[EM] PR, Approval ballots, "power"

[Adam Tarr]

>if I am a voter, my "power" for
>a given set of winners is the sum of
>
>([TotalOfAllPower] / [NumberOfSeats]) / [NumberOfVotersForThisCandidate]

>(Every ballot initially has strength: (TotalOfAllPower)/(NumberOfAllVoters).

>2. The strength of every ballot who voted for this candidate is reduced by:
>((TotalOfAllPower)/(NumberOfSeatsTotal)) / (VotersForThisCandidate).

I don't follow what these variables (especially "power") mean.  Please 
explain exactly what they are.

>It seems
>a desirable quality that the Approval winner is always elected.

Not necessarily.  Foe example, if the candidates are left of center, right 
of center, and center, and you're electing two seats, then electing center 
(the probably approval winner) will result in a lopsided slate of 
candidates.  Some voters are over-represented, and others are 
under-represented.  The same would be true with left, left-center, center, 
right-center, and right, with four seats.

This sort of problem is an inherent weakness of any "sequential" PR method, 
which elects one candidate, adjusts some weights, and then elects the next 
candidate.  If you wrote your simulation to actually step through every 
possible slate of candidates, and find the one that equalized voter "power" 
to the greatest extent possible, you would probably avoid these issues.

>Any thoughts?

Only that you may as well look at the PAV links I provided earlier:  Here's 
the initial thread about it:

http://groups.yahoo.com/group/election-methods-list/message/6367

and here's some commentary I had before (which is particularly germane to 
your approach):

http://groups.yahoo.com/group/election-methods-list/message/8744

-Adam
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