# [EM] Two Condorcet Winners?

Elisabeth Varin/Stephane Rouillon stephane.rouillon at sympatico.ca
Sun Aug 18 13:49:40 PDT 2002

```Mike wrote:

I've always said that standards are entirely subjective. Your standards
are
different from mine, and
may your methods have great success with people who share your
standards.
The only way to
be wrong about standards is to say that your standards are best, or that

someone else's standards
are wrong, ot that your standards are more objective than someone
else's.

Maybe saying you lack some objectivity are not the appropriate terms.
It is not exactly what I mean, sorry for my improper english vocabulary.

In the same way I apologize for using the term "claim" which was, to my
understanding an equivalent to "publicize" or " makes public". I
recognize you
proved what you "claimed" or simply "informed others".
What I mean follows.
strategy" criteria. You seem to accept that Condorcet methods using
"relative margins"
produce a ranked winners list that minimizes the biggest ranking
reversal.

All I say is that this second mathematical criteria is the best
algebraic definition
I am able to fit with the definition of fairness.
I would not find fair a method that would output A as a winner if it
represents
overulling the judgement of 70% of the voters about one pairwise, if
there is
another solution that would give B as a winner and only overules the
judgement
of 53% of voters in this other ranked list.

You could argue that if my method does not pass your defensive strategy
criteria,
thus voters do not necessarily vote sincerely so my result is flawed
from start.
I told you that in a similar way, methods that pass your defensive
strategy criteria
are flawed in the same way because producing a complete ranking of
preference can harm
a voters own preference. So even these methods are flawed from the start
because
we - usually - do not know the outcome of an election at the beginning
and there is no
garantee voters will vote sincerely.

Mike wrote:

Yes, truncation can change the outcome with wv. Truncation can also
change
the outcome with
margins methods, relative margins methods, and with any rank balloting
method. The difference
is that with wv, truncation won't steal the election from a
majority-supported CW, as it will with
margins and relative margins.

This is where I think we can see the problem.
I agree that: (please quote me entirely on this in the future)
"With wv, truncation won't steal the election from a
majority-supported CW, as it will with
margins and relative margins."
WHEN YOU CONSIDER THE CW DEFINED WITH WV.
(I am not shouting just underlining our difference of opinion).

I believe there can be two different CW, one CW(wv) using winning votes
and another
CW(rm) using relative margins.
"So with wv, truncation won't steal the election from a
majority-supported CW(wv), as it will with
margins and relative margins, but
IT WILL STEAL THE ELECTION FROM A MAJORITY-SUPPORTED CW(rm)
as it will with margins and relative margins.

Now, I do believe the CW(rm) is the "right winner" when both exists and
are
different for the reasons explained previously.

For me sincerity is prevalent to fairness, but you haven't reach that
point yet
If you could produce a method that can garantee to voters to protect the
CW(rm)
and make them vote sincerely, thus I think I would admit the input is
not flawed.
And I could accept that a sincere result is better than the fairest
result obtained
from a flawed input...

Mike wrote:

shown that, in every
nonprobabilistic method, there can be incentive for strategy. No one
ever
claimed that  that
doesn't apply to wv methods.  But we can choose what kinds of strategy
we'll
have incentive for,
and how badly we'll need them, and under what conditions, and whether or
not
all  the Nash
equilibria involve those strategies.

I think too there is no way to remove all strategies.
Removing some of them could be usefull I you
could attach a low probability for the occurrence of
the remaining cases.
My engineer macroscopic evaluation tells me your criteria
makes the "strategical issue" probality go from very rare to still very
rare
but obviously I could be wrong. It is however very difficult to
evaluate because we would need to approximate the ability of
identical voters to regroup and to organize so to exploit this
strategical
opportunity. I believe less than a handfull of voters with the exact
set of preferences would go under such a process and thus this is why
I obtained very low probabilities.

Sorry Mike for lacking adequate terms, I hope it is clear enough.
I do my best.
An english version of my best multiple-winners method
should be on the Electoral_systems_designers site soon.
It is under study by Commissions for Electoral Reforms
of Quebec's government and parliament (both entities
decided to look at electoral reform in the same time).

Steph.

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