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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]
This is justified by the fact that, due to the square root law of Penrose, the a priori voting power (as defined by the Penrose–Banzhaf index) of a member of a voting body is inversely proportional to the square root of its size. Under certain conditions, this allocation achieves equal voting powers for all people represented, independent of ...
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[1] [2] [3] It states that the a priori voting power of any voter, measured by the Penrose–Banzhaf index scales like /. This result was used to design the Penrose method for allocating the voting weights of representatives in a decision-making bodies proportional to the square root of the population represented.
In contrast to this 2-stage application, the article currently deals with 1-stage systems only, as applies to the Banzhaf indexes of people in referendums or the Banzhaf indexes of delegations in parliaments. It would be interesting to show how these indexes translate to the indexes of the people electing the delegations.
The Shapley-Shubik power index for these command games are collectively denoted by a power transit matrix Ρ. The authority distribution π is defined as the solution to the counterbalance equation π=πΡ.
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.