From: [EMAIL PROTECTED] on behalf of Jobst Heitzig
Sent: Tue 9/13/2005 1:38 PM
To: [EMAIL PROTECTED]
Subject: Re: [Condorcet] Why Schulze is Better than DMC
Dear Jeff!
You wrote:
> [Jobst, the fact that *you*
think DMC simple and CSSD more complex does not make it so. -- JRF]
I was
talking about the tallying process there.
[That was not clear from the
context, which implied that DMC would be easier to explain, not easier for a
computer's CPU to calculate. Since CPU cycles are cheap, I for one do not care
about the simplicity that you go on to explain. BTW, we covered this ground
before, so let's please drop it here. -- JRF]
It is not a matter
of
opinion whether DMC or CSSD is easier to tally. To the contrary,
there
are well-established mathematical measures of complexity which
show
quite clearly that it is easier to determine the DMC winner than
the
CSSD winner: DMC's order of complexity is n^2, CSSD's is n^3, where n
is
the number of candidates. This means that when doubling the number
of
candidates, the time to apply DMC will approximately be multiplied
by
four, while the time to apply CSSD will approximately be multiplied
by
eight. Another measure of complexity is how many words you need
to
explain the algorithm. It has been pointed out over and over by
various
experts here that also from this point of view DMC is
easier.
Of course, there are also other *kinds* of simplicity, other
than the
tallying simplicity. For example, the question is different when we
ask
how easy it is to *vote* rather than how easy it is to
tally:
Those versions of DMC which use an explicit approval cutoff ask
the
voter for more information and can thus be considered more complex.
But
this amounts to say that giving voters more freedom of _expression_
is
making voting more complicated. If we don't like this, we should
perhaps
propose Approval Voting and no rankings based method at all, since
the
difference in ballot complexity between an approval-only ballot and
a
rank-only ballot is larger than that between a rank-only ballot and
a
rank-ballot with optional approval cutoff.
Those versions of DMC
which use a standard ranked ballot (with implicit
approval) are no more
complex to vote than CSSD from the point of view
of ballot
complexity.
But voting complexity can also be measured by how complex it
is to find
suitable strategies. Here the situation is even more debatable,
it
seems: Finding a suitable strategy involves understanding the
tallying
process, hence it seems that the simpler tallying process of DMC
should
make it somewhat easier to find good strategies in DMC. This is
most
obvious from the fact that in the most probable situation where there
is
a sincere Condorcet Winner, say X, the obvious strategy to guarantee
the
sincere outcome in DMC is to approve X and everyone I prefer to X.
It
can immediately be seen that in this way no faction which prefers
some
other candidate, say Y, to X can change the fact that X defeats
Y
doubly. In CSSD, it is not so obvious what we can do to guarantee
that
the sincere Condorcet Winner actually wins without voting an
insincere
ranking, is it?
Also, the information I need in order to
anticipate the CSSD winner in
case of a cycle seems to be more precise than
the information I need to
anticipate the DMC winner. For DMC, I would need to
have reliable
polling information about what the likely directions of the
defeats are
and what the likely approval order is. For CSSD, on the other
hand, I
not only need to know the direction of the defeats but also
need
reliable polling information about the *strengths* of these defeats.
It
seems more problematic to me to anticipate which defeat is weakest
than
to anticipate which candidate is least approved.
In all, the only
aspect in which CSSD seems simpler than DMC with
explicit approval seems to
be the ballot. And I did not read a single
reason why DMC with *implicit*
approval could be considered more complex
than CSSD.
Yours,
Jobst
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