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）。一个投票规则是基于票差的，当且仅当任意两场选举若产生相同的候选人之间一对一胜败票差时，该投票规则在这两场选举中产生相同的结果。尽管这是一个数学上自然的、值得考虑的不变性性质，但应否将其视为投票规则的规范性公理则不甚明确。本文针对输出为任意类型（无论是候选人集合、排序、概率分布等）的投票规则，探讨了这一问题。我们证明：一个投票规则是基于票差的，当且仅当它满足某些具有更清晰规范性内涵的公理。其中一个关键公理是我们所称的偏好平等性，其表述为：若两名投票者均将候选人 $x$ 排在候选人 $y$ 的紧邻上方，则其中任意一名投票者改为将 $y$ 排在 $x$ 的紧邻上方，其对选举结果的影响与另一名投票者做出此改变时相同，从而每位投票者对 $y$ 优于 $x$ 的偏好被平等对待。