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.