Fairness, votes against, and Condorcet(x)

Mike Ossipoff dfb at bbs.cruzio.com
Sun Apr 21 04:16:11 PDT 1996

Steve Eppley writes:
> Mike Ossipoff wrote [in "Brief reply to Steve"]:
> >Steve asked why 0 is a fairer value for x than 1/2 or 1. Because
> >it should be up to the voter to choose whether or not he/she wants
> >to express preferences between a particular pair of alternatives. 
> >If x is other than 0, then compulsory preferences are counted, which
> >may not be what the voter intended. So flexibility & democratic freedom
> >are reasons for x = 0. Reasons for not counting preferences that the
> >voter never voted. Besides, I claim that it just doesn't make sense
> >to count you as voting preference that you didn't vote, especially
> >a pair of opposite preferences, which couldn't both reflect your
> >genuine preferences.
> I can see why it might be wrong to count indifference as partial
> votes against two popular twins when they're paired.  
> But what about when the candidates aren't twins, like Nader and Dole
> in the {Clinton > Dole=Nader} ballots?  If I was one of these voters,
> I probably would have undergone an evaluation process which told me 
> to prefer Dole over Nader on some issues but Nader over Dole on others. 
> So there's a case to be made for splitting that vote of indifference
> into half a vote against each (x = .5).

You can't prefer Nader to Dole and also prefer Dole to Nader. Sure,
on some issues a person could prefer one, and on some issues the
other, but he still either is indifferent or prefers 1 to the other,
but _doesn't_ prefer each to the other. Sure, if you're indifferent
because your reasons for liking Dole better than Nader just balance
out your reasons for liking Nader better than Dole, then you could
say you have a preference, in some amount, for each over the other.
Ok, what amount? Who's to say that 1/2 of a full-strength preference
is what you feel each way? Why not a full preference? 

Flexibility is desirable, especially when x = .5 gives a different
election result from x = 0. When we don't count you as voting
any prefernces that you didn't vote, you can still give 1/2 of
a preference to Dole over Nader & 1/2 of a preference to Nader
over Dole: Flip a coin to choose which to vote over the other.
If there are only 1 or 2 voters who feel that way, then they
aren't likely to change the election result. If there are lots,
enough to have an effect, then if they flip a coin to choose
which to vote over the other, then the result will be the same
as if they'd all given .5 to Nader over Dole & .5 to Dole over
Nader. So we can consider it a freedom issue. Do you want to be
forced to give prefernce votes between candidates between whom
you don't want to give preference votes?

No, inventing preferences that people never voted is undemocratic
& violates the voter's wishes. In the event that the voter really
wanted to give .5 for Dole over Nader & .5 to Nader over Dole, then
he could do so probabilistically.

Another thing: if you're forced to give .5 to each of 2
candidates that you don't rank, that can make truncation have the
effect of order-reversal. Truncation by one side can cause the
Condorcet winner to have a good size majority against him--sometimes
a bigger majority than the truncators' candidate has against him.
Truncation, even innocent, nonstrategically-intended truncation
could steal the election from a Condorcet winner and give it to the
truncators' candidate.

In other words, forcing the voter to give prefernce votes that
he didn't vote would prevent Condorcet's method from having its
important lesser-of-2-evils property.

> It would also look more "right" to me if the method gives the same
> winner with 
>   20 Clinton > Dole=Nader 
> as with 
>   10 Clinton > Dole  > Nader 
>   10 Clinton > Nader > Dole

Sure, and it would look more right if removal of a non-winning candidate
didn't change the election result. (the Independence From Irrelevant
Alternatives Criterion--IIAC). But there's no method that meets other
important criteria & also meets IIAC. Methods with rankings as their
input can't even meet the Pareto & Non-Dictator criteria if they
meet IIAC. The Pareto criterion says, in single-winner elections, says
to never elect an alternative to which everyone prefers something else.
The Non-Dictator Criterion says that there must not be any voter who
single-handedly determines the winner in every election.

Point-Assignment (Weighted Voting) doesn't violate IIAC, but it
violates the Majority Winner Criterion: It can fail to elect an
alternative that is the 1st choice of a majority.

So, though IIAC makes sense, and would be nice to have, it would
be a costly thing to have, in terms of what we'd have to give
up to have it. 

So do you want that symmetry you spoke of, instead of getting rid
of the lesser-of-2-evils problem?

Besides, why should it be symmetrical like that? Why should no
preferences between A & B be counted the same as equal preferences
for each over the other?? If you agree that votes-against are
important (either because of the standards that are met, or because
of other reasons), then those two things shouldn't be counted the
same, since no preference between A & B is not a vote against each.

Sure, in a 2-way race the effect would of course be the same. But
be careful about applying what would work in a 2-way race an election
between more than 2 alternatives. It's no longer just between A &
B, and there's no reason why no prefernces should count like equal

> Maybe my evaluation told me I prefer Dole over Nader on some issues,
> Nader over Dole on some, and *like* both on others.  Then I might want
> to set x such that 0 < x < .5.

Flip a coin, to probabilistically give .5 of a preference vote for each
over the other.

> Maybe my evaluation told me I prefer Dole over Nader on some, Nader
> over Dole on some, and *dislike* both on others.  Then I might want
> to set x such that .5 < x < 1.
> Maybe my evaluation told me I dislike both Dole and Nader intensely 
> on all issues.  Then I might want to set x = 1.
> On the other hand, allowing x > .5 might violate the one-person 
> one-vote principle.  I'm not sure...

It probably wouldn't because if you vote Nader,Clinton,Dole, you're
casting a vote against Clinton & a vote against Dole. So there's
no reason why you shouldn't be able to cast full-strength preference
votes against 2 alternatives. But letting you cast one for A against
B & for B against A, so as to give A & B bad scores seems to be more
in the spirit of a Point-Assignment system, and would be abused
as it would in a Point-Assignment system. Conservatives would use
that way of giving especially big negative point scores to the
progressives & Democrats, etc., and the progressives & Democrats
would do the same. So it seems to me that it's best to only count
expressed preferences, to avoid turning the method into a point

No problem with .5 though, _as long as you don't force the voter
to be counted with preference votes he didn't cast_. As I said
, you can do that probabilistically if you so wish. And what if
you, instead, wanted to give .27 of a prefernce vote for Dole over
Nader, &, say, .31 prefernce vote for Nader over Dole. You can do
that probabilistically also: Put 10 identical pieces of paper into
a paper bag, each with one of the 10 numerals on it. Draw one out.
Write it down. Return it to the bag. Draw again, & write the numeral
to the right of the 1st one. If the 2 numerals together make a
number of at least 58, then don't vote for either over the other.
If they don't, but they make a number of at least 27, then
vote for Dole over Nader. Otherwise vote for Nader over Dole.

But these things should be up the voter.

> >Aside from that, Condorcet doesn't meet the standards & criteria that
> >I've been talking about if we make up preferences that people didn't
> >vote.
> How does Condorcet(.5) fail to meet them?  How does a Condorcet(x(vij)), 
> which lets each voter specify the "x" to use in each indifferent
> pairing, fail?  (I'm not proposing this method, since it would be 
> hard for the voters to understand what's expected of them.  So maybe 
> you won't want to spend time answering this second question.)

It could make truncation, whether innocent or strategically-intended,
have the effect of order-reversal, stealing the election from a
Condorcet winner & giving it to the truncators' favorite. (A Condorcet
winner is an alternative which, when compared separately to each one of
the others, is preferred to it (even if not ranked over it) by more
voters than vice-versa).


True preferences:

46%: Dole, Clinton, Nader
20%: Clinton
34%: Nader, Clinton, Dole

Actual rankings:

46%: Dole  (truncation)
20%: Clinton
34%: Nader, Clinton

As before this creates a circular tie. But where, when we don't
force voters to give preference votes that they didn't choose to
vote, Clinton, the Condorcet winner wins, and truncation could
never elect someone with a majority against him unless everyone
has a majority against him--if count un-voted preferences, if
we count the Dole voters as giving .5 for Nader over Clinton &]
.5 for Clinton over Nader, then Dole wins.

That means that Condorcet's method would lose the most important
part of its properties, & would no longer meet the standards that
it meets.


As for letting the voter choose the value for x, that's no problem,
since it's the voter himself/herself who is choosing to do that.
I agree that it would complicate the rules too much, to no real
purpose. For even more flexibility, the voter could indicate
some reduced value for every one of his/her preferences, if he/she
so chooses. Again, it would complicate voting rules too much, without
gaining any properties or standards compliance.

> [To keep the subject lines from diverging needlessly, how about
> avoiding replacing them with comments like "Brief reply to
> so-and-so"?  The body of the message can make it clear that it's
> just a brief reply.] 

Sure, in fact some mailers indicate in the index the length of
the letters, so the word "brief" isn't needed. But if the title
doesn't say whom it's to, then it could sometimes be to any of
several people, on a particular topic. But, sure, I have no problem
with leaving the topic line as-is rather than indicating to whom
I'm replying. But often the topic of the discussion changes, and
then it's necessary to change the title. Maybe then it would
be best to add "...was _____". But maybe the new subject line
would be sufficient to tell people what one is replying to.

Anyway, I have no problem with not indicating to whom I'm replying
int he subject line.

> --Steve
> .-


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