---------- Forwarded message ---------- From: Raph Frank <raph...@gmail.com> Date: Tue, Apr 27, 2010 at 2:51 PM Subject: Re: [EM] Proportional election method needed for the Czech Green party - Council elections To: Peter Zbornik <pzbor...@gmail.com>
On Tue, Apr 27, 2010 at 9:18 AM, Peter Zbornik <pzbor...@gmail.com> wrote: > thanks for your information and the short explanation on STV. > I was thinking about d'Hondt's method in general. D'Hondt is equivalent to the Jefferson Method. It is clearer why that is proportional. 1) pick an initial divisor 2) divide each party's vote total by the divisor 3) For each party round down to the nearest whole number of seats 4) If the total number of seats is correct, then finish 5) Otherwise, update to a better divisor and repeat (go to 2) Lots of divisors will give the correct number of seats, but they always give the same number of seats per party. So, you take each party's vote total, divide it by a number and then round downward. This means that the method is proportional, except for rounding errors. The divisor will work out to be around (votes cast)/(seats). Sainte-Lague rounds to the nearest whole number rather than rounding downwards. This is why Sainte Lague is fairer (though there can be strategy issues for smaller parties). Anyway, the process for d'Hondt is equivalent to: The initial divisor is set equal to the number of votes received by the largest party. When you divide all the other parties' totals by this value, they all give a fraction less than one, so none of the other parties receive any seats. The largest party gets 1 seat. This is the same as d'Hondt. When updating the divisor, we reduce it by just enough so that 1 additional seat is assigned. If party has N seats and V votes, then the divisor must drop below divisor = V/(N+1) before it will get the next seat. So, according to the update rule, we reduce the divisor so that at most one more party gets a seat. Therefore, we need to find the party who gets its next seat at the highest possible divisor. So, we pick the party with the highest V/(N+1) and we set the divisor so that they get 1 more seat. So, we set the divisor to slightly below the above number. This means that the party who has the highest V/(N+1) gets the next seat in each step. However, this is exactly what d'Hondt does. It just doesn't calculate the divisors at each step.
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