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Computer model of the Banzhaf power index from the Wolfram Demonstrations Project. The Banzhaf power index, named after John Banzhaf (originally invented by Lionel Penrose in 1946 and sometimes called Penrose–Banzhaf index; also known as the Banzhaf–Coleman index after James Samuel Coleman), is a power index defined by the probability of changing an outcome of a vote where voting rights ...
The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
The Shapley–Shubik power index was formulated by Lloyd Shapley and Martin Shubik in 1954 to measure the powers of players in a voting game. [ 1 ] The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players in an n -player game .
Above μ can be vector valued (as long as the function is defined and differentiable on the range of μ, the above formula makes sense). In the argument above if the measure contains atoms μ ( t I ) = t μ ( I ) {\displaystyle \mu (tI)=t\mu (I)} is no longer true—this is why the diagonal formula mostly applies to non-atomic games.
The Roman assemblies provided for weighted voting after the person's tribal affiliation and social class (i.e. wealth). Rather than counting one vote per citizen, the assemblies convened in blocs (tribes or centuries), with the plurality of voters in each bloc deciding the vote of the bloc as an entity (which candidate to support or whether to favor or reject a law, for instance).
John Francis Banzhaf III (/ ˈ b æ n z. h ɑː f /; [1] born July 2, 1940) is an American public interest lawyer, legal activist, and law professor at the George Washington University Law School. He is the founder of an antismoking advocacy group, Action on Smoking and Health . [ 2 ]
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An alternative formula was proposed by Grigorii Golosov in 2010. [9]= = + which is equivalent – if we only consider parties with at least one vote/seat – to = = + (/) Here, n is the number of parties, the square of each party's proportion of all votes or seats, and is the square of the largest party's proportion of all votes or seats.