中文摘要：

在阐明二元随机偏好所存在缺陷的基础上,提出了一种更具普适性的随机偏好表示方法一概率分布型随机偏好,并论证了这种表示方法的完备性（即该方法可以表示所有可取的随机偏好）.然后基于概率分布型随机偏好,将Borda悖论涉及的两种投票规则推广为随机情况,分析随机偏好下Borda悖论的发生规律,并进一步从权值向量和投票人数两方面比较所得结论与确定性偏好下Borda悖论的异同,分析出现差异的原因.

英文摘要：

On the basis of illustrating the weakness of stochastic preferences based on strict order（SPSO）,this paper proposes a more universal representation which is called stochastic preference based on the probability distribution of extreme preferences（SPPDEP）,and demonstrates the completeness of SPPDEP,i.e.,SPPDEP can represent all feasible stochastic preferences.With SPPDEP,it extends two voting rules referred to as Borda＇s paradox into stochastic mode,and analyzes the occurrence regularities of Borda＇s paradox in this mode.Furthermore,comparing with the occurrence regularities of Borda＇s paradox in determinating mode,it discusses the similarities and differences between the two modes,and analyses for the reasons for those differences.