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 $n$. In addition, positive involvement can be replaced by negative involvement (if a candidate $x$ loses in an initial preference profile, then adding a voter who ranks $x$ uniquely last cannot cause $x$ to win). In a previous note, we proved an analogous result assuming an additional axiom of ordinal margin invariance, which we now show is unnecessary for an impossibility theorem, at least if the desired voting method is defined for five-candidate elections.

翻译：我们证明不存在满足以下条件的偏好投票方法：同时满足孔多塞赢家准则与输家准则、正向参与准则（若候选人$x$在初始偏好分布中获胜，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$n$投票者可解性准则（若$x$在初始计票中与其他候选人并列获胜，则通过增加至多$n$位投票者可使$x$成为唯一获胜者）。该不可能性定理对任意正整数$n$均成立。此外，正向参与准则可替换为负向参与准则（若候选人$x$在初始偏好分布中落败，则增加一位将$x$唯一排在末位的投票者不会导致$x$获胜）。在先前的笔记中，我们在假设序数边际不变性公理的前提下证明了类似结论，而本文表明该公理对于不可能性定理并非必要——至少当所讨论的投票方法需适用于五候选人选举时如此。