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John Banzhaf is a legal scholar associated with the mathematical study of the Banzhaf index. His university profile identifies the index bearing his name.^[ref]

The probabilistic Banzhaf index averages a player's marginal contribution over all coalitions not containing that player, each given equal weight. In a simple cooperative game, it is the probability of changing a losing coalition into a winning one when every other player joins independently with probability $1/2$. Its sum over players need not equal the grand-coalition value: in a three-player majority game each player has index $1/2$, giving total $3/2$ despite $v(N)=1$. This convention differs from both the raw count of pivotal coalitions and the normalized Banzhaf index.

The name refers to John Banzhaf, whose 1965 paper addresses the mathematical analysis of weighted voting.^[ref]

By John Banzhaf. The author's own reference page identifies the article as Rutgers Law Review, volume 19, starting p. 317, 1965. That bibliographic evidence does not imply that the article's complete text was inspected.

Author's reference page: banzhaf.net/about/BanzhafIndexofVotingPower.html