The reinforcement axiom under sequential positional rules

The reinforcement axiom roughly states that when an alternative is selected by two different constituencies, it must also be selected by their union. Hare and Coombs rules are special cases of sequential positional voting rules, which are known to violate this axiom. In this article, we first show that reinforcement can be violated by all such rules. We then evaluate, by the use of Monte Carlo simulations and the Fishburn–Gehrlein technique, the proportion of profiles at which this phenomenon occurs.