Shapley-Shubik/Banzhaf power indices

power_indices.rb

# coding: utf-8
require 'mathn'

class PICalc
  def initialize name, parties
    @name = name
    @parties = parties
    @total = parties.values.inject :+
    @perms = parties.to_a.permutation.to_a
  end

  def ss pass_rate
    thresh = @total * pass_rate
    dic = Hash[@parties.map{|k,| [k, 0] }]
    @perms.each do |pe|
      sum = 0
      key = pe.each{|k, v| break k if (sum += v) > thresh }
      dic[key] += 1
    end
    show :'Shapley-Shubik', pass_rate, dic, @perms.size
  end

  def b pass_rate
    thresh = @total * pass_rate
    dic = Hash[@parties.map{|k,| [k, 0] }]
    ptotal = @parties.size ** 2
    (1...ptotal).each do |vec|
      sum = 0
      @parties.each_with_index{|(_, v), i| sum += v * vec[i] }
      @parties.each_with_index do |(k, v), i|
        next if vec[i] == 0 and not (sum...sum+v) === thresh
        next if vec[i] == 1 and not (sum-v...sum) === thresh
        dic[k] += 1
      end
    end
    show :Banzhaf, pass_rate, dic, ptotal
  end
  
  def show type, rate, dic, total
    puts "#{type} Power Indices of #@name\n(over #{rate} seats needed)"
    puts dic.sort_by{|_, v| -v }.map!{|k, v| "#{k}\t#{v / total}" }
    puts
    self
  end
end

{ #http://www.shugiin.go.jp/itdb_annai.nsf/html/statics/syu/kaiha_m.htm
  衆議院: {
    民主: 311,
    自民: 119,
    公明: 21,
    共産: 9,
    社民: 7,
    他: 13,
  },
  #http://www.sangiin.go.jp/japanese/joho1/kousei/giin/173/giinsu.htm
  参議院: {
    民主: 120,
    自民: 85,
    公明: 21,
    共産: 7,
    社民: 5,
    他: 4,
  },
}.each{|_| PICalc.new(*_).ss(1/2).ss(2/3).b(1/2).b(2/3) }