The house size effect and the referendum paradox in U.S. presidential elections

Barthélémy et al. (2014), extending the work of Neubauer and Zeitlin (2003), show that some U.S. presidential elections are subject to a ‘House size effect’ in that the winner of the election, i.e., the candidate who wins a majority of electoral votes, depends on the size of the House of Representatives. The conditions for the effect relate to the number of ‘Senate’ versus ‘House’ electoral votes won by each candidate, but the relationship is not straightforward due to ‘locally chaotic’ effects in the apportionment of House seats among the states as House size changes. Clearly a Presidential election that is subject to the House size effect exhibits the referendum paradox, i.e., the electoral vote winner is the popular vote loser, for some House sizes but not for others.