[EM] Fundamental & Derived Standards. 1p1v?

[MIKE OSSIPOFF]

Since Adam suggested that those using the 1-person-1-vote criterion
(1p1v) should justify it, instead of just expecting people to take
it as a given, I haven't noticed anyone trying to justify 1p1v.

Of course I've been saying that standards don't need justification,
but that isn't really true of all standards. Even my own favorite
standards can be justified in terms of more fundamental standards.

For single-winner voting systems, a criterion is a yes/no test. It
might be justified by, and intended to test for, some standard, but
it could also be that a criterion is its own standard.

We could call a standard a "fundamental standard" if it's advocates
don't justify it in terms of other standards, if, for them, the
standard's value is obvious and not in need of justification in terms
of something else.

We could call a standard a "derived standard" if it is justified in
terms of another standard (which could itself be a fundamental standard
or a derived standard).

So which of those is 1p1v? Criterion? Fundamental standard?
Derived standard?

That's the first question that 1p1v advocates should answer. If you
say that it's a fundamental standard, then that won't do,
because 1p1v is a rule-criterion, a criterion whose requirement is
purely about a method's rules. As opposed to a results-criterion.
Sure you can still say that, to you, 1p1v is a fundamental standard,
but few here will accept a rule-criterion as a fundamental standard.

IRV advocates use rules-criteria that are really just restatements of
IRV's definition.

And, of course, if you say that 1p1v is a criterion that you don't
call a standard, or that it's a derived standard, then you've got to
justify 1p1v in terms of other standards. Any chain of standard
justifications has to eventually come to rest on a fundamental standard.

I've been using LO2E & majority rule as fundamental standards, though
they're really derived standards. All I've been saying is that they're
important because they're important to lots of people. I only meant
that as a practical observation: If you propose a method that fails
those standards, then it will be bad news for your proposal when
people find out that your method fails those widely-held standards.

But LO2E & majority rule can be justified in terms of more fundamental
standards:

It's been recently pointed out here that lack of majority rule results
in instability because one submajority after another could repeatedly
replace the previous one in government. Yes, and additionally,
having a dissatisfied majority doesn't make for stability.

Also, surely the undesirability of dissatisfaction is a fundamental
standard, and so we don't want to dissatisfy an avoidably large group
of voters. If a majority of all the voters indicate that they prefer
X to Y, they're saying that if we elect X or Y, it shouldn't be Y.
So if we elect Y, depending on the situation, we could be dissatisfying
an avoidably large group of voters, depending on whether or not that
majority pairwise vote is in a cycle containing no smaller majorities.

So the desirability of majority rule, as I've defined it here in
previous postings, follows from the fundamental standard that
dissatisfaction is undesirable, and so we should avoid dissatisfying
an avoidably large group of voters.

Also of course majority rule can be justified in terms of social
utility, which also makes sense as a fundamental standard.

LO2E? If a method requires drastic defensive strategy to avoid majority
rule violations, and if voting is sincere, then we have a majority
rule violation. If people bury their favorite because of the LO2E
problem, they're concealing who their favorite is. A voting system can't
respond to unexpressed preferences, and when the voting system isn't
taking into account the favorite of a large number of people, that
can't be so good for SU. Sure, sometimes LO2E strategizers guess right,
but they won't always. Myerson & Weber showed, for example, that
Plurality can keep on having _any_ two parties, other than the bottom
two, as the perceived and actual frontrunners in every election,
from now on. The LO2E voter says, "Well, just as the tv said, my
favorite got very few votes [maybe because he didn' vote for him],
and so I'd better keep on voting for the lesser-evil." So that lesser-evil 
will always seem necessary to that voter.


I don't call these proofs, of course, but I've told of some ways in
which majority rule & LO2E can be justified in terms of fundamental
standards.


By the way, if 1p1v advocates consider 1p1v not to be a fundamental
standard, but as one that needs justification, let me assist you by
bringing up the relevant situation:

Say in Approval, Smith beats Jones by a small margin, and that lots
of Smith voters also voted for John Doe. The Jones voters voted only
for Jones. Do the Jones voters have cause for complaint? Why?
Smith outpolled Jones because the people indicated that more prefer
Smith to Jones than Jones to Smith. Of what relevance is it that
the Smith voters also like John Doe better than Jones?

In determining whether Smith will outpoll Jones or vice-versa, every
voter has equal power.

But the 1p1v advocate might say, "But the Smith voters, when they
voted also for John Doe, had more irons in the fire, they had more
possibilities covered. They were made better off by their additional
John Doe vote."

Ok, now you're talking about ballot-expectation, and I've told why
Approval is about 3 times better than Plurality in regards to
equal ballot-expectation.

You say that you don't like Plurality anyway, but Plurality is what
we'd be replacing with Approval, in the U.S.'s partisan elections,
and in other countries' Plurality elections. And do you think that
Plurality violates 1p1v? If not, then any measure by which Approval
does better than Plurality obviously isn't the 1p1v justification that
you want.

There's been some beginning of an effort to justify 1p1v in terms
of voting power. But the ability of a ballot to cancel out any
other ballot makes it difficult to say that Approval gives some
voters more power than others. And, as I said, everyone has equal
say on whether or not Smith will outpoll Jones. And no one has
shown us a measure of voting power in which another method is better
than Approval. So if you want to use unequal voting power to justify
1p1v, you need to do a lot more than you've done so far.

So what is 1p1v--criterion, fundamental standard, or derived standard.
And if it isn't a fundamental standard, then how would you justify
it in terms of a standard that you call fundamental?

Mike Ossipoff




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