Stable set and voting rules

We consider a voting situation where a society has to decide on the rule to use when choosing among two alternatives in the uncertain future. Our analysis is related to the set up of Barbera and Jackson [Barbera, S. and Jackson, M. (2004), 'Choosing how to choose: Self-stable majority rules and constitutions', Quarterly Journal of Economics 119 (3), 1011-1048.]. While they consider finite societies in our set up the economy has an infinite amount of agents. We define a binary dominance relation over the set of decision rules and determine the von Neumann and Morgenstern stable set of voting rules. It turns out that the stable set always exists and is unique in the infinite economy's case. The stable set is, however, not a singleton. Additionally the stable set contains the set of self-stable voting rules that is the solution concept used by Barbera and Jackson.