[EM] Election-Methods Digest, Vol 76, Issue 7

[Jameson Quinn]

Indeed, all forms of MCA satisfy mono-add-plump (unless a non-compliant
method is used to choose the finalists for the runoff in MCA-IR or MCA-VR).

In fact, they satisfy an slightly stronger criterion, let's call it
mono-add-antiplump. You cannot cause Y to win by adding a ballot which
doesn't approve Y (that is, votes them at the lowest rating possible).

Also, I agree: thanks, Kristopher, your explanation of monotonicity is
great.

JQ

2010/10/19 <fsimmons at pcc.edu>

> Thanks for the clarification, Kristopher.
>
> Also, if I remember correctly, we have another kind of monotonicity that is
> really a weak form of Participation, namely "mono add plump,"  which means
> that
> if a new ballot is added that "bullet votes" for candidate A, then A's
> probability of winning should not decrease.
>
> It seems to me that this milder form of participation should be attainable.
>
> Forest
>
> > Date: Tue, 19 Oct 2010 08:39:53 +0200
> > From: Kristofer Munsterhjelm
> > To: kathy.dopp at gmail.com
> > Cc: election-methods at lists.electorama.com
> > Subject: Re: [EM] MCA on electowiki
> > Kathy Dopp wrote:
> >
> > > The mathematical definition of increasing monotonicity says
> > when I
> > > increase the independent variable, the dependent variable likewise
> > > increases (for voting, when I increase votes for a candidate, that
> > > candidate's chance of winning increases.) Or the mathematical
> > > definition of nondecreasing monotonicity says, when I increase the
> > > independent variable, the dependent variable never decreases (for
> > > voting when I increase votes for a candidate, the candidate's
> > chances> of winning never decreases.)
> > >
> > > I would say by any standard normal mathematical definition of
> > > monotonicity, if a voting method fails the Participation
> > Criterion you
> > > linked to, it also fails to be monotonic.
> > >
> > > Adding votes or increasing ranking for a candidate, should not cause
> > > that candidate to lose whereas he otherwise might have won.
> > To me,
> > > that is just another way of stating nonmonotonicity.
> >
> > Using Woodall's terms, the full name of what we usually call
> > "monotonicity" on this mailing list is "mono-raise". That is:
> > monotonicity regarding raising (ranking higher) a candidate.
> > There are
> > many other forms of monotonicity: for instance, mono-add-top
> > (adding a
> > vote that ranks a candidate first shouldn't make the candidate
> > lose),
> > mono-append (adding a candidate to a truncated ballot should not
> > make
> > that candidate lose), and so on. See
> > http://www.votingmatters.org.uk/ISSUE3/P5.HTM for the full list.
> >
> > Any of these might be called monotonicity criteria, since they
> > involve
> > situations where ballots are added or altered in a way that is
> > seemingly
> > favorable for the new candidate, and the method fails the
> > criterion if
> > the candidate loses.
> >
> > As for Participation, Woodall says: "There is also the following
> > property, which is not strictly a form of monotonicity but is
> > very close
> > to it. (...) Participation. The addition of a further ballot
> > should not,
> > for any positive whole number k, reduce the probability that at
> > least
> > one candidate is elected out of the first k candidates listed on
> > that
> > ballot. ".
> > It is, unfortunately, a very strict criterion. Only voting
> > methods that
> > consist of point systems with point system tiebreakers (not
> > necessarily
> > the same tiebreakers) can fulfill it. A point system is one
> > where you
> > give the first candidate on a ballot x points, the second y
> > points, the
> > third z points, etc. DAC/DSC is in this sense a series of point
> > systems,
> > each breaking ties of the last.
> >
> >
> > In summing up: what we call "monotonicity" is just one form of
> > monotonicity, that is true; and it is unfortunate but also true
> > that
> > most complex systems fail Participation.
> >
> ----
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