A methodological note on a weighted voting experiment

We conducted a sensitivity analysis of the results of weighted voting experiments by varying two features of the experimental protocol by Montero et al. (Soc Choice Welf 30(1):69-87, 2008): (1) the way in which the roles of subjects are reassigned in each round [random role (RR) vs. fixed role (FR)] and (2) the number of proposals that subjects can simultaneously approve [multiple approval (MA) vs. single approval (SA)]. It was observed that the differences in these protocols had impacts on the relative frequencies of minimum winning coalitions (MWCs) as well as how negotiations proceed. 3-player MWCs were more frequently observed, negotiations were much longer, subjects made less mistakes, and proposal-objection dynamics were more frequently observed, under the protocol with FR and SA than under the protocol with RR and MA.