[EM] an entropy formula for the effective number of parties
rahyman at sbcglobal.net
Fri Dec 14 06:58:26 PST 2012
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?
Here is a physics alternative to the "effective number of parties" formulas mentioned on the Wikipedia page:
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
-------------- next part --------------
An HTML attachment was scrubbed...
More information about the Election-Methods