Simple games with many effective voters

The strategic behavior of legislators depends on the information available before and during the legislation process. It is well established in the literature that interested parties such as voters and agenda setters can influence the outcomes of the process through strategic manipulation when they are sufficiently informed. When only partial information on the individual and collective preference is revealed the question of manipulability boils down to how much information must be revealed before a learner is able to use it strategically? This paper applies a model of single agent learning to address this question. Our results show that learning collective preferences in this setting is possible but hard, giving explicit bounds on the amount of information required. The proofs use a Ramsey type theorem for simple games showing that games with many effective voters embed games from at least one of three well-characterized families.