Choosing Voting Systems for Two-Tier Voting Behind the Veil of Ignorance: An Experiment

There are many situations in which different groups make collective decisions by committee voting, with each group represented by a single person. A natural question is what voting system such a committee should use. Concepts based on voting power provide guidelines for this choice. The two most prominent concepts require the Banzhaf power index to be proportional to the square root of group size or the Shapley-Shubik power index to be proportional to group size. Instead of studying the choice of voting systems based on such theoretical concepts, in this paper, I ask which systems individuals actually prefer. To answer this question, I design a laboratory experiment in which participants choose voting systems. I find that people behind the veil of ignorance prefer voting systems following the rule of proportional Shapley-Shubik power; in front of the veil subjects prefer voting systems benefiting their own group. Participants’ choices can only partially be explained by utility maximization or other outcome based concepts.