Another flaw in monotonicity

[Blake Cretney]

On Tue, 3 Nov 1998 20:16:08    Mike Ositoff wrote:

>Plurlity does commit a violation very similar to nonmonotonicity,
>but marginally less bad. Because, as David said, it can force
>you to vote a less-liked alternative over your favorite, then
>your participation in the election can produce a result worse
>than would have happened if you'd stayed home instead of voting.
>
>Any of the rank-methods proposed here can do that too. And in
>the rank methods, even a sincere ranking can cause a worse result
>for you than if you hadn't voted. Of course when Margins or IRO
>forces you to vote something over your favorite, that makes it
>even worse.

This is essentially the same problem as NOSHOW.  Basically, the idea
is that it is possible in the ranked methods that a vote can cause
someone you rated higher lose to someone you rated lower, to the
extent of defeating your first choice or electing your last choice.
All of the ranked methods people are proposing (except Borda) have
one or the other of the aforementioned problems, and Schulze, 
Smith//Condorcet and LCM (my method) have both.

This sounds bad, but to be important, a criterion must have more
than rhetorical value, so we should look for a justification for
it.

It's fairly obvious that this is not a strategic problem.  No one
could possibly have enough information to know to use the "not
voting" strategy, and if they had enough, they would find a
different strategy even more effective.  I think this can be
seen from the NOSHOW examples presented in the past.

So, what we're talking about is a criterion that attempts to show
a method is behaving capriciously, like I believe a violation of 
monotonicity or reverse-consistency does.  That is, that a 
method that violates the Adverse Result Criterion can't really
be finding the best guess for best candidate based on the 
evidence provided (the ballots).

The argument would be, that if the method views A as the best
guess, and someone else votes for A in first place, the best
guess cannot now be B.  And if all they did is vote for A
alone in first place, I would agree.  However, if they provide
other information, I think this could effect the answer.  So,
for example, if the only reason B wasn't winning before is
that it had a big loss to C, then decreasing that loss could
make B look like a much better candidate.  Even better than
A.

Of course, this isn't the individual voter's intention.  But
fulfilling each individual voter's intentions is the same as
making a method strategy-free, it is impossible.  Instead, I
think we should look at the vote as if it were evidence
entered into a court.  The evidence of the voter's preference
will usually help the higher ranked over the lower ranked,
as the "court's" job is to determine the best candidate based
on voter opinion, but in some exceptional cases, it may make 
sense to use the evidence in a way the voter did not intend.
If this results in better candidates winning, there isn't a
problem.

>Approval is the method that doesn't do that. When proposing VA,

A method where each voter gives each candidate a numeric score,
and the candidate with the highest total score wins, will pass
this criterion.  Approval is just a special case of this method
where the only scores allowed are 0 and 1.

Of course, these methods give up other things.  Like, for example,
the idea that if a candidate is the first choice of a majority,
it will be guaranteed to win, without any massive strategic voting 
effort being necessary. 

>one tolerates that fault, because of VA's big strategic advantages.
>But what's the reward for tolerating it with Margins or IRO? :-)
>
I don't, of course, believe that VA has any strategic advantages
over Margins.  We've discussed that at length.  And I don't think
much is required to outweigh the Adverse Result Criterion, as
I only think it is useful for its rhetorical power.

---

Blake



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