Condorcet(x( ))

[Mike Ossipoff]

Steve Eppley writes:
> 
> Mike O wrote:

[Again, though I've unsubscribed, I'm answring a few letters
that already arrived from singlewinner]

> >I chose, for my Condorcet proposal, to not count any preferences
> >not expressed by the voter, for 2 reasons:
> >1. Why count, on the voter's behalf, what he didn't say?
> 
> Counting ties as "zero votes against" is "counting", in a way.  The

In the sense that if you count something as zero you get the same
result as if you hadn't counted it (for additive purposes).

But the definition that I've been giving for Condorcet's method
is clear about that. It talks about how many voters have ranked
1 candidate over another. A different method could be defined
that also counts how many have ranked that other alternative
equal to it, and then count those ballots at half value. But
that would be a different method. Condorcet himself didn't
say anything about counting un-voted prefrences either, so far
as I know.

And, if you don't rank A or B, so we count that as half of a preference
for A over B, and half a preference for B over A, we're attributing
contradictory preferences to you. Either you prefer A to B, or
you prefer B to A, but you sure don't prefer each to the other.
But, the fact is that you haven't indicted preference for either
over the other. So why count such preferences?

> word count has more than one meaning, so we need to be careful about

Maybe, but "not counting" has 1 meaning.

> what is meant by claims that counting as zero is different from
> counting as some other value.  Counting as zero is interpreting the
> vote in that pairing as being "not against" both candidates, since
> nonzero means "against".

Yes, the voter isn't saying that either is better than the other.
He certainly isn't trying to say that each one is better than
the other.

> 
> The voter isn't able to say one way or the other what his/her equal
> rankings mean.  I think that if asked, the typical voter would give
> the same Yes answer to the following two questions: (1) Do you want
> vote full strength against your least preferred candidate?  (2) Do

A full strength vote for _whom_ against them? The candidates ranked
higher? Absolutely. The candidate ranked the same? Why? I wouldn't
rank them the same if I wanted to be counted for 1 over the other.
And why would I want to be counted for each one over the other?


> you want to vote full strength against your two equally-least
> preferred candidates?  Doesn't a Yes answer to the second question 

Again, the question is for _whom_ do you want to cast a full-strength
vote agains those 2 unranked candidates? For everyone you've
ranked? Of course. Should you be compulsorily forced to vote 
each of them against the other? If the voter should have the choice
of what preference votes he wants counted in his behalf, then surely
we shouldn't insist on counting things he didn't say.

> mean this voter would want x as large as possible in that pairing?

No. He's indifferent between them. He's casting a full-strength vote
against both of them, but he isn't helping either one beat the other,
or shouldn't be, unless he wants to. In a votes-against count, by
not ranking 2 alternatives, if we count you as voting each one over
the other, then whichever one beats the other, you're counted as one
of the voters who prefer to it that one that beats it. That simply
isn't true. You don't prefer that one to it. You haven't espressed
any preference.


> 
> Here's an illustrative example, a 3-way race between Good, Evil1, and 
> Evil2.  One voter's ballot: {Good > Evil1 = Evil2}
> I chose the candidate's names from this one voter's perspective.  
> Other voters might see things differently, producing a close election 
> and maybe a circular tie.  Not counting ballots like this against both 
> Evil1 and Evil2 in their pairing might throw the election from Good 
> to one of the evils.  

Good. I fully admit that different results are gotten when we
count un-expressed preferences. If you voted only for Good, and
no one else, your truncated ballot could create a circular tie,
even though Evil1 was Condorcet winner, and would have won
had you voted it 2nd.

If we count you as not voting any prefernce that you didn't _willingly_
vote, then Evil 1 can't have a majority against it. If we
invent a preference vote by you for Evil 2 against Evil 1,
then you (unwillingly) can be making Evil1 be beaten with
a majority ranking Evil2 over it. Result: As you said, Good
might win. That's bad. It means that your truncation has stolen
the election from Condorcet winner Evil1. It means that I would
have to quit saying that no defensive strategy is needed unless
order-reversal is attempted. The possiblilty of mere truncation
would be enough to make it necessary for Evil2 voters to
rank Evil 1 equal to their favorite, insincerely. Drastic defensive
strategy needed even without anyone using order-reversal. I posted
an example about his a while back. Either on this list or on
the other one.

> 
> Maybe the voting system *should* infer the voter wants his/her
> ballot to count full strength against the last ranked (or unranked, 
> when the ballot is truncated).

Certainly. It should infer that the voter wants to be counted full
strength for everyone he's ranked against everyone he hasn't
ranked. But to infer (mutually contradictory) preferences that the
voter never voted is contrary to his wishes, and screws up Condorcet's
properties.


> 
> >2. Condorcet would lose its lesser-of-2-evils properties if
> >voters were counted as giving preference votes that they
> >never indicated.
> 
> Would you elaborate?  How is this true of Condorcet(.5) and 
> Condorcet(x2()), where x2() is one of the formulas I suggested a 
> couple days ago?

It's as I described above, in the Good, Evil1, Evil2 example.

The Condorcet winner can never have a genuine majority against
him. But any system that falsifies preferences that weren't voted
can create a fake majority against a Condorcet winner, allowing
truncation to steal the election from it, and taking away the
assurance that defensive strategy is never needed unless order-reversal
is attempted on a scale sufficient to change the election result.

This is important, because order-reversal isn't likely, but
truncation is quite common. It's happend in every rank-balloting
election I've participated in, it seems to me. It will always happen
in public political elections. Let's not let truncation make
defensive strategy necessary.

It can also be said that, with Condorcet, even if everyone mistakenly
believed a certain alternative to be the best compromise they
can get (Condorcet winner), and everyone included it in their
ranking, and no one included in their ranking any alternative tht
they like less, this couldn't ever give the election away to
that alternative if there's a Condorcet winner ranked over it
by a full majority.

I call that "Invulnerability to Mis-Estimate". That kind of
mis-estimate will be quite common in public political elections,
and many others too.

But if we falsify preferences that a voter never voted,then we
lose that important property.
> 
> If this is true, I'll lose interest in x<>0.
> 
> --Steve
> .-
> 


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