On May 10, 2010, at 2:20 AM, Kevin Venzke wrote:
You have to give me a reason why I should start with
margins or else it won't occur to me.
See (***) below. That's my best guess on why someone might like margins.
There is no reason to vote "absolutely
equal" unless that's just how you sincerely feel. Strategically it's
like voting 5/10 in Range.
I agree that mandatory full rankings would collect more information
and in principle voters that have hard time deciding whether A is
better than B or not could just flip a coin and statistics would
balance the situation even if they make the wrong decision or are
convinced that the candidates are equal. Equal rankings are mostly
used for convenience. On the other hand there is no big reason to ban
equal ranking either. And especially if there are numerous candidates
truncation (equal ranking of remaining candidates) is a quite natural
way to handle the unknown and probably irrelevant candidates.
To me the description of minmax(margins) (that uses
directly the concept of margins) as "elect the candidate
that needs least additional votes to win all others" is at
the same time both an exact definition of the method and a
description of who would be the ideal winner. According to
this philosophy one should elect the candidate that would
face least opposition after being elected (by people that
would have preferred some candidate X to the winner and
could join forces to oppose try to harm the elected winner).
I think there are many kind of elections where the used
criteria to determine the optimal winner may be different.
This philosophy is thus not the only possible philosophy but
it is certainly one that could be considered even ideal in
some/many single-winner elections.
That's fine. Feel free to use margins where it makes sense.
(***) This was the viewpoint of sincere interest to use
minmax(margins) because it offers a good utility function for certain
kind of elections. This utility function can also be seen to be a good
general purpose single-winner election method target (i.e. not just a
special solution for a special case).
For example WV has much better FBC-efficiency than margins. I tested
this
some time ago and would have to find it, but it's easy to see why: In
margins if you need to weaken a defeat against your compromise, you
can
do it *faster* by just ranking him ahead of your real favorite.
Ok, now we are entering the world of strategy related criteria. So far
I only tried to justify why margins is good with sincere votes. In the
area of strategies there are vulnerabilities in both directions. Maybe
another discussion for another day.
The point is not that WV uses approval, it's that it works well with
a voter expectation that truncation has a certain significance. Maybe
the Plurality criterion explains this well enough. Maybe the principle
that voters would understand actually is approval.
Plurality criterion is a special criterion since it assumes that
ranked candidates are somehow approved. I think it should not be used
on methods that do not make such assumptions. In margins pure rankings
based approach seems to be the normal way to read the ballots.
In general I don't like the idea of hidden approval cutoff after the
ranked candidates very much (or any other positive vs. negative
borderline after the ranked candidates). That is because in general I
think that voters should be encouraged to give as full rankings as
possible in the Condorcet methods. Only the truly irrelevant
candidates are ones that most voters could just ignore. If voters
start truncating any potential winners of the competing sections then
the good properties of Condorcet methods get easily lost. The best
compromise candidates are no longer identified.
P.S. My biggest fears with winning votes is that
it might
in some real elections (with sincere votes)
produce a result
that people do not find natural.
10: A>B=C
20: A>B>C
16: A>C>B
01: B>A=C
01: B>A>C
26: B>C>A
03: C>A=B
03: C>A>B
20: C>B>A
This set of votes is cyclic. B and C are from the
same wing
(they support each others). But should C win (as
in most
methods with winning votes) although B has more
first
preferences than C and also A supporters like B
more than
C?
As long as A loses I don't care that much. If voters
care so much about
a 2% difference in FPs then we are generally in
trouble. (What principle
does margins adhere to that prevents this from being a
problem in
general?) And not even half of the A voters supported
B.
If A represents the left wing then the left wing voters
said "we prefer B to C if right wing gets majority and one
of their candidates wins". In the left wing there were more
voters that didn't maybe care or found all the right wing
candidates to be equally bad than in the right wing. That is
natural. Within the right wing B seems to be clearly more
popular than C, so the right wing agrees with the left wing
that B is better than C. The only remaining tricky part is
that the votes are cyclic. Can we derive some such logic
from that cycle that C should win instead of B?
Why all this talk about B:C, why don't you talk about A:B?
Most methods and we two seem to agree that A should not win. (There is
the cycle still and that could maybe be used to argue something else.)
If this scenario is important I can't imagine what else is too.
This scenario is important to me since these votes could well
materialize in a real life election. Many other example threat
scenarios on the EM list are ones that are likely to occur only in the
minds of the election method experts but this one could really happen
in real life, and regular voters and media could start wondering why
the method failed to see the obvious looking widely spread opinion
that B is better than C. (This could be a bit like IRV failing to
elect the Condorcet winner, although maybe not as obvious case to
argue about because of the involved cycle.)
There are also some cases where truncation
could be related to strategic behaviour but in large real
life elections this is hopefully marginal and mostly not
rational.
Highly unlikely if "strategic behavior" includes not voting for the
worse of two frontrunners. That is a defensive strategy, so if you're
not including that I'm not sure what you mean.
There may well be many voters that truncate candidates that they
consider to be strong competitors of their favourites. I noted already
above that such behaviour may easily ruin the good properties of
Condorcet methods. I hope that this behaviour would be marginal and I
also think that it is luckily in most cases irrational. On the other
hand I'm sure that we can not fully get rid of it. (I was planning to
reply something to Forrest Simmons on this topic. Maybe soon. One key
point is that if people don't rank the moderate candidates (plausible
winners) of the competing sections then the more radical ones may
easily win. That would ruin one key idea of the Condorcet methods and
could even lead to their failure after being implemented in some
society.)
Juho
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