On May 27, 2010, at 4:07 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.
Well, you can argue with voters or you can argue with me. I personally
don't see value in what margins wants to substitute, so I don't see
that margins has a good reason for failing Plurality.
The reason could be related to the margins concept (level of
opposition against the winner as measured in margins) or strategies.
For example with votes 48: A>B, 3: B, 49: C margins (typically) elects
A but plurality criterion says that in deterministic methods the
winner must not be A. If B would win (as in typical WV methods) then
there would be complaints "why did B win although A beats B with a
huge margin". If C would win (as in IRV) then the complaints would
maybe be milder, but A's worst defeat in margins is anyway smaller
than C's although C has 1% worth more first preferences than A. On the
strategy side the sincere opinion of the B voters was maybe B>A. In
that case the 3% strategic voters stole the victory quite easily from A.
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).
They are similar but whether the different incentives are significant
can't easily be proven.
Yes. In this example we are probably talking more about efficient
campaign, propaganda and claims towards media, politicians and regular
voters than about mathematical proofs.
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.
Yes. If I thought that Forest thought failing FBC was unacceptable
then
when I guess whether an FBC-failing method is decent to him, I would
say probably not. If he thinks Mono-add-top is crucial and Plurality
is
not then I guess margins is a decent method for him.
Yes, all good good looking criteria. One more key criterion that was
not mentioned yet is later-no-harm.
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.
There is no voter who wanted X to win. The issue is that it is cut and
dry that X is better than Y; Z may be better than either but we may
not
be able to easily show it. It's no different from Pareto there.
Yes, typically we are talking about cycles where there is always an
argument why someone else is better than the winner. (When there are
cycles many voters might actually consider some random tie solving
method to be a fair method.)
Juho
Kevin
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