Three models are presented in which two players agree to share power in a particular ratio, but either player may subsequently "fire" at the other, as in a duel, to try to eliminate it. The players have positive probabilities of eliminating each other by firing. If neither is successful, the...

In U.S. presidential elections, voters in noncompetitive states seem not to count — and so have zero voting power, according to the Banzhaf and other voting-power indices — because they cannot influence the outcome in their states. But because the electoral votes of these states are...