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上海财经大学,Shufe,Shufe,*,理论分析框架,上海财经大学,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,第七讲 其它多数规那么,?公共选择与政治立宪?,第6、8、9章,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,讲义提纲,最多票数规那么,孔多塞规那么,黑尔机制,库姆斯机制,波尔达计票,赞成投票,点投票,否决投票*,过程比较 ,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,一、最多票数规那么,最多票数Plurality规那么的含义,在投票过程中,每一个个体将自己的选票投给自,己最喜爱的对象候选人或者议案,获得选票,数最多的对象将获胜。,最多票数规那么的优点,简单且相对合理:结果获得了相对“多数的,支持,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,最多票数规那么的问题,可能产生对局部人有利但对其它个体极端不利,的极端主义议案和或候选人;产生低效率,的结果平均效率,中选人与政治机构的权威性,二次选举Double election的引进,规那么的含义:一起表决,得到两个获得最多票,数支持的议案和或候选人;投票人继续就,上述两个备选对象进行选举,多数支持者获胜,二次选举的意义表1 返回,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,表1 二次选举,投票人,偏好排序,V,1,(8),Y,V,W,Z,X,V,2,(7),X,V,W,Z,Y,V,3,(5),Z,W,V,X,Y,V,4,(3),V,X,W,Z,Y,V,5,(2),W,Z,Y,V,X,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,二、孔多塞规那么,投票均衡,特殊例子,一般情形,投票循环悖论Voting cycling paradox,根本类型,主要问题,孔多塞规那么的适用性,返回,返回,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,一投票均衡:特殊例子,假设,5个决策个体集体决定某一公共产品的规模,税收制度:同一税制Uniform taxation,个体最优选择图1,个体的需求曲线与最优选择,具体例子:,简单多数均衡表2,中位数投票者Median voter,多数投票均衡Majority voting equilibrium,返回,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,元,D,5,D,4,D,2,a,/,n,D,1,d,(,D,3,),O,x,1,x,2,x,3,x,4,x,5,x,图1 中位数投票模型,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,民主决策的个体行动根底:具体例子,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,表2 简单投票多数支持率比较表,比较组,支持x3的个体,反对x3的个体,两者之比,x,3,对x,1,3、4、5或2,1或2,4:1或3:2,x,3,对x,2,3、4、5,1、2,3:2,x,3,对x,4,1、2、3,4、5,3:2,x,3,对x,5,1、2、3或4,5或4,4:1或3:2,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,一投票均衡:一般情形,中位数定理Median Voter Theorem:对于,一维待决策议案x,假设所有投票者的偏好在x是,上是单峰的,那么,多数规那么投票的结果为中,位数投票者所偏好的方案。,上海财经大学,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,概念定义与说明:,a.理想点Ideal point:假设xi*是个体i的理想,点,当且仅当对所有xxi*,都有uixi*,uix;,上海财经大学,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,定理证明,*,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,二投票循环悖论:根本类型,一维议案,双峰偏好Double-peaked preference,多元议案,二维组合,返回,上海财经大学,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,效 甲,用 乙,丙,x y z,图6,双峰偏好,1、,一维议案,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,2、多元决策,表3,个体,第一选择,第二选择,第三选择,甲,T,H,D,乙,H,D,T,丙,D,T,H,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,理想点、效用山Utility mountain与无差异,曲线图3,二元议案时的投票循环图4,向前,3、二维组合,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,y,U,A,A,(,x,A,,,y,A,),x,图3 理想点与无差异曲线,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,y,U,C,U,A,A,D U,B,C,E,K,B,x,图4 二元议案时均衡的不存在性,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,二 循环悖论:存在的问题,问题的具体性质,非决定性集体非理性,日程控制Agenda manipulation,问题的严重程度,循环出现的概率,返回,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,投票循环的概率,表4 议案个数为3时无多数胜者的概率,人数,概率,人数,概率,1,0.000,15,0.082,3,0.056,17,0.083,5,0.069,19,0.083,7,0.075,21,0.084,9,0.078,23,0.084,11,0.080,25,0.084,13,0.081,0.088,注:前提假设是所有序有同样的机会被每一个个体采用。,资料来源:吉尔博(1952)、加曼与凯明(1968)以及尼米和韦斯博格(1968)。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,表5 无多数胜者概率的极限制,方案数,概率,人数,概率,1,0.000,20,0.681,2,0.000,25,0.730,3,0.088,30,0.765,4,0.176,35,0.791,5,0.251,40,0.812,10,0.489,45,0.829,15,0.609,注:前提假设是所有序有同样的机会被每一个个体采用。,资料来源:尼米和韦斯博格(1968)。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,个体偏好的调整,修改投票的规那么,投票程序的修正,三孔多塞规那么的适用性,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,一维:个体偏好类型,二维:,理想点的空间分布,多元:,个体偏好组合类型,个体偏好的同质性程度,1、个体偏好的调整,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,1理想点的空间分布,探索性分析,(a)点分布在同一直线如图5;,(b)增加的点对称分布在过均衡点的直线上,一般性条件,返回,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,y,A,C,B,x,图5 多元(维)议案与均衡,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,个体偏好的空间分布理想点分布,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,2个体偏好的组合形式,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,3 个体偏好结构的同质性,a.具有相同偏好的多数的存在,就足以保证多数规那么均,衡的存在,而不管其他人的偏好如何Kramer,1973;,Buchanan,1954;,b.循环发生的概率会随具有相同偏好人数比例的增多而递,减Williamson 与 Sargent,1976;Gehrlein与 Fishburn,1967。,c.财政竞争与财政联邦主义,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,2、对投票规那么的修正,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,3、投票程序的修正,逐步淘汰法,加权赋值法,返回,上海财经大学,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,三、黑尔机制,黑尔机制Hare system的含义,个体在选票上以第一、第二、第三的方式对所有候选对,象做出排序。在偏好排序给定的根底上,根据首要偏好,的情况来进行淘汰和选择,如果有候选人所获得的选票数超过一半,即有半数以上,的人将候选人置于首位,那么,他就将宣布获胜,但如果没有,那么具有最少数的、投票人将其排在首位,的候选对象将被淘汰出局,而他所获得的所有选票将转,移给排在第二位置的候选对象,继续该过程直到有一个候选对象能获得多数支持为止,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,黑尔机制的运作结果表2,表2,选择过程,Y,X,Z,V,W,第一次计票,8,7,5,3,2,第一次淘汰与第二次计票,8,7,7,3,第二次淘汰与第三次计票,8,10,7,第三次淘汰与第四次计票,10,15,最终获胜者,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,优点,与最多票数规那么比较:保证那些能够吸引,“最多数但是为大多数所反对的备选议,案不会中选,黑尔机制的性质,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,缺乏,平均效率:被少数人排在最前面但在整体层面上,平均排序较高的备选对象可能被排除。比方说,V和W。,孔多塞效率:由于淘汰的依据是被最少数的人排,在最前面的备选对象,孔多塞胜者可能被过早地,淘汰出局。也就是说,即便存在孔多塞胜者,孔,多塞胜者不一定能得到选择,比方说V。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,四、库姆斯机制,库姆斯机制Coombs system的含义,依次被集体决策过程所淘汰的是被最多的人排在,最后的议案和或候选人。具体来说,就是在,所有的议案中,每一投票者都指出被他排在最后,面的议案,然后删除被最多的投票人排在最后面,的议案,并按照同样的方法对剩下的个议案进行,表决,继续该过程直到只有一个议案为止,该议,案就是最终的获胜议案。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,库姆斯机制的运行结果,表3,投票过程,Y,X,Z,W,V,第一次计票,15,10,0,0,0,第一次淘汰与第二次计票,15,10,0,0,第二次淘汰与第三次计票,18,0,7,第三次淘汰与第四次计票,18,7,最终获胜者,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,库姆斯机制的性质,与黑尔机制的共性:排斥极端议案、孔多塞胜者,可能未能得到选择,与黑尔机制的差异:黑尔机制倾向于选择被多数,人所支持的对象;库姆斯机制倾向于选择被最少,人所厌恶的对象,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,五、波尔达计票Berda count,波尔达计票方法的具体过程,波尔达计票方法的合理性,波尔达计票方法存在的问题,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,1.波尔达计票方法的具体过程,投票过程,考虑一个一般性的有n位成员就m个议案进行表决,的集体决策环境。就某一公共投票者而言,假设个,体对于议案的排序是P。于是可以按照议案排序的先,后顺序给予每一个议案一个分数等价于是存在m,个等级:居于最前面的议案得m分,第二位的得,m-1分,最后的议案得1分。在赋值的根底上,,把每个议案的得分进行加总,得分最高者宣布获胜,具体例子,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,表4,议案,加权票数,总计,(8),(7),(5),(3),(2),y,5*8=40,1*7=7,1*5=5,1*3=3,3*2=6,61,z,2*8=16,2*7=14,5*5=25,2*3=6,4*2=8,69,w,3*8=24,3*7=21,4*5=20,3*3=9,5*2=10,84,v,4*8=32,4*7=28,3*5=15,5*3=15,2*2=4,94,x,1*8=8,5*7=35,2*5=10,4*3=12,1*2=2,67,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,2.波尔达计票方法的合理性,平均效率:波尔达计票往往会选择平均排序水平,相对较高的议案比方说V;它有,利于消除极端主义的议案或者候选人,孔多塞效率:在孔多塞胜者存在的情况下,波尔,达计票一般会选择孔多塞胜者。当然,也有例外。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,3.波尔达计票方法存在的问题,波尔达计票方法可能引发个体战略性行为,波尔达计票方法不满足“无关备选对象的独立性,Independence of irrelevant alternatives性质,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,六、赞同投票Approval voting,赞同投票方法运作的具体方式,对于所有的备选对象,个体对于自己赞成的,备选对象投赞成票,而对自己不赞成的投反,对票。然后加总所有的赞成票数,票数最多,的备选对象中选。就赞同投票而言,其等价,于个体赋予自己赞同的备选对象的权数为1,,对于不赞同的备选对象赋予的权重为0。,在赞同投票方式下,个体所投的票数可能不,一样,除非规定赞同票的票数。特别地,假设,所有个体都只投一票,那就是最多票数规那么,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,赞同投票,表5,限定,票数,备选对象,获胜者,x,y,z,v,w,2,10,8,7,18,7,v,3,10,10,7,23,25,w,4,15,10,25,25,25,z、v、w,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,七、点投票Point voting,点投票方法,给每位投票者一定的点数,比方说100点,投票者,可以根据自己对于议案或候选人的偏好强度将自,己的点数分配给各个议案或各位候选人。然后加,总各个议案或候选人所得到的点数,按照点数的,多少来确定最终的胜者。点投票的过程是个体分,配和赋予权重的过程,又叫“点分配方法Point distribution method。,具体例子假设个体根据偏好强度分配点数。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,表6 议案强度分布假设与计算结果,V,1,(8),Y24,V22,W20,Z18,X16,V,2,(7),X60,V15,W10,Z8,Y7,V,3,(5),Z38,W35,V22,X5,Y0,V,4,(3),V40,X20,W19,Z18,Y3,V,5,(2),W28,Z21,Y18,V17,X16,V(y)=286;V(z)=486;V(w)=518;V(v)=545;V(x)=665,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,点投票方法的性质,假设个体按照偏好强度真实投票,那无论是从平,均效率还是从孔多塞效率的角度来看,规那么运,行的效率水平都会有一定的保证,投票规那么存在战略性行为的鼓励,假设将所有点分配给最偏好的备选对象,点,投票退化为最多票数规那么。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,八、否决投票,否决投票Voting by veto的含义,给定议案下的议案否决,议案集合的选择和提供,否决投票程序的性质总结,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,1.否决投票Voting by veto的含义,每位参与投票的成员通常是委员会成员都,给出一个议案;,由一个随机过程来确定否决投票的顺序,参与,投票的人就按照随机过程所确定的顺序就其中,的一个投否决票,直到最后只剩下一个议案为止,该议案就是否,决投票的胜者,个体二元选择:选择议案与否决议案 ,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,2.给定议案下的议案否决:一个例子,表7,议案,投票人,V,1,V,2,V,3,a,1,1,2,3,a,2,3,1,2,a,3,2,3,1,a,0,4,4,4,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,1否决次序为V1V2V3时的个体选择与集体选择,表8,V,1,与V,2,的选择,V,3,可能的选择,V,3,的最优选择,胜者,a1、a2,a3、a0,a0,a3,a1、a3,a2、a0,a0,a2*,a1、a0,a2、a3,a2,a3,a2、a1,a3、a0,a0,a3,a2、a3,a0、a1,a0,a1*,a2、a0,a3、a1,a1,a3,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,1否决次序为V1V2V3时的个体选择与集体选择,表8(续),V,1,与V,2,的选择,V,3,可能的选择,V,3,的最优选择,胜者,a3、a1,a2、a0,a0,a2,a3、a2,a1、a0,a0,a1,a3、a0,a1、a2,a1,a2*,a0、a1,a2、a3,a2,a3,a0、a2,a1、a3,a1,a3,a0、a3,a1、a2,a1,a2*,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,2否决次序、个体选择与最终结果,表9,否决次序,个体最优选择,最终结果,V1V2V3,a2,a3,a0,a1,V1V3V2,a2,a1,a0,a3,V2V1V3,a3,a2,a0,a1,V2V3V1,a3,a1,a0,a2,V3V1V2,a1,a2,a0,a3,V3V2V1,a1,a3,a0,a2,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,3给定议案下否决投票过程的性质,结果确实定性与对循环的防止:循环为每一个议,案有1/3的获胜概率所取代;,决策结果与否决的次序有关,但次序是随机决定,的,因而不会存在人为的日程控制问题。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,3.议案集合的提供与选择:一个例子,表8,议案,投票人,V,1,V,2,V,3,a,1,1,2,3,a,2,3(2),1,2,a,3,2(3),3,1,a,0,4,4,4,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,1个体议案提供决策的特点性质,如果个体能够提高自己议案在其它个体偏好排序,中的地位,那么,该议案获胜的概率会得到显著,的提高。在表8所给出的例子中,除了否决次序为,V1V2V3这一情形之外,在其它的否决次序下,a2,均会称为获胜议案。,为了提升自己所提议案获胜的概率,个体有考虑,其它个体利益的鼓励。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,1个体议案提供决策的特点性质续,否决投票的鼓励效应在人数众多的情形中得到充,分的表达。就再分配问题而言,此时最终所选择,的往往是最公平的议案,次公平的议案虽然能得,到选择,但概率很低,而其它的议案根本无法得,到选择Mueller,1978),Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,2否决议案的鼓励效应证明:根本设定,根本设定,个体议案给出,其公平性由 ei定义和衡量。,按照公平性程度对其进行排序:p1、p2、pn、,pn+1,假设否决次序为:V1、V2、Vn,为便于分析,定义Vi所否决的议案为ri,并定义Ei,为Vi以后所有个体(包括Vi本人)所否决的议案集,合;,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,2否决议案的鼓励效应证明:具体过程 ,表9,i,ri,Ei,可能获胜议案集,V1,p3,或p2或p1,p,2,p,1,V2,p4,或p3或p2,p3,p2,p1,V,n-2,p,n,或p,n-1,或p,n-2,p,n+1,p,n,p,n-1,或,p,n+1,p,n,p,n-2,p,n-2,p,n-3,p,1,或,p,n-1,p,n-3,p,1,V,n-1,p,n,或p,n-1,p,n+1,p,n,或p,n+1,p,n-1,p,n-1,p,n-2,p,1,或p,n,p,n-2,p,1,V,n,p,n+1,p,n+1,p,1,p,2,p,n,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,4.否决投票性质的总结,鼓励效应与对个体利益的考虑,确定性与对循环的防止,对公共产品提供扩展,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,九、过程比较,孔多塞效率,功利主义效率,返回,上海财经大学,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,孔多塞效率,表9,投票机制,备选议案数,3,4,5,7,10,最多票数规则,79.1,69.4,62.1,52.0,42.6,赞同投票,76.0,69.8,67.1,63.7,61.3,二次选举,96.2,90.1,83.6,73.5,61.3,黑尔机制,96.2,92.7,89.1,84.8,77.9,库姆斯机制,96.3,93.4,90.2,86.1,81.1,波尔达计票,90.8,87.3,86.2,85.3,84.3,梅里尔(,Merrill,,1984)考虑25个投票者,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,功利主义效率,表10,投票机制,备选议案数,3,4,5,7,10,最多票数规则,83.0,75.0,69.2,62.8,53.3,二次选举,89.5,83.8,80.5,75.6,67.6,黑尔机制,89.5,84.7,82.4,80.5,74.9,库姆斯机制,89.7,86.7,85.1,83.1,82.4,孔多塞准则,93.1,91.9,92.0,93.1,94.3,波尔达计票,94.8,94.1,94.4,95.4,95.9,梅里尔(,Merrill,,1984)考虑25个投票者,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,第8讲 作业,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,习题1,在班长的选举过程中,在参选者为多个的,情况下,就最多票数规那么、二次选举、黑,尔机制、库姆斯机制等投票规那么来说,你,倾向于选择采用什么样的规那么来进行班长,的选举?请说明自己的观点并说明理由。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,习题2,?公共选择与政治立宪?第八章思考题的第四,题:采用最多票数规那么情况下,如果你是第四,组中的一名投票者,在知晓其它个体偏好的情,况下,你会如何进行投票?请就自己所选择的,投票方式说明自己的理由。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,习题3,在备选对象数为多个的情况下,如果采用加权,排序法来进行选择,就波尔达计票、赞成投票,与点投票这几种规那么而言,你倾向于选择采用,什么样的规那么来进行集体选择?请说明自己的,观点并说明理由。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,作业5,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,习题6,试就孔多塞准那么和波尔达计票这两种集体选择,规那么进行比较,就三者的优劣性进行评价并说,明自己的理由。,返回,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,上海财经大学,End,Thanks!,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2021 Aspose Pty Ltd.,
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