[EM] Three rounds

[Raph Frank]

On Mon, Nov 10, 2008 at 11:59 PM, Juho Laatu <juho4880 at yahoo.co.uk> wrote:
> --- On Mon, 10/11/08, Raph Frank <raphfrk at gmail.com> wrote:
>
>> From: Raph Frank <raphfrk at gmail.com>
>> Subject: Re: [EM] Three rounds
>> To: juho4880 at yahoo.co.uk
>> Cc: election-methods at lists.electorama.com
>> Date: Monday, 10 November, 2008, 7:59 PM
>> On Mon, Nov 10, 2008 at 4:05 PM, Juho Laatu
>> <juho4880 at yahoo.co.uk> wrote:
>> > One could e.g. force supporters of the
>> "eliminated" candidates to approve more than one
>> candidate (at least one of the "remaining"
>> candidates) (instead of just bullet voting their second
>> preference). On possible way to terminate the algorithm
>> would be to stop when someone has reached >50% approval
>> level.
>> >
>> > Also in "non-instant" runoffs one could e.g.
>> force the voters to approve at least one on the
>> "remaining" candidates. (One could eliminate more
>> than one candidate at different rounds.)
>>
>> That is kinda like Bucklin, though without the approval
>> threshold
>> changing in each round for all voters.
>>
>> The process could be
>>
>> 1) Each candidate is designated a strong candidate
>> 2) Each ballot is considered to approve the highest ranked
>> strong
>> candidate and all candidates ranked higher.
>> 3) If the most approved candidate has > 50%, then that
>> candidate is elected.
>> 4) Re-designated the least approved strong candidate a weak
>> candidate
>> and goto 2).
>
> Yes, could go this way.
>
>>
>> It still suffers from centre squeeze effects, though.
>>
>> For example
>>
>> 45: A>B>C
>> 9: B>A>C
>> 46: C>B>A
>>
>> Round 1
>>
>> A: 45
>> B: 9
>> C: 46
>>
>> no winner, B designated 'weak'
>>
>> Round 2
>>
>> A: 54
>> B: 9
>> C: 41
>>
>> A wins.
>
> How about continuing and allowing the C supporters to compromise and approve also B. (Just didn't use the 50% termination rule this time.) After this round B would win and there would be no more interest to compromise (all voters already either approve the to be winner or would approve it as a compromise).

If you just keep keep declaring candidates as 'weak' until all
candidates are weak, then it is basically approval voting.

Once someone passes 50%, that candidate is declared as the potential
winner.  All ballots are then considered to also approve candidates
that they prefer to the potential winner.

So,

45: A>B>C
Approves A (as highest strong candidate)

9: B>A>C
Approves A (as highest strong candidate)
Approves B (as weak candidate)

46: C>B>A
Approves C (as highest strong)
Approves B (as preferred to potential winner)

A: 54
B: 55
C: 46

Ofc, it might just be easier to just pick the condorcet winner :),
though I am not sure that the above method would always elect the
condorcet winner.