著名的孔多塞陪审团定理是投票理论的基本理论基础。基于该定理仅限于所有投票个体对方案的偏好选择都必须具有相同的概率,而这种情况在现实投票中是不可能发生的,因此实际上它只是给出了一般情况的一个特例。本文实质性地扩展了孔多塞陪审团定理,建立了每一名投票个体对方案的偏好选择都具有各自不同概率的情况下,投票群体使用多数偏好规则对方案作出严格偏好选择概率的恰当陪审团定理。同时,给出了由所建立定理确定的群体严格偏好概率的若干重要性质。最后,还证明了当投票个体人数无限增多时,由该定理确定的群体严格偏好概率将趋于其最大极限值1。
The famous Condorcet jury theorem provides the theoretical foundation for voting theory. Based on this theorem, it is only limited that all voters must have the same probability in their preference for the alternatives, which is impossible to happen in real voting, so in fact it only gives a special case of the general situation. This paper substantively extends the Condorcet jury theorem, and establishes a proper jury theorem for the relationship between the probability of the voting group using the majority preference rule to make a strict preference choice for the alternatives when each voter has its own different preference probabilities for the alternatives. At the same time, some important properties of the group strict preference probability determined by the established theorem are given. Finally, it is also proved that when the number of voters increases infinitely, the group strict preference probability determined by this theorem will tend to its maximum limit value of 1.
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