[EM] Three rounds

[Juho Laatu]

Right, the method is not Condorcet compliant.

40 A>B>C
25 B>A>C
35 C>B>A

B supporters must compromise first and approve also A. Next C supporters must approve also B (maybe approving additionally only B at this round is enough although B is a weak candidate now). A wins although B is the Condorcet winner.

(The rule that I used was something like "those voters whose most approved candidate among those candidates that they approve is least approved must approve one more candidate (or multiple if ranked equal) except if that would mean approving the most approved candidate".)

Juho


--- On Tue, 11/11/08, 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: Tuesday, 11 November, 2008, 1:21 PM
> 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.