[EM] Approval ballots. Two to elect. Best method? (Andy Jennings)

[Forest Simmons]

Continuing as promised ..

Suppose that there are to be w winners, and the ballots are still approval
style:

For each w_tuple of candidates, let p1, p2, ... be the respective
probabilities of selection of the respective candidate by random ballot
(restricted to the w-tuple), and let p0 be the probability that a random
ballot would not approve any of the candidates in the w-tuple.

Elect the w-tuple with the largest value of  min(p1, p2, ...) - p0.

To Be Continued ...

On Thu, Dec 3, 2015 at 1:30 PM, Forest Simmons <fsimmons at pcc.edu> wrote:

>
>
> This query has lead me to some interesting ideas:
>
> Approval Ballots.  Two to elect:
>
> For each pair of candidates {X1, X2}, let p1 and p2 be the respective
> probabilities that X1 or X2 would be selected by a random approval ballot
> drawing (restricted to our pair of candidates), and let p0 be the
> probability that a random ballot would approve neither X1 nor X2.  Elect
> the pair with the greatest value of min(p1, p2) - p0.
>
> This actually gives two methods, since there are two natural ways of
> selecting a candidate by random approval ballots.
>
> The first way is to select ballots at random until the approval set for
> one of them has non-empty intersection with the set from which we are to
> select a winner.  The names of the candidates are drawn randomly from a
> hat.  The first name drawn of a candidate in the intersection set is the
> name of the winner.
>
> The second way starts out as above, but once the first non-empty
> intersection set is determined, additional ballots are drawn as needed to
> narrow down the intersection to one candidate, the winner.
>
> More later ...
>
> From: Forest Simmons <fsimmons at pcc.edu>
>> To: EM <election-methods at lists.electorama.com>,         Andy Jennings
>>         <elections at jenningsstory.com>
>>
>>
>> How about thie following ideas?
>>
>> Elect the pair that covers the most voters (i.e. that leaves the fewest
>> voters with nobody that they approved elected).  In case of ties, among
>> tied pairs elect the one whose weaker member has the most approval.
>>
>> Or this variant:  If no pair covers more than 70 percent of the voters,
>> elect the pair that covers the greatest number of voters.  Otherwise
>> consider all pairs that cover at least 70 percent of the voters to be
>> tied.  Then among tied pairs, elect the one whose weaker member has the
>> greatest approval.
>>
>>
>> From: Andy Jennings <elections at jenningsstory.com>
>> > To: Election Methods <election-methods at electorama.com>
>> > Subject: [EM] Approval ballots. Two to elect. Best method?
>> >
>> > SPAV?
>> > 1. Candidate with most approvals wins.
>> > 2. That candidate's voters have their voting weight halved (or
>> multiplied
>> > by 1/3).
>> > 3. Remaining candidate with most points wins.
>> >
>> > STV-like?
>> > 1. Choose quota Q = one-third (or one half) of voters.
>> > 2. Candidate with most approvals wins.  (T = # of approvals)
>> > 3. That candidate's voters have their voting weight multiplied by
>> > max(1-(Q/T), 0)
>> > 4. Remaining candidate with most points wins.
>> >
>> > Monroe-like?
>> > 1. For each pair of candidates, find the voter-assignment which
>> maximizes
>> > the number of voters assigned to a candidate they approved, such that no
>> > more than half the voters are assigned to one candidate.
>> > 2. Elect the pair which satisfies the most voters.
>> >
>> > Others?  Toby, what are your favorite PR methods at the moment?  Can you
>> > give a short explanation of how Phragmen/Ebert would work with only two
>> to
>> > elect?
>> >
>> >
>> >
>> > Specifically, I'm worried that in practically every approval-ballot PR
>> > method, if there is a candidate you really like, but are sure that she
>> can
>> > get elected without your vote, you gain an advantage by not approving
>> > them.  Is there any method that minimizes that incentive?
>> >
>> > ~ Andy
>> >
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20151203/972306f2/attachment.htm>