The ability of groups to implement efficiency‐enhancing institutions is emerging as a central theme of research in economics. This study explores voting on a scheme of intergroup competition, which facilitates cooperation in a social dilemma situation. Experimental results show that the competitive scheme fosters cooperation. Competition is popular but the electoral outcome depends strongly on specific voting rules of institutional choice. If the majority decide, competition is almost always adopted. If likely losers from competition have veto power, it is often not, and substantial gains in efficiency are foregone.