[EM] proportionally electing a number of candidates to a parliament whose size is determined by the voting method

[Richard Lung]

Binomial STV does this because all the preferences are counted, 
including blanks, so that a quota or more of non-preferences may oblige 
a seat or more to remain vacant. The count is not only of NOTA blank 
ballots but of all unrecorded preferences.
At its most basic, a first order Binomial STV, there is just one 
election count of all preferences. And one exclusion count of all 
reversed preferences.

Richard Lung.


On 10/11/2016 23:00, Ross Hyman wrote:
> Last month or so someone wrote on the list about using a voting method to both elect candidates proportionally and to determine how many winning candidates there should be.
>
> The Phragmen* method produces a proportional list from approval style ballots and can be used to determine the number of seats that there should be to maximize representation.
>
> If candidate A is Nth on the list, the Representation is N*V_A/(S_A+1), that is N times the priority that elected candidate A.  The representation is a measure of the number of ballots that are fairly represented.  Note that if V candidates elected all m of the first m candidates, then the representation is V for m seats.  If V/2 ballots elected m/2 of the candidates and another V/2 ballots elected another m/2 of the candidates, the representation is also V for the m seats.  If there is one candidate approved by every ballot, then that candidate will be elected into position 1 and representation will be maximized for a one seat parliament.  In general, the representation can go up or down or stay the same as function of parliament size.
>
> The number of elected candidates can be chosen to be the smallest number of elected candidates in which representation is maximized, or chosen to be the smallest number of elected candidates in which the representation exceeds some fraction of the total number of ballots.
>
> *Phragmen method:
> Starting with each ballot’s load set to zero, at each stage candidates are elected to the list that minimize the maximum load.  The load to elect candidate A is (S_A +1)/V_A, where S_A is the total load of all ballots that approve candidate A and V_A is the total number of ballots that approve candidate A.  Alternatively one can talk about maximizing the priority V_A/(S_A +1).  After the candidate with the lowest load or highest priority is elected, the loads of each ballot that elected that candidate, say A, are changed to the load (S_A +1)/V_A.
> ----
> Election-Methods mailing list - seehttp://electorama.com/em  for list info


-- 
Richard Lung.
http://www.voting.ukscientists.com
Democracy Science series 3 free e-books in pdf:
https://plus.google.com/106191200795605365085
E-books in epub format:
https://www.smashwords.com/profile/view/democracyscience

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20161111/19e21e6b/attachment.htm>