Borda rule as an almost first-order stochastic dominance rule

In single-winner elections and individuals expressing linear orderings, an alternative has first-order stochastic dominance if the cumulative standing for this alternative at each rank is higher than that of the other alternatives. It is well-known that this criterion may fail in ranking the competing alternatives since the first-order stochastic dominance winner may not exist in some situations. Making an adaptation of a centrality measure from network theory, we introduce in this note a rule, called the almost first-order stochastic dominance rule, which selects the alternative having first-order stochastic dominance if such an alternative exists, otherwise it selects the alternative which is close to achieve first-order stochastic dominance. It turns out that this rule is equivalent to the well-studied Borda rule. This result highlights an unknown property of the Borda rule.