[EM] Relative Margins

[MIKE OSSIPOFF]

Steph--

I admit that you've proved that relative margins is better than
winning-votes...by your standards.

I always point that out in discussions like this. Any method can
be the best, depending on what you want.

Everyone who values your standards highest should call relative margins
the best.

The fact that your standards don't address the concerns expressed by
voters certainly doesn't mean that your standards are wrong.

My defensive strategy criteria measure for the standards of
majority rule, and getting rid of the lesser-of-2-evils problem.
Those are the concerns that we hear about most from voters and
reformers. Other, less widely-shared, standards are valid too, however.
If you want to offer a relative margins method as a public proposal,
you merely have more work to do, because you'll have to convince people
that your standards should be important to them. I want to express
my encouragement in that undertaking.

But when we talk about the standard of ethics, fairness to the
voter, maybe things aren't quite so relativist. Of course the
reason why we want a measure of defeat strength is so that we can
determine which defeat(s) to drop, or to not keep. When the people
have collectively voted in favor of a pairwise defeat, we're tampering
with, overruling the expressed public will if we drop that defeat.

Overruling a publicly chosen defeat is an undesirable necessity. But
at least we can try to minimize the number of people being overruled
when doing so.

If A pairbeats B, 50 to 40, and if we don't drop that defeat, we're
not overruling those 40 people who opposed the defeat. They were
overruled in the voting, when they were outvoted, and the people chose
to affirm that defeat. So how would we overrule someone? By dropping
the defeat. Then we're overruling the public choice, and there are
50 people who have justification to object. So, if fairness to voters
is the standard, we want to minimize the number of voters whom we
overrule when dropping, or not keeping, a defeat. The people who voted
in favor of the defeat are overruled when we drop or skip the defeat.

Of course you could say that we should instead look at the sum of
all the voters overruled in all the defeats that are dropped. Maybe
that requires an as-yet unproposed method, or maybe Ranked-Pairs(wv)
already fills the bill.

If it requires a new method, one that doesn't meet all the criteria
that the wv methods meet, then of course we'd have a choice to make,
a familiar situation with voting systems. If the new method were 
complicated, that would strongly count against it as a public proposal.
You wrote:

But using ranked pair in this manner brings back Mr.
Ossipoff ghost
of
TRC.

I reply:

I don't use the Truncation-Resistance Criterion. I defined it
almost a decade ago, but it only applies meaningfully to pairwise-
count methods. SFC & GSFC apply usefully & meaningfully to all
methods, and they generalize TRC.

You continue:

The fact is Mr. Ossipoff is right: truncating preferences
can harm my
favourite
using margins or relative margins.

I reply:

No, that isn't what I say. On a topic closest to the one you're
talking about, SFC & GSFC say what I say. If you want to limit
the discussion to truncation, and pairwise-count methods, then
with margins or relative margins, truncation can cause big
majority rule violations, and a defensive strategic need to
reverse preferences.

You continue:

But what he does not
say is: NOT
truncating
can harm my favourite using winning votes. So strategy is
still an
issue, but
one we cannot avoid for the moment...

I reply:

If I led you to believe that wv is entirely strategy-free, then
I lied. Gibbard & Satterthwaite showed that no nonprobabilistic
method can make that claim.

A defensive strategy in wv, the best such strategy, in my opinion,
is defensive truncation. In situations where offensive order-reversal
is being used against you, then it can succeed if you don't defensively
truncate. But in your margins or relative margins, it can succeed
if you don't defensively order-reverse. Which situation is worse?

I don't claim that wv is completely strategy-free, only that it
isn't as strategy-ridden as margins & relative margins.

Mike Ossipoff



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