Gaining power through enlargement: Strategic foundations and experimental evidence

Power indices suggest that adding new members to a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the original members may actually gain even if voters are bargaining over a fixed budget. We show that this phenomenon can occur as an equilibrium of a non-cooperative bargaining game based on the Baron-Ferejohn (1989) model of legislative bargaining. We implement this game in the laboratory and find that power can be gained by adding new members as the theory predicts.