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

Jameson Quinn jameson.quinn at gmail.com
Fri Dec 14 07:59:23 PST 2012

```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 <rahyman at sbcglobal.net>

> 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"
> 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.
>
>
>
>
>
> ----
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>
>
>
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>
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