Lesser of 2 evils

[Mike Ossipoff]

After writing his own version of one of the "lesser-of-2-evils guarantes"
that I'd sent to him, Bruce asked 2 questions:

Is this analysis correct?

Answer: No

If not, then why not?

Answer: For the same reason I told you last time you asked
        the same question.

I'll repeat the answer for you. My reply this morning was brief,
because I to leave. 

What you don't seem to understand is that in an election there
can't be 2 or more voter majorities consisting of entirely
separate sets of voters. If that's too complicated, tell me
and I'll try to find a simpler way to say it.

I said that if a majority rank A over B, then there should
be a way that the members of that majority can vote that
will ensure that B won't win, and this doesn't require
voting A equal to or over anything they prefer to A, or
voting a less-liked alternative over a more-liked one.

In your A,B,C example that means that the majority ranking A
over B can prevent B from winning. It means that the majority
ranking B over C can prevent C from winning. And it means
that the majority ranking C over A can prevent A from winning.
And of course it means that the drastic defensive strategies
named in the above paragraph aren't needed to make that possible.

So yes, you're right as far as that: Each of those majorities,
with their overlapping membership has that power.

Where you go wrong is when you, in your version, say that it
must be possible for them to all simultaneously do that. I
didn't say that; only you said that. Again, is there a simpler
way I can word that?

Supppose, for instance, that the majority ranking A over B
decides to make sure that B can't win. They need only make
sure that C doesn't have a majority ranking anything over
it. Since B has such a majority against it, and they can
ensure that C won't, that means they can ensere that B can't
win, by Condorcet's method's choice rule.

Now, you want the voters ranking B over C to have that same
power? No problem; they do. You want them to be able to do
that simultaneously? Again, I have to agree with you:
That's a ludicrous suggestion. You made it, I didn't.

It's ludicrous because, for 1 thing, the majority ranking
B over C must include some of the voters ranking A over B.
Why? Because there are only 100% of the votrs, and if more
than 50% rank A over B, and if none of them rank B over
C, that just doesn't leave a majority to rank B over C.
As I said, there can't be 2 or more disjoint majorities
of voters in an election. "Disjoint" means that they don't
share any members. 

Those voters who ranked A over B, and want to ensure that B won't
win, have to make sure that something else won't have a majority
against it. This can easily be accomplished if sufficient A voters refuse
to vote B over C. So, you see, your ludicrous suggestion of
all those overlapping majorities defeating someone simulataneously
wouldn't work. The voters who want B to lose can only do that
by ensuring that something else is less beaten than B. 

Anyway, the brief & simple answer is that I never said they
could all simultaneously ensure the defeat of the alternative
they want to defeat. Each of those majority sets could defeat
whom they want to. But your fallacy is your belief that all
of those majorities consist of separate voters. For each 1
of them to have the power to do that isn't the same as
saying that they all have the power to do it simultaneously.

Anyway, as I defined Condorcet's method, it's a rule for picking
a single winner. We'd previously agreed that if that rule
should return a tie, some tie-breaker would pick a winner.
So there's no way that all 3 alternatives could be defeated
in the election anyway, if 1 has to win.

Also, you've managed to "misunderstand" 1 of the criteria that
I've sent you, but you don't mention the ohters. Do you
want an explanation of 1 or more of them too?

So far, I've defined several criteria:

Truncation resistance
Invulnerability to Mis-Estimate
Generalized Majority Criterion
Defensive Strategy Criterion

***

Mike










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