[EM] James A. didn't read SDSC before expounding on it
jarmyta at antioch-college.edu
Wed Nov 24 02:35:57 PST 2004
James Green-Armytage here, replying to Mike Ossipoff...
Mike, you wrote:
>James A. was in too much of a hurry, and didn't notice that our SDSC
>definition is accompanied, immediately preceded, by a definition of
>two candidates equal.
You're right, I missed that every time I read the definition. My mistake.
>Anyway, of course what you need to do then, is define your own criterion.
Okay, fair enough. It's not your criterion, then, it's my criterion,
which was inspired by your criterion. Or, perhaps it's Steve Eppley's
"sincere defense" criterion. Anyway, it's a criterion that I find to be
>If so, are you sure that by a majority giving 100 points to X, and 0
>to Y, and ranking X over Y, that ensures that Y can't win
[using the cardinal pairwise method]
>? Can you
Yes, I think it is logically certain. Let's say that there are 100
voters. So a majority consists of at least 51 voters. So let's say that 51
voters rank X over Y, rate X at 100, and Y at 0. X has a pairwise victory
over Y, and the weighted magnitude of the defeat is 5100. In order for the
X>Y defeat to be overruled (assuming that the completion method is
beatpath, ranked pairs, or river), there needs to be a chain of defeats
from Y to X such that all of the defeats have a weighted magnitude of more
than 5100. This is impossible. Why? 51 voters give Y a rating of 0.
Therefore, the strongest possible defeat that Y could possibly have over
another candidate would be 4900. This should hold for any number of voters
"n", as long as a majority is defined as being a number greater than n/2.
>IIf so, then your method indeed meets your stronger version of SDSC.
>The usefulness of that depends on how much influence they're having on X1
>X, when they rank X1 over X, but rate X equal to X1. Even if technically
>they're still voting X1 over X, to what extent are they actually helping
>win against X? If not much, then your method's compliance with that
>stronger version of SDSC is a hollow victory. Though you're voting X1
>X, you're doing so in a way that's surely less effective than if you'd
>ranked X1 over X in ordinary wv Condorcet.
I think that you're contributing quite a lot to the X1>X comparison. It
counts as a plain old whole vote, just like in any other pairwise
comparison method, unless there is a majority rule cycle.
I remember that you had a concern for a situation where many voters cast
ballots as follows: Nader 100 > Kerry 100 > Bush 0. You were worried that
a lesser of two evils problem would persist, barring Nader from having a
fair shot at victory. I pointed out that if Nader is a Condorcet winner,
it will not matter at all what the ratings were... likewise if Bush or
Kerry are Condorcet winners. The only circumstance where the vote will not
count as heavily against Kerry is if there is a Nader>Kerry>Bush>Nader
cycle. In this case, your vote will count maximally towards the Kerry>Bush
defeat, and not towards the Nader>Kerry defeat. If there was a
Nader>Bush>Kerry>Nader cycle, then once again your ratings wouldn't matter.
So, I don't think that there is a serious lesser of two evils problem
because Nader has a perfectly fair chance of winning even if his
supporters are relatively protective of the "lesser evil" (in their view,
at least) candidate Kerry... because this kind of "protection" will not
prevent Nader from being identified as a Condorcet winner, if he genuinely
To expand out example, let's imagine that there is another candidate whom
you like better than Nader. Let's arbitrarily call this candidate
"Josiah". Let's say that you cast a ballot as follows: Josiah 100 > Nader
99.01 > Kerry 99 > Bush 0. Let's assume that we're using the "maximizing
in scale provision".
If there is a Nader>Kerry>Bush>Nader cycle, your vote will count almost
maximally (99.98+ points) towards the Kerry>Bush defeat, as before. If
there is a Bush>Kerry>Nader>Bush cycle, your vote will count maximally
(100 points) towards the Nader>Bush defeat, as before. If there is a
Josiah>Nader>Kerry>Josiah cycle, your vote will count almost maximally (99
points) towards the Josiah>Nader defeat. If there is a
Kerry>Nader>Josiah>Kerry cycle, your vote will count maximally (100
points) towards the Josiah>Kerry defeat. And so on. This is just to show
that you can still make meaningful ratings gaps between multiple
candidates whom you like better than your "safety" candidate(s) (Kerry, in
this case), because of the maximizing in scale provision.
P.S. Please stop calling me "James A." I would prefer "James", "James
G-A", or "James Green-Armytage".
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