选举理论模型及其在解决多候选人内蕴不确定性问题中的应用

Voting Theory for Multiple Candidates to Resolve Intrinsic Uncertain Problems of Election

简单选票模型,利用多数票为优胜的选举规则,建立一套分析结构以支持传统意义下的计票过程,分析废票对选举结果的影响并给出不确定性出现的条件.复合选票模型利用多组特征矩阵,向量和置换群为基础变量,形成一套稳定的选举分析系统.这套系统具有特征索引族以置换变化下不变性,区分候选人特有的概率特征向量.文中的主要结果建立一套选举权威机制,利用综合索引指数可区分排序方式,辅助解决选举中当多个候选人在持有相同选票时难以区分胜负的内蕴不确定性问题.

This paper proposes two voting models - the Simple Ballot Model (SBM) and the Component Ballot Model (CBM) - to solve the intrinsic uncertainty problems in an election when multiple candidates (more than two) gain the similar number of votes. The SBM establishes an analytical framework to support traditional counting procedures for an election under the plurality rule. As the margin of error in a fair election is always very small, it is extremely unfair to ignore abundance of valid votes already counted and to only concentrate on a minority of rejected votes in separating the multiple candidates. Therefore, the most essential issue for a voting system is the extraction of additional information from dominantly valid votes to improve the separable property between candidates. To extract additional information from votes, the CBM uses multiple feature matrices, probability feature matrices, vectors and permutation group as basic components. It creates a stable\|voting mechanism under permutation invariant on feature indexing families to distinguish probability feature vectors. The important result of the paper is to establish a voting authority statement for multiple candidates in order to resolve the uncertain problem of an election in a sequence of calculable operations on significantly distinguishable feature indexes.