A Note on a Weighted Voting Experiment: Human Mistakes in Cooperative Games

We conducted a sensitivity analysis of results in weighted voting experiments by varying the following two features of the protocol by Montero et al. (2008): (a) the way subjects' roles are reassigned in each round (random versus semi-fixed roles) and (b) the number of proposals that subjects can approve simultaneously (multiple versus single approval). We found that the possibility of simultaneously approving many proposals (multiple approvals) may result in more confusion and mistakes by subjects than the case without such a possibility (single approval). We also found that frequencies of minimal winning coalitions (MWCs) observed under the protocol with semi-fixed roles and single approval are consistent with our hypothesis: each subject prefers a MWC in which his or her relative weight is larger, and the probability of each MWC occurring depends on a score in the social ordering determined by the Borda count, when there is no veto player.