An experimental study on learning about voting powers

We investigate experimentally whether subjects can learn, from their limited experiences, about relationships between the distribution of votes in a group and associated voting powers in weighted majority voting systems (WMV). Subjects are asked to play two-stage games repeatedly. In the second stage of the game, a group of four subjects bargains over how to divide fixed amount of resources among themselves through the WMV determined in the first stage. In the first stage, two out of four subjects in the group, independently and simultaneously, choose from two options that jointly determine the distribution of a given number of votes among four members. These two subjects face a 2 ~ 2 matrix that shows the distribution of votes, but not associated voting powers, among four members for each outcome. Therefore, to obtain higher rewards, subjects need to learn about the latter by actually playing the second stage. The matrix subjects face in the first stage changes during the experiment to test subjects' understanding of relationships between distribution of votes and voting power. The results of our experiments suggest that although (a) many subjects learn to choose, in the votes apportionment stage, the option associated with a higher voting power, (b) it is not easy for them to learn the underlying relationships between the two and correctly anticipate their voting powers when they face a new distribution of votes.