[EM] an entropy formula for the effective number of parties

Ross Hyman 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...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20121214/b61c5719/attachment-0004.htm>

More information about the Election-Methods mailing list