Talk:Penrose method

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[edit] Talk:Penrose method/CSV

Here is a CSV file that you can use to do your own Penrose analysis. It uses data from List of countries by population as of December 15, 2005. At the bottom are world totals. See Talk:Penrose method/CSV Captain Zyrain 17:57, 15 December 2005 (UTC)

[edit] Fractional...

Is it just me, or is everyone else seeing that this list shows fractional seats? The article doesn't propose any method for rounding these numbers. Wouter Lievens 13:34, 3 July 2006 (UTC)

For me the relevant question is how strong is the population increase before another seat is added. I've checked and come to the conclusion that consistent rounding up of seats results in the lowest average span of population change covered by an increase of seats if that makes it clear. 84.190.216.158 09:52, 1 November 2007 (UTC)

[edit] Information vs. filler

  1. Does this article really need the 200 row table detailing countries' populations and their Penrose numbers? I'm not an expert in Wikipedia mark-up, but is there some way to minimize (and to expand) the table on demand? Give it another, related page?
  2. An account of Penrose's reasoning would be much more illuminating than just the results. Does anyone have the mathematical background for this?

--75.15.153.109 08:51, 11 June 2007 (UTC)

The reasoning behind the square root method is:
1) Penrose defines the "voting power" of an individual as the probability that his vote can tip the balance, all other votes are random events with equal probability of 1/2 for yes/no.
2) When there are N votes you need to calculate the probability p for half of them voting yes, which can be done using the binomial distribution (probability mass function)
3) You need to get rid of the the nasty factorials using Stirling's approximation and get the surprisingly simple equation p=(2/(pi N))^1/2 which is the voting power (as defined by Penrose) for an idivisual and it is proportional to 1/sqrt(N).
4) To compensate for this you need to weight the representative's votes with the square root of N. see e.g. http://arxiv.org/ftp/cond-mat/papers/0405/0405396.pdf 131.111.117.97