On Jan 21, 2010, at 9:29 AM, Kristofer Munsterhjelm wrote:
robert bristow-johnson wrote:
i think that the answer is "no", if a Condorcet winner exists and
that all bets are off if a CW does not exist, except, perhaps for
these "strategy-resistant" methods such as Markus Schulze's
method. i sorta understand it, but since he hangs here, i think
Markus should address the question if the Schulze method is spoiler
free.
Most Condorcet related problems occur only when there is no Condorcet
winner (i.e. there is a top level cycle in the group preferences).
Sincere or artificially generated cycles are the root cause of both
problems with sincere votes (e.g. spoiler related problems) and
strategic voting related problems in Condorcet.
Different Condorcet methods (e.g. Ranked Pairs, Schiulze) are quite
similar in the sense that the basic vulnerabilities of Condorcet
methods exist in all of them (e.g. the basic burial scenarios). Their
differences between the most common Condorcet methods are quite small
in the sense that in real life elections they almost always elect the
same candidate. Their differences are mostly related to how well they
can resist strategic voting. Another point of view is to compare which
method elects the best/correct winner with sincere votes.
What is good in all the common Condorcet methods is that their
vulnerabilities to strategies (and their differences in general) may
very well be so small in typical real elections (large, public, with
independent voter decision making, with changing opinions and less
than perfect poll information) that strategic voting will not be a
problem. Also their differences with sincere votes (e.g. spoiler
related problems) are quite small in real life elections.
Here's one simple spoiler related example as a response to Kathy
Dopp's request.
35: A>B>C
33: B>C>A
32: C>A>B
I this example there are three candidates in a top level cycle. If any
of the candidates would not run that would mean that there is a
Condorcet winner, and that winner would be different in each case.
Let's say that the method we use will pick A as the winner. If B would
not run then the votes would be 35: A>C, 33: C>A, 32: C>A and C would
win. B is thus a spoiler from C's point of view.
I note however that these spoiler cases in Condorcet are not as common
as in many of the other methods. In practice it may be that there is
no need to worry about these cases. Maybe Kathy Dopp's comparisons
will reveal something about how problematic the spoiler effect is or
is not in Condorcet. Not also that in the example above B was not a
minor party candidate (often term spoiler refers to minor candidates)
but a pretty strong candidate.
MAM/Ranked Pairs is also pretty strategy-resistant and is easier to
understand. Schulze has the advantage of producing better results in
some cases (closer to Minmax), but if "ability to describe to the
public" is important, then Ranked Pairs wins there.
Could someone please provide me with an example of the spoiler
effect occuring with the Condorcet method of counting rank choice
ballots or tell me why the spoiler effect doesn't happen with
Condorcet in a few words?
(...)
i would say that (with the CW existing), it's spoiler-proof.
Yes. If there's a CW and a candidate is added, and that candidate
doesn't create a cycle, then the winner doesn't change. All the
"tricky" stuff happens when there is a cycle, or the candidate makes
one.
The advanced methods can claim further resistance: Schulze and
Ranked Pairs both make their winner decision independent of
candidates not in the Smith set. River is independent of Pareto-
dominated alternatives - a candidate is Pareto-dominated if
everybody who ranks both him and some other (specific) candidate,
rank the other candidate above him (e.g. X is Pareto-dominated by Y
if all voters who rank both X and Y say Y>X, and there's at least
one such voter).
I imagine these resistances would mostly come into play in smaller
elections. Still, they're nice to have, and their existence
immediately tells parties not to try exploiting certain weaknesses
(because it won't work).
Yes, in small elections (with few voters only) it may be possible to
know the opinions of each voter and agree about the applied strategy
with the strategizing voters. In typical large real life elections
many of the vulnerabilities are not practical and sincere voting may
be the best strategy to most if not all voters.
Many of the criteria would be nice to have. One must however remember
that often they have two sides. Winning something in some area may
mean losing something in another area (e.g. the LNH property of IRV
has been discussed widely on this list recently) especially when
trying to fix the last remaining problems of the Condorcet methods.
And if one assumes that strategic voting will not be meaningful in the
planned elections then one should pay attention also to performance
with sincere votes, not only to the resistance against strategies.
Different elections may also have different requirements, so the
question of which one of the methods is best may depend also on what
kind of winner one wants to get (e.g. in some cases the best winner
could be found outside the Smith set).
Juho
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