Enlargement and the Balance of Power: an Experimental Study

Many important decisions are taken according to weighted majority rule. Power indices predict that enlargement of the 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 existing voters may actually gain, a phenomenon known as the paradox of new members. We test for this effect using laboratory experiments. Participants propose and vote on how to divide a budget according to weighted majority voting rules, and we measure the voting power of a player by his average payoff in the experiment. By comparing voting power across voting bodies of varying size, we find empirical support for the paradox of new members. Our results also allow an assessment of the predictive performance of standard power indices.