几何法求解三个候选人时的投票结果

用排列组合来计算对投票结果的预测,过程较复杂,而采用几何法代替组合学方法,计算各种投票结果出现的概率,方法简单直观.首先定义了投票者类型的概念,并用几何法表示了候选人的投票类型,得出了产生多数票循环的类型组合,并针对该类型组合给出了结果断面三角形.然后将三角形划分成四个区域,得到了投票结果和这四个区域的对应关系.最后利用三角形计算了在不同投票人数时,各种投票结果出现的概率.

Voting Outcomes of Three Candidates Using Geometry Compute

The process of forecasting voting outcomes is complex by combinatory.But it is intuitive and simple by geometry instead of combinatory to compute probabilities of kinds of voting outcomes.First,the concept of voters' types was defined and the voters' types were denoted with geometry when there were three candidates.The types' combinations which cause cyclic majorities is obtained and the result-profile triangle is gaven.Second,seperating the triangle to four regions,the relations between voting outcomes and the four regions are gained.Last,applying the triangle the appearing probabilities of voting outcomes were computed with n voters.