On 06/26/2012 04:34 PM, Michael Ossipoff wrote:
Kristofer:
You said:
Similarly, if you pick two states/parties j and k, Webster minimizes the
absolute value of S_j/P_j - S_k/P_k, i.e. the difference between "seats
per population" (share of influence per person) of state j and k.
[endquote]
Of course you can't mean that. You're referring to Webster's transfer
property:
If, starting with the Webster allocation, one state gives a seat to
another state, then that will increase the difference between their s/p.
It certainly will never decrease it.
That pair difference minimization only applies to two states during a
transfer of a seat.
The RangeVoting page says what you quoted me as saying. I'll quote more
literally.
Under "Pairwise optimality properties",
http://rangevoting.org/Apportion.html :
"Let S_k be the number of seats for state k and P_k be its population.
For all j,k, Adams minimizes |S_j - S_k P_j/P_k|.
Dean minimizes |P_j/S_j - P_k/S_k|
Huntington-Hill minimizes |S_j P_k/(S_k P_j) - 1|
Webster minimizes |S_j/P_j - S_k/P_k|
(...)".
Seems pretty unambiguous to me!
By the way, according to the same RangeVoting page, the method you
wished to see (that minimizes max s/p) is Jefferson (D'Hondt). See the
global properties list, #4. Unfortunately, Jefferson is biased in favor
of large parties.
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