On May 27, 2010, at 3:01 AM, Kevin Venzke wrote:
Hi Juho,
--- En date de : Mer 26.5.10, Juho <[email protected]> a écrit :
The following criterion is similar to
Plurality. Does
it have a name?
If the number of ballots on which X beats Y is
greater than
the number of
ballots on which Y is ranked, then Y cannot be
elected.
Any decent method that doesn't satisfy it?
This criterion is strictly stronger than Plurality, so
I'd have to ask
whether you think any decent methods fail Plurality.
Probably the answer
is no, not really.
This says that all typical margins based Condorcet methods
would not be "decent". One could ask the question also in
the reverse direction. All methods violate some criteria
that look good at least at first sight. Which property of
the plurality criterion (or the new criterion) makes it a
mandatory requirement for all election methods (or Condorcet
or ranked methods)?
Personally I would allow Plurality failures for a good reason.
But I think that most people would generally not be accepting. This
would
be because of a view that there is such a thing as "support"
involved in
voting for a candidate and this can't be found when one truncates a
candidate. So when you compare a candidate X who is the favorite of 10
voters, and you can't find that many voters who "support" Y on their
ballots in any way, something seems wrong when Y wins. The thought is
why would you ever need to elect Y when you could just elect X? It's
similar to Pareto in that sense.
Yes, in ballots where the position of truncated (or shared last)
candidates looks clearly different than the position of other
candidates the voters may get the impression that thy are supporting
all others and not supporting the truncated / shared last candidates.
And they may vote this way and dislike methods that do do not respect
their impression on what should happen with respect to candidates with
lots of first preferences vs. candidates with less any higher than
last preferences. But on the other hand all methods need not have such
implicit approval/support assumptions.
It depends also a lot on the environment if one should optimize the
method so that it will perform well under all (sincere and/or
strategic) circumstances or if it should look good to the average
voters and politicians so that it will have a chance of getting
adopted. If one wants e.g. to promote Condorcet methods one could (in
theory) listen to the discussion for a while and then pick a method
that looks best in the observed discussion environment (the behaviour
of all Condoret methods is anyway quite similar in typical elections).
There could be also other criteria that people want to see
implemented. They might for example hate "favourite betrayal", and
that could make all Condorcet methods unusable. If people study
election methods in detail they must accept that all the best election
methods will violate some nice looking criteria.
Btw, in the example above I guess the plurality criterion doesn't
requite that X should win. Also some other candidate with sufficient
number of above last rankings could win. In that sense methods that
meet the plurality criterion might not be an exact match to the needs
of that voter who wanted X to win with 10 votes.
Really I have no idea what Forest has in mind by "decent." Maybe he
does find margins or MMPO to be decent. I believe he even accepts
random
methods if there's a point to them, so who knows.
Random methods are an interesting group here. I tend to see
deterministic ((except when we have exact ties)) methods as methods
that should be used by default in most elections. But there can be
also methods where random/probabilistic choices are acceptable or
maybe exactly what we want. In the same way I tend to see the
compromise seeking nature of Condorcet methods to be appropriate for
most single-winner elections, but also in this case, there could be
elections where we have some other targets. Also elections where the
ballots should collect approvals / list of supported candidates and
the method should put lots of weight on these measured opinions are
possible. I'm just not sure if that should be the main rule or
reserved only for elections where such properties are really needed.
Juho
Kevin
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