[EM] Schulze and Margins was: Reversal Software output6/9/1999

Markus Schulze schulze at sol.physik.tu-berlin.de
Fri Jun 25 11:42:51 PDT 1999

Dear Blake,

you wrote (25 Jun 1999):
> > Your argumentation is strange. It seems to me that you assume that
> > if a given voter has absolutely no informations about the opinions and
> > the voting behaviour of the other voters this voter will (to calculate
> > his optimal strategy) assume that the opinions of the other voters
> > are distributed randomly and that the other voters don't use any
> > strategy.
> If I assume they are distributed randomly, it doesn't matter whether
> this is the result of strategy or not, so the second assumption is not
> an issue.  You're right though, that I have been basing optimal
> strategy in the absence of information on the assumption of random
> distribution.  If you don't agree that this is correct, then what
> would you describe as the optimal strategy with no information about
> how others are voting.

I don't think that it is a promising criterion to say that for a voter,
who has absolutely no informations about the opinions and the voting
behaviour of the other voters, voting sincerely should be an optimal
strategy. The following problems will occur:

1. It is not possible that a given voter has no informations about
the opinions and the voting behaviour of the voters because every voter
has at least informations about his own opinion and his own voting
behaviour. Of course, this sounds esoteric. But the problem is that if
this voter discovers that even if he has no informations about the
other voters there is a better strategy than voting sincerely then he
cannot assume anymore that the other voters vote sincerely.
In other words: If this voter finds a strategy which is better than
voting sincerely, then this voter has to assume that also the other
voters will use this strategy.

2. The optimal strategy of a voter who has absolutely no informations
about the opinions and the voting behaviour of the other voters also
depends on the absolute preferences (von Neumann-Morgenstern utilities)
of this voter. In other words: If you want to apply your criterion that
for a voter who has no informations about the other voters it should be
a useful strategy to vote sincerely, you have to make assumptions about
the typical distribution of the absolute preferences of a voter.
But as you might already know from FPTP, Borda, Approval Voting or IRO,
the result you will get will depend sensitively on the assumption
of this distribution of absolute preferences.

> > > > Voters don't tend to use order-reversal. But they tend to
> > > > truncate if they have to fear that an additional ranking could
> > > > hurt their already ranked candidates.
> > >
> > > Are you saying that voters will truncate if an additional ranking
> > > merely "could" hurt, or will they truncate only if it on average
> > > does hurt?
> > 
> > I don't understand what you mean. As Schulze meets the Condorcet
> > Criterion, you know the answer to your above question.
> IRV advocates often state, correctly, that in a given Condorcet
> method (both Margins and VA), additional rankings CAN hurt one's
> favourite.  There is a tendency to over-interpret statements of this
> form, so a reader of this statement might think that it implies that
> additional rankings will in general hurt your favourite, and that it
> is therefore good strategy to only rank one candidate.  This is,
> however, not what it means, and truncation is not in general a good
> strategy.

I prefer the following formulation: If IRO is used then an additional
voter cannot change the winner from his highest ranked candidate to
another candidate. Donald G. Saari calls this "Positive Involvement
Criterion." Douglas R. Woodall calls this "MONO-ADD-TOP."

Markus Schulze

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