A range voting generalization is the following:
The score that the ith ballot assigns to the ath candidate is s_i,a. v_i,a is
the vote assigned to candidate a from the ith ballot. The optimal v_i,a is
determined iteratively.
For each candidate set
1) choose an initial v_i,a. such that sum_a v_i,a =1, where the sum is over
candidates in the candidate set.
2) The total score for a candidate in the set is determined from s_a =
sum_i v_i,a s_i,a. The lowest score is a lower bound for the candidate set
score.
3) Form the adjusted vote w_i,a = v_i,a/s_a.
4) The adjusted vote for each ballot is w_i = sum_a w_i,a.
5) The new v_i,a = w_i,a / w_i. Proceed to step 2.
The candidate set with the highest score wins the election.
--- On Sat, 10/1/11, Toby Pereira <[email protected]> wrote:
From: Toby Pereira <[email protected]>
Subject: Re: [EM] PR approval voting
To: "Ross Hyman" <[email protected]>,
"[email protected]" <[email protected]>
Date: Saturday, October 1, 2011, 11:25 AM
Presumably this could also be used for range voting with a fairly simple
modification. It would just set a limit on the fraction of someone's vote that
could be used for each candidate. If you scored a candidate 3 out of 10, then
no more than 0.3 of your vote could go to that candidate, regardless of whether
the rest remained unused.
From: Ross Hyman <[email protected]>
To: [email protected]
Sent: Saturday, 1 October 2011, 5:07
Subject: [EM] PR approval voting
The following PR approval voting procedure is an approval limit of Schulze STV
A score for each candidate set is determined in the following way: The vote
of each ballot is distributed amongst the ballot's approved candidates in the
candidate set. The score for each candidate set is the largest possible vote
for the candidate in the set with the smallest vote. The candidate set with
the highest score wins the election.
example: 2 seats
approval voting profile
10 a
6 a b
2 b
5 a b c
4 c
The possible candidate sets are: {a b}, {a c}, and {b c}.
score for {a b} determined from
10 a
11 a b
2 b
score for {a b} = 11.5
score for {a c} determined from
16 a
5 a c
4 c
score for {a c} = 9
score for {b c} determined from
8 b
5 b c
4 c
score for {b c} =
8.5
set {a b} wins.
Schulze uses a maximum flow algorithm to distribute the votes optimally on each
ballot for each candidate set. Here is another algorithm.
v_i,a is the vote assigned to candidate a from the ith ballot. The optimal
v_i,a is determined iteratively.
1) Initially, the vote for each ballot is distributed equally between all the
candidates in the candidate set that are approved by that ballot.
2) The total vote for a candidate in the set is determined from v_a = sum_i
v_i,a. The lowest vote is a lower bound for the candidate score.
3) Form the adjusted vote w_i,a = v_i,a/v_a.
4) The adjusted vote for each ballot is w_i = sum_a w_i,a.
5) The new v_i,a = w_i,a / w_i. Proceed to step 2.
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