[Election-Methods] Which monotonicity?

Stéphane Rouillon stephane.rouillon at sympatico.ca
Tue Jan 15 11:28:43 PST 2008

I am fed up a bit with that discussion about non-monotonicity because it 
depends how
monotonicity is defined.  IRV is monotonic when you consider adding or 
ballots with you preffered candidate as first choice. IRV is non-monotonic 
you consider highering or lowering the positions of your preferred candidate 
on several ballots...

Maybe some concision and precision in the definitions would help.
Could we use 2 different names for monotonicities please?
Or maybe they exist and I don't know these definitions...

S. Rouillon

>From: Jonathan Lundell <jlundell at pobox.com>
>To: Steve Eppley <SEppley at alumni.caltech.edu>
>CC: election-methods at electorama.com
>Subject: Re: [Election-Methods] Why monotonicity?
>Date: Tue, 15 Jan 2008 08:38:36 -0800
>On Jan 15, 2008, at 8:22 AM, Steve Eppley wrote:
> > The strategy of raising a candidate in order to defeat it may
> > legitimately be counted as one more strategy in the voter's toolbox of
> > strategies, but I think the (narrow) question here is whether the
> > number
> > of manipulable scenarios is greater given non-monotonic methods, given
> > the same set of candidates and same voters' preferences.  To my
> > knowledge, this has not been demonstrated.
> >
> > Furthermore, since the assumptions of the same set of candidates and
> > same voters' preferences are dubious--candidates may adopt different
> > positions on the issues, and make different decisions about whether to
> > run, given a different voting method--monotonicity may be unimportant
> > even if it does reduce the number of manipulable scenarios.
> >
> > I think all we can say for sure about the desirability of monotonicity
> > is that, all else being equal, it's better to be monotonic.
>I'm reminded of Douglas Woodall's argument that STV's monotonicity
>failures occur in scenarios where it's not obvious to begin with which
>candidate(s) "ought" to be elected.
> > There are certain regions in which it is quite clear who ought to be
> > elected, and in these regions STV elects the candidate that one
> > would expect. But in the middle there is a grey area, where it is
> > not at all clear who ought to be elected, and it is in this grey
> > area that STV behaves in a somewhat haphazard manner; it is really
> > doing no more than making a pseudo-random selection from the
> > appropriate candidates, and it is here that small changes in the
> > profile of ballots can cause perverse changes in the result.
> >
> > The effect of this is to blur the result of an STV election. Nobody
> > is being wrongly elected, because the problem only arises in the
> > region where one cannot say for certain who ought to be elected
> > anyway. And there is no systematic bias that would, for example,
> > favour one political party rather than another. But the accuracy
> > with which the person or persons elected in an STV election can be
> > said to represent the views of the voters is less precise than it
> > would be if this sort of anomaly did not arise.
> >
> > The obvious question at this point is whether one can find a system
> > that retains the essential features of STV while avoiding this sort
> > of anomaly. The answer depends on what one regards as the essential
> > features of STV. As we shall see in a later article, it is not
> > possible to avoid this anomaly without sacrificing at least one
> > property that many supporters of STV regard as essential.
> >
>...by which he means later-no-harm.
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