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  • Further mapping: a win and a near miss

    Jun 9, 2022 GIS voting

    In this post we look at two Divisions from the recent Federal election: the inner city seat of Melbourne, and the bayside seat of Macnamara. Up until the recent election, Melbourne was the only Division to have a Greens representative. Macnamara, previously known as "Melbourne Ports" has been a Labor …

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  • Post-election mapping

    Jun 5, 2022 GIS voting

    This continues on from the previous post, trying to make some sense of the voting in my electorate of Wills and the neighbouring electorate of Cooper. Both these electorates (or more formally "Divisions"), as I mentioned in the previous post, are very similar in their geography, demography, and history. Last …

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  • Post-election swings

    May 22, 2022 GIS voting

    So the Australian federal election of 2022 is over as far as the public is concerned; all votes have been cast and now it's a matter of waiting while the Australian Electoral Commission tallies the numbers, sorts all the preferences, and arrives at a result. Because of the complications of the voting system, and of all …

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  • Voting power (7): Quarreling voters

    Jan 24, 2021 voting algebra python

    In all the previous discussions of voting power, we have assumed that all winning coalitions are equally likely. But in practice that is not necessarily the case. Two or more voters may be opposed on so many issues that they would never vote the same way on any issues: such a pair of voters may be said to be …

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  • Voting power (6): Polynomial rings

    Jan 22, 2021 voting algebra python

    As we have seen previously, it's possible to compute power indices by means of polynomial generating functions. We shall extend previous examples to include the Deegan-Packel index, in a way somewhat different to that of Alonso-Meijide et al (see previous post for reference). Again, suppose we consider the voting game …

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  • Voting power (5): The Deegan-Packel and Holler power indices

    Jan 14, 2021 voting algebra python julia

    We have explored the Banzhaf and Shapley-Shubik power indices, which both consider the ways in which any voter can be pivotal, or critical, or necessary, to a winning coalition. A more recent power index, which takes a different approach, was defined by Deegan and Packel in 1976, and considers only minimal winning …

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  • Voting power (4): Speeding up the computation

    Jan 6, 2021 voting algebra julia

    Introduction and recapitulation Recall from previous posts that we have considered two power indices for computing the power of a voter in a weighted system; that is, the ability of a voter to influence the outcome of a vote. Such systems occur when the voting body is made up of a number of "blocs": these may …

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  • Voting power (3): The American swing states

    Jan 3, 2021 voting algebra

    As we all know, American Presidential elections are done with a two-stage process: first the public votes, and then the Electoral College votes. It is the Electoral College that actually votes for the President; but they vote (in their respective states) in accordance with the plurality determined by the public vote. …

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  • Voting power (2): computation

    Dec 31, 2020 voting algebra

    Naive implementation of Banzhaf power indices As we saw in the previous post, computation of the power indices can become unwieldy as the number of voters increases. However, we can very simply write a program to compute the Banzhaf power indices simply by looping over all subsets of the weights: 1def banzhaf1(q,w): 2 …

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  • Voting power

    Dec 30, 2020 voting

    After the 2020 American Presidential election, with the usual post-election analyses and (in this case) vast numbers of lawsuits, I started looking at the Electoral College, and trying to work out how it worked in terms of power. Although power is often conflated simply with the number of votes, that's not necessarily …

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