近程度,即个体偏好偏离量指标来动态调整和确定的。而投票阶段权重则根据每一轮投票中的个体偏好集中程度来进行分析和确定。分析结果表明,考虑投票人权重的投票选择方法能够提高群体偏好认同度,提高投票选择效率,降低决策成本;而考虑了投票阶段权重的投票方法能够充分考虑每一阶段投票信息对最终选举结果所产生的影响,使选举结果更合理。
其次,针对“单票制”个体偏好,本文研究了投票者在交替式投票和非交替式投票两种模式下的个体偏好集结过程,并提出不同的投票选择方法。在非交替式投票模式下,我们首先以奥运会主办城市的投票表决问题为例,分析了真实投票和策略投票过程及存在的问题。基于存在的问题,提出了基于投票效力指数的多阶段投票选择方法。在交替式投票模式下,提出了基于双射软集合和集结算子的投票阶段权重确定方法,为不同投票阶段偏好信息的集结提供了一种可供借鉴的新方法。分析结果说明,基于投票效力指数的投票选择方法能够更真实地反映出投票人的偏好顺序,也能在一定程度上防止投票人的策略性投票行为。
最后,针对不确定个体偏好,本文以“多票制”规则下有效票中的弃权信息为分析对象,通过建立基于不完备软集合和Vague集的不确定信息分析模型,对有效选票中的弃权信息进行估算,并分析了不确定状态下单一投票阶段的选择过程,在此基础上提出了多阶段投票选择方法。分析结果表明,对不确定信息的分析和估算可以将候选人之间的不确定状态转化为确定状态或可忽略的不确定状态,这对于确定群体偏好和候选人排名具有重要的参考价值。
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.
引文
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