[EM] PR approval voting

[Ted Stern]

On 03 Oct 2011 12:23:10 -0700, Toby Pereira wrote:
>
> I noticed on your page that you suspect that all multi-winner
> methods fail participation. I don't think that's the case. I would
> suggest that Forest Simmons's Proportional Approval Voting passes
> it. Also I think my versions of Proportional Approval Voting and
> Proportional Range Voting pass.

Since I wrote that, I have come to believe (but still haven't proved)
that Approval-based methods will generally pass participation and
IIAC.

A range based method will pass participation, at least in
single-winner, if it doesn't adjust ratings.

In many cases my version of Range Transferable Vote will elect winners
without having to raise ratings to meet quota.  It only fails
participation in those cases where the quota is not met, which most
often happens on the last or penultimate seat.

Is your PRV method quota-based?  If so, does it pass Droop
proportionality?  If so, how do you deal with elevating preferences if
no candidate achieves a quota?

Ted

>
> From: Ted Stern <araucaria.araucana at gmail.com>
> To: Election Methods <election-methods at lists.electorama.com>
> Cc: Ted Stern <araucaria.araucana at gmail.com>
> Sent: Monday, 3 October 2011, 19:45
> Subject: Re: [EM] PR approval voting
>
> I'd like to stick my oar in here, to point out that I have an
> implementation of Range Transferable Vote, which can be used with
> Droop or other quotas, that implements PR.
>
> Code for it is located here:
>
>     https://github.com/dodecatheon/range-transferable-vote
>
> It reduces to Approval Transferable Vote in the case of range(0,1).
>
> I had to make one change to it recently to fulfill the Droop
> proportionality criterion, which states that if a faction distributes
> its votes among L candidates, and has enough votes to elect K <= L
> quotas, then the method will elect K candidates from the set of L
> candidates.
>
> For RTV, this meant that I had to find a way to elevate range
> preferences in the event that no candidate achieves a quota.
>
> The way I implement this is to increase non-zero ratings incrementally
> (up to maximum score) until at least one candidate makes quota.
>
> This pushes RTV into the territory of Bucklin-style methods, and
> therefore it does not satisfy the Independence from Irrelevant
> Alternatives criterion, even in the single-winner case.
>
> Ted
>
> On 01 Oct 2011 09:25:45 -0700, Toby Pereira wrote:
>>
>> 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 <rahyman at sbcglobal.net>
>> To: election-methods at lists.electorama.com
>> 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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>>
>> ?
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