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Version 4 (Panagiotis Louridas, 05/07/2010 03:52 pm)

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h1. Calculation of Voting Power
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This is a project hosting software for calculating the voting power of voters with weighted votes in an assembly.
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The software is open source and released under the terms of the "BSD license":http://www.opensource.org/licenses/bsd-license.php.
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h1. Overview
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A common error is the assumption that, in weighted voting, the power of a voter is their voting weight. In reality, although the weight of a voter is important, we must take into account the weights of the other voters, as well as the decision making rule, in order to arrive at a conclusion about the actual voting power each participant in the vote has.
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The term _voting power_ refers to an index that captures the power of a voter to influence the outcome of a voting process. There have been several definitions of voting power in the literature, although they remained outside the discussions of mainstream politics until late in the 20th century; what's more, definitions of voting power were proposed, forgotten, and reinvented during the years. Perhaps the most intuitive definition is the one given by "Lionel Sharples Penrose":http://en.wikipedia.org/wiki/Lionel_Penrose in 1946; according to this definition, the voting power of a voter is the probability that they can swing the vote. This is known as the Penrose index or the "Penrose Banzhaf index":http://en.wikipedia.org/wiki/Penrose%E2%80%93Banzhaf_index, after "John Francis Banzhaf III":http://en.wikipedia.org/wiki/John_F._Banzhaf_III who reinvented the index in 1965.
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The index is as follows:
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* Suppose we have _n_ voters, each with a specified weight.
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* The voters are free to vote as they please.
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* All votes are _yes_ or _no_.
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* There is a rule that decides when a vote passes; it may be 50% of the weights of the proponents (simple majority), or some other figure; in addition, it may require that a number of voters also support (a given quorum).
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* A voter is critical in a vote if without them the vote does not pass, but with them it passes. That is, the vote must be a swing vote, decided by the voter.
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* Count the number of critical votes for a voter.
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* Take all possible partitions of voters in yes and no camps.
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* Divide the number of critical votes for a voter by the number of all possible voter partitions.
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* The result is the probability that the voter can swing a vote.
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The above definition does not lead to a practical procedure for non-toy problems, as suffers from combinatorial explosion regarding the enumeration of swings and the partitions; hence, one has to find an alternative method to calculate it for many real-world assemblies.
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h1. The Software
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The software consists of a "Perl script":http://code.grnet.gr/projects/voting-power/repository/entry/voting_power.pl that calculates the Penrose index. It calculates the index by a Monte Carlo method: it generates a large number of voter groups and determines the percentage of those where a voter is critical; this is the Penrose index for the voter. Currently it does not give a confidence interval for the estimate it provides; however, since there will be a number of voters with identical weights, one can check how accurate the results are by noting the differences between voters with identical weights.
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To use the program, type
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<pre>
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perl voting_power.pl < voter_file
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</pre>
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The input file is a text file containing in each line the id of the voter, a colon, and the number of votes, e.g.:
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<pre>
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France:4
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Germany:4
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Italy:4
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Belgium:2
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Netherlands:2
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Luxembourg:1
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</pre>
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(These were the weights of the countries that formed the first European Economic Community in the "Treaties of Rome":http://en.wikipedia.org/wiki/Treaties_of_Rome in 1957 - 1958. Interestingly, Luxembourg had a vote but no voting power.)
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The voting rule and the precision is specified by the following switches:
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<pre>
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-q, --quorum
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     Set the quorum (number of voters required to reach decision)
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-s, --samples
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     Set the number of samples
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 -t, --threshold
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     Set the threshold (amount of votes required to pass)
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</pre>
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h1. Support
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For questions, comments, suggestions, etc., you may contact its author, Panos Louridas. The address is the author's surname at the hosting organisation (grnet in greece).