[EM] An ABE solution

[Jameson Quinn]

I agree it's silly to create complicated rules for a two-slot ballot. But,
though Forest didn't quite say so, I also think that FBC and (voted ballot)
Condorcet are not incompatible for a 3-slot ballot.

Jameson

2011/11/22 Chris Benham <cbenhamau at yahoo.com.au>

> Forest,
>
> "When the range ballots have only two slots, the method is simply
> Approval, which does satisfy the
> FBC."
>
> When you introduced the method you suggested that 3-slot ballots be used
> "for simplicity".
> I thought you might be open to say 4-6 slots, but a complicated algorithm
> on 2-slot ballots
> that is equivalent to Approval ??
>
> "Now consider the case of range ballots with three slots: and suppose that
> optimal strategy requires the
> voters to avoid the middle slot.  Then the method reduces to Approval,
> which does satisfy the FBC."
>
> The FBC doesn't stipulate that all the voters use "optimal strategy", so
> that isn't relavent.
> http://wiki.electorama.com/wiki/FBC
>
> http://nodesiege.tripod.com/elections/#critfbc
>
> Chris  Benham
>
>
>
>
>
>   *From:* "fsimmons at pcc.edu" <fsimmons at pcc.edu>
> *To:* C.Benham <cbenhamau at yahoo.com.au>
> *Cc:* em <election-methods at electorama.com>; MIKE OSSIPOFF <
> nkklrp at hotmail.com>
> *Sent:* Tuesday, 22 November 2011 11:11 AM
> *Subject:* Re: An ABE solution
>
>
>
> From: "C.Benham"
>
> >
> > Forest Simmons, responding to questions from Mike Ossipff, wrote
> > (19 Nov
> > 2011):
> >
> > > > 4. How does it do by FBC? And by the criteria that bother some
> > > > people here about MMPO (Kevin's MMPO bad-example) and MDDTR
> > > (Mono-Add-Plump)?
> > >
> > > I think it satisfies the FBC.
> >
> > Forest's definition of the method being asked about:
> >
> > > Here’s my current favorite deterministic proposal: Ballots are
> > Range
> > > Style, say three slot for simplicity.
> > >
> > > When the ballots are collected, the pairwise win/loss/tie
> > relations are
> > > determined among the candidates.
> > >
> > > The covering relations are also determined. Candidate X covers
> > > candidate Y if X
> > > beats Y as well as every candidate that Y beats. In other
> > words row X
> > > of the
> > > win/loss/tie matrix dominates row Y.
> > >
> > > Then starting with the candidates with the lowest Range
> > scores, they are
> > > disqualified one by one until one of the remaining candidates
> > X covers
> > > any other
> > > candidates that might remain. Elect X.
> >
> >
> > Forest,
> >
> > Doesn't this method meet the Condorcet criterion? Compliance
> > with
> > Condorcet is incompatible with FBC, so
> > why do you think it satisfies FBC?
>
> When the range ballots have only two slots, the method is simply Approval,
> which does satisfy the
> FBC.  Does Approval satisfy the Condorcet Criterion?  I would say no, but
> it does satisfy the "votes only
> Condorcet Criterion." which means that the Approval winner X pairwise
> beats every other candidate Y
> according to the ballots, i.e. X is rated above Y on more ballots than Y
> is rated above X.
>
> Now consider the case of range ballots with three slots: and suppose that
> optimal strategy requires the
> voters to avoid the middle slot.  Then the method reduces to Approval,
> which does satisfy the FBC.
>
>
> >
> >
> > http://lists.electorama.com/pipermail/election-methods-
> > electorama.com/2005-June/016410.html
> >
> > > Hello,
> > >
> > > This is an attempt to demonstrate that Condorcet and FBC are
> > incompatible.> I modified Woodall's proof that Condorcet and
> > LNHarm are incompatible.
> > > (Douglas R. Woodall, "Monotonicity of single-seat preferential
> > > election rules",
> > > Discrete Applied Mathematics 77 (1997), pages 86 and 87.)
> > >
> > > I've suggested before that in order to satisfy FBC, it must be
> > the case
> > > that increasing the votes for A over B in the pairwise matrix
> > can never
> > > increase the probability that the winner comes from {a,b};
> > that is, it
> > > must
> > > not move the win from some other candidate C to A. This is
> > necessary
> > > because
> > > if sometimes it were possible to move the win from C to A by
> > increasing> v[a,b], the voter with the preference order B>A>C
> > would have incentive to
> > > reverse B and A in his ranking (and equal ranking would be
> > inadequate).>
> > > I won't presently try to argue that this requirement can't be
> > avoided
> > > somehow.
> > > I'm sure it can't be avoided when the method's result is
> > determined solely
> > > from the pairwise matrix.
>
> Note that in our method the Cardinal Ratings order (i.e. Range Order) is
> needed in addition to the
> pairwise matrix; the covering information comes from the pairwise matrix,
> but candidates are dropped
> from the bottom of the range order.
>
> In the two slot case can the approval order be determined from the
> pairwise matrix?  If so, then this is a
> counterexample to the last quoted sentence above in the attempted proof of
> the incompatibility of the CC
> and the FBC.
>
> Forest
>
>
>
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>
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