We prove that there is no preferential voting method satisfying the Condorcet winner and loser criteria, positive involvement (if a candidate $x$ wins in an initial preference profile, then adding a voter who ranks $x$ uniquely first cannot cause $x$ to lose), and $n$-voter resolvability (if $x$ initially ties for winning, then $x$ can be made the unique winner by adding some set of up to $n$ voters). This impossibility theorem holds for any positive integer $n$. It also holds if either the Condorcet loser criterion is replaced by independence of clones or positive involvement is replaced by negative involvement.
翻译:我们证明不存在满足孔多塞赢家准则与输家准则、积极介入性(若候选人$x$在初始偏好剖面中获胜,则增加一位将$x$唯一排在首位的投票者不会导致$x$落败)以及$n$投票者可解性(若$x$初始与其他候选人并列获胜,则可通过增加至多$n$位投票者使$x$成为唯一获胜者)的优先投票方法。该不可能性定理对任意正整数$n$均成立。若将孔多塞输家准则替换为克隆独立性,或将积极介入性替换为消极介入性,该定理依然成立。