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Power indices suggest that adding new members to a voting body may increase the power of an existing member, even if the number of votes of all existing members and the decision rule remain constant. This phenomenon is known as the paradox of new members. This paper shows that the paradox has theoretically occurred in the EU using the leading model of legislative bargaining. Furthermore, it is possible for a majority of members to be in favor of enlargement, even if voters are bargaining over a fixed budget.

The Paradox of New Members in the Council of Ministers: A Noncooperative Approach