The Paradox of Coalition Trading

Abstract

We present a model of coalition formation in a multiparty and multiparliament system in which several parties can agree on simultaneously exchanging their votes in a set of parliaments. Given this possibility, a party, acting rationally in its own self-interest, could accept sharing oversized majority coalitions in some parliaments with numerically superfluous partners. We present a formal argument in instances with diverse numbers of parties and parliaments. We propose a newly invented and refined parliamentary power index in order to measure and compare the benefits of different coalition strategies. We also present empirical evidence of situations prone and adverse to this paradoxical but rationally self-interested behaviour by parties acting in local parliaments in Spain.