It does this by taking a page from STV and dealing with votes that are in surplus of what is needed to get the candidate elected.
If
V = the current value of the vote
M = the amount of candidates on the ballot currently in the winner's circle
The quota of normal SAV is:
V = 1/M + 1
Or, using hte webster (St. Lague) quota it would be:
V= 1/M2+1 (I think..)
I'm going to add two new statistics to that quota:
W = The amount of votes within the desired quota (such as the Hare quota of Votes/Seats, or the droops quota of (Votes/Seats +1) +1)
S = The amount of votes in surplus of this quota
The new quota would be:
V = S+(W * (1/M + 1))
Now you are only reducing the votes by the votes that they needed to cast - not the ones in excess. Therefore, it doesn't have the same reason to withold votes from candidates that are likely to win anyway, and I have yet to create a race where this system and Simmons' system produced different results, yet this is much simpler, possibly more simple than STV.
Alternatively, you could only divide the votes of a random subset of the voters proportionate to the amount under the quota. And even simpler system, which is actually a version of the one used in Ireland and Australia, but it obviously has variable results, unlike the new quota which I proposed.
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