In the context of voting with ranked ballots, an important class of voting rules is the class of margin-based rules (also called pairwise rules). A voting rule is margin-based if whenever two elections generate the same head-to-head margins of victory or loss between candidates, the voting rule yields the same outcome in both elections. Although this is a mathematically natural invariance property to consider, whether it should be regarded as a normative axiom on voting rules is less clear. In this paper, we address this question for voting rules with any kind of output, whether a set of candidates, a ranking, a probability distribution, etc. We prove that a voting rule is margin-based if and only if it satisfies some axioms with clearer normative content. A key axiom is what we call Preferential Equality, stating that if two voters both rank a candidate $x$ immediately above a candidate $y$, then either voter switching to rank $y$ immediately above $x$ will have the same effect on the election outcome as if the other voter made the switch, so each voter's preference for $y$ over $x$ is treated equally.

翻译：在排序投票的背景下，一类重要的投票规则是基于票差的规则（也称为成对规则）。如果一个投票规则在任意两次选举产生候选人之间相同的胜败票差时，都会给出相同的选举结果，则该规则是基于票差的。尽管从数学角度考虑这是一种自然的恒定性，但将其视为投票规则的规范性公理是否合理尚不明确。本文针对输出形式任意的投票规则（无论是候选人集合、排序、概率分布等）探讨了这一问题。我们证明：一个投票规则是基于票差的，当且仅当其满足若干具有更明确规范性内涵的公理。其中关键公理是我们提出的"偏好平等性"，即若两名投票者均将候选人$x$排在候选人$y$的紧邻上方，则任一投票者改为将$y$排在$x$紧邻上方所产生的影响，与另一投票者做出相同改动时的影响完全一致，这意味着每位投票者对$y$优于$x$的偏好被平等对待。