[EM] Answer about CR equivalency

[MIKE OSSIPOFF]

The question was asked:

Also, how is this strategically equivalent to Approval? Could you give
some examples?

I reply:

First an example, then an argument.

Say in 2002, you prefer Nader best, but you believe that Gore & Bush
are the only 2 candidates likely to be equally or nearly equally
highest in vote-totals.

And say the method is 0 to 10 CR. What do you do? You give Gore
10 points and Bush 0 points. Of course you give Nader 10 points too.

Because you believe that it will be between Gore & Bush, you give Gore
the maximum points assignment and Bush the lowest points assignment.
Just as you'd do if it were 0,1 instead of 0 to 10.

Say we do an Approval balloting, and whatever Approval strategy you're
using says to vote for certain candidates and not others.

Say we then do another Approval balloting, with the results to be
added to the first one. In a big election, your single votes to the
candidates aren't enough to change the Pij. And of course your utilities 
haven't changed either. So your strategy in that 2nd
Approval balloting is the same as in the 1st one. Likewise if it's
done again...

If that's done 10 times, that's the same as a 0 to 10 election. You've
given maximum points to those candidates for whom you'd vote in Approval, 
and minimum points to the rest.

You continued:

Personally I prefer the levels to be scored 1 (Full vote/point), 0.5 (Half
vote/point) and 0 (No vote/points). This would probably be easier for the
voter.

I reply:

As was already pointed out, there's much satisfaction, for many people,
in giving someone a _negative_ point. And that's really closer to the
reality of what you're doing. For instance, in Approval, when you
vote for Smith and not for Jones, what counts is that you're voting
between Smith & Jones in case they're tied or neartied. It doesn't
matter what we call those point assignments. They're a high and a low.
It makes more sense to represent the low by a negative number. Maybe
we should call Approval -1,1.

Incidentally, if you give 1 to one candidate and -1 to the rest, and
I give -1 to one candidate and 1 to the rest, we're both voting for
the same number of candidates. We're just distributing the highs and
lows differently. Effectively thatg's true in Plurality too, where
we give a high to one candidate and a low to each of the others.

We're both voting among the same number of pairs of candidates.

Sure, someone who votes for half the candidates votes among more pairs.

But you could vote for half too, if you wanted to. You don't like
half of them? Ok, we've compared Approval and Plurality for voters who
like different numbers of candidates, and have shown that if it's unfair to 
the voter who votes among fewer pairs because of the
number that he likes, Approval is about 3 times fairer than Plurality.

Mike Ossipoff




It's been argued that 0,1,2 or 0,.5,1 is simpler than -1,0,1 because
they don't have a negative number. But -1,0,1 is simpler because it
only has integers, and, aside from zero, it only has one magnitude of
integers.





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