How would that work using the other formula? (I know I'm kinda just being lazy here, but I think other people would be interested.)
Jameson 2012/12/14 Ross Hyman <[email protected]> > example using entropy formula > two parties that split the vote equally: > 1/2 , 1/2 effective number of parties n_a=2 > One of these parties divides equally: > 1/2, 1/4, 1/4 effective number of parties n_b= 2sqrt(2) > now the other party also divides equally: > 1/4, 1/4, 1/4, 1/4 effective number of parties n_c= 4 > > n_b/n_a = n_c/n_b = sqrt(2) > > Splitting one party has the same effect on the ratio, regardless if the > other party has split or not. > > > > --- On *Fri, 12/14/12, Ross Hyman *wrote: > > > Consider that there are a number of parties, with the ith party having > vote fraction P_i. Now consider that you can divide the parties into two, > left parties and right parties. Call the vote fraction for the left parties > P_L and the vote fraction for the right parties P_R. Use the effective > number of parties formula to determine the effective number of left parties > N_L and the effective number of right parties N_R. Using the entropy > formula, if only N_L changes, the ratio of the new number of total > effective parties over the old number of total effective parties depends > only on P_L, the new N_L and the old N_L. It will not depend at all how > the right parties divide up their votes. No other formula will do this. > > > > > Interesting. When is it different from the other formula? > > Jameson > > > Here is a physics alternative to the "effective number of parties" > formulas mentioned on the Wikipedia page: > http://en.wikipedia.org/wiki/Effective_number_of_parties > > Based on the concept of entropy, a sensible formula for the effective > number of parties = exp(-sum_i P_i log(P_i)) > > where P_i is the portion of the votes or portion of seats for party i. > sum_i P_i =1. > > It is sensible because for an election where n parties get 1/n of the vote > each and the rest of the parties get zero votes, the effective number of > parties from the entropy formula is n. > > > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > >
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