When can AV defeat a majority winner

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Jan 15 19:27:39 PST 2002

Let me first say that when we say "AV" in this discussion, we mean
Approval, not the Alternative Vote. In some countries IRV is called
"the Alternative Vote", and abbreviated "AV".

The original letter with this subject line gave a good answer and
covered the subject well, but I'd like to add a little:

Say there are 3 candidates: Favorite, Middle, & Worst. Favorite is
your favorite, and Worst is your last choice, and Middle is
an inbetween compromise or lesser-evil.

For Favorite to lose even with a majority of 1st choice support,
you & other Favorite voters would have to believe that Favorite
is likely to have fewer votes than Worst. Likewise for the mis-estimate
in the opposite direction, when you mistakenly refuse to support
Middle because you believe that Favorite has a majority. Either way,
the error happens because you misjudge between Favorite having a
majority and Favorite having fewer votes than Worst.

That's a big mis-estimate to make. Of course it's easier if Middle
has very little 1st choice support, but that's exactly the situation
where IRV will dump a sincere CW compromise and jump to an extreme.
Where IRV will _reliably_ do that.

So failure is easier in Approval, and automatic in IRV under those
conditions. What are the consequences of that failure with those 2

With Approval, if you think Favorite has fewer votes than Worst, and
you vote for Middle, and the other Favorite voters do, then, admittedly
Middle will win.

If you  believe that Favorite might have a majority, and so you
refuse to vote for Middle, then it's reasonable to assume that everyone
has access to the same polling information, even when it's wrong,
and so it's reasonable to say that the Worst voters believe that
Worst will get fewer votes than Favorite, and
they'll vote for Middle. The result is that Middle wins instead of
Worst, even though you didn't vote for Middle.

So, when Approval fails, it tends to err by electing the middle.
When IRV fails, it errs by jumping to an extreme. Either failure is
undesirable. Avoidably electing Middle would be a nuisance. Avoidably
dumping the sincere CW and jumping to an extreme could be more than
a nuisance.

Middle probably won't do as much long-term harm as an extreme candidate
might. And, if Approval elects Middle, even though Favorite has a
higher vote total than Worst does, the Favorite voters will then
know that next time they needn't vote for Middle or his party.
Approval quickly & reliably homes in on the voter median & stays there.

Richie's letter implied that only in Approval, but not in IRV,
is there a strategy incentive & problem, because no one knows how the
others will vote. But say that you know that Middle is closer to Worst
than to Favorite (as he is in our U.S. elections, where Democrat is
Middle). That's not implausible; it's how it is. Say that all 3
candidates are, as near as anyone can guess, roughly the same in terms
of 1st choice support, or that you otherwise expect that there's
a majority preferring Middle to Favorite.

Suppose that, like so many lesser-of-2-evils progressives, you
consider it really important to make sure that Worst doesn't win.
Do you sincerely rank Favorite in 1st place? Why would you? Favorite
can't win. But by voting for Middle in 1st place, you can protect
Middle from the possibility of immediate elimination, and of losing
to Worst even if a majority prefer Middle to Worst. So the only
vote that makes sense for you, from an instrumental standpoint, is
to vote Middle in 1st place, dumping your favorite.

Both voting systems require strategy. But Approval's strategy never
includes voting someone over your favorite.

The IRV scenario described above isn't implausible, and your
strategic incentive needn't be based on detailed knowledge, contrary
to what Richie said. It can be the result of the same lack of information 
that Richie talked about in connection with Approval
strategy. The experience in Australia, where 3 different Australians
have told me that it's common to insincerely uprank a lesser-evil
to 1st place, shows that, contrary to what the IRVies continually claim,
IRV's incentive to dump favorites is found in actual elections.

Likewise, contrary to IRVie misunderstanding, IRV's nonmonotonicity
happens without voters having detailed knowledge or making impossible

I meant to reply to Richie's standard bullshit in the _Science_ letter,
but didn't get around to it, I'm almost ashamed to say. But not quite
ashamed to say, because we only have so much time for distasteful
chores like trying to fight the IRVie ant-invasion.

Of course they probably wouldn't print my reply anyway. I don't know
why they published Richie's letter either, unless it's because he
had a physicist sign it. Being a physicist certainly qualifies someone
on voting systems. Notice, though, that the physicist's name was last
in the list, with Richie and his CVD friend listed first.

The person who wrote the letter whose subject line is quoted in
this letter's subject line should forward his reply to _Science_,
on the chance that they might print it. Or if they don't print it,
at least they'll read it.

Mike Ossipoff

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