[EM] Approval Voting vs Instant Runoff Voting

[Forest Simmons]

I'm responding after a lot of excellent answers that I cannot improve
upon.

You do make an excellent point that it is not possible to deduce what
voters will do in an approval election, even when both their utilities and
the information available to them are presumed to be quite precise.

Like others who have commented, I don't hold this against Approval. The
most calculating, rational voter may have externalities that affect his
decision but cannot be effectively incorporated into the model. One
dimensional utilities are not totally adequate for modeling our material
needs, let alone our thoughts, feelings, hopes, fears, etc.

So without making me think less of Approval, this ambiguity does make me
face the reality that any comparison of Approval with another method that
starts from utilities and known amounts of information ... any comparison
of that type is not as cut and dried as one would hope for.

Someone mentioned that some people are more willing to take risks than
others.  Here's some thoughts along those lines:

Would you rather pay a penny for one chance in ten thousand at winning 200
dollars or pay the same amount for a 100% chance at winning two cents? 
The expected payoff is the same, and most of us would agree that the first
option is for the (slightly) more adventurous spirit, because it deals
with the small chance for the big payoff.
  
In a lone mark plurality election John and Sally both prefer Nader over
Gore over Bush, and both are convinced that Gore has a chance of winning
the election and Nader doesn't.  Sally votes for Nader, and John votes for
Gore.  Which is the risk taker? 

At first blush we would say Sally is the risk taker.  But John is the one
who is counting on the tiny probability that his vote will be pivotal in
the election.  As long as Gore wins or loses by more than a one point
margin, John may well regret that he passed up his 100% chance to show
a little support for Nader. There is a teeny tiny (teensy weensy in some
circles) chance that John's vote will be pivotal in saving Gore's skin. In
that case he will be glad that he kept Bush out of office, considering it
well worth the twinge of regret for not showing support for Nader. (He's a
nice guy;  he'll understand.) 

John is the one who opts for the small chance with the big payoff. Sally
is the safe voter; she has 100% chance of getting her two cents ... the
satisfaction of showing support for Nader and the Greens, and a negligible
chance of missing out on an opportunity of being a pivotal saviour of
Gore, a dubious distinction at any rate.

A personal note:  When I gave this line of reasoning to acquaintances who
were planning on defecting to the Gore camp here in Oregon where the
chance is tiny that one vote would decide between Bush and Gore, and also
tiny that Oregon's electoral votes would be pivotal, the common response
was, "What if everyone thought like you?" 
 
My reply; "If everyone thought like I, then everyone would prefer Nader,
and everyone would vote safely by voting an 100% chance of showing support
for him. If everybody thought like I, the right man would win." 

Of course, I was teasing them a little with that response, because their
real question was intended to be, "What if every one had the policy of
giving support to a cause they actually believed in instead of worrying
about the small chance of their vote being pivotal in a lesser of two
evils gambit?"

I'm not so sure that would be such a bad state of affairs in the long run.

Apparently they think it's like inoculations.  If everyone else gets
them, I don't have to, because the disease will be wiped out.  Let the
other voters do all the worrying about who wins the election. I'll take
the luxury of supporting the cause I like best. Am I just being selfish? 

Not, for example, if I truly believe that my sure support for the cause is
worth more than some Quixotic vision of saving some lesser evil. For me
Bush in office plus 3% support for the Greens is a better outcome than
Gore in office and 2% for the Greens. Of course 5% for the Greens would
have been much better (because of the qualifying threshold) but Gore's
very ineptness made the race so close that Nader's less loyal fans
abandoned ship to save Gore.  Gore truly spoiled the Greens' 5% quest.

I think it's more selfish for the Gore supporters to expect the Greens to
abandon their cause to bolster a dud candidate with a thinly veiled
sell-out-the-people agenda. More registered Democrats voted (directly) for
Bush than for Nader.  Why should I, who am registered with the Green
party, regret not having tried to bail out the Democrats? 

In any case, I'll never spend my energy trying to persuade voters to vote
insincerely. I'll never say anything bad about voting their conscience,
either, even if it requires them to vote insincerely for some "higher
good". But I think that people are often led away from sincere voting on
pretty flaky pretenses, including misleading polls and amateurish utility
estimates that leave out many important "externalities" like integrity,
loyalty, long term effects on movements, etc.

And people are too quick to equate "lesser evil" with "greater good". We
like to think we're out-foxing the devil, but he's just toying with us. 
Who would have thought that Clinton and company, after all their populist
campaign rhetoric, would be the ones to dismantle welfare, ram through
NAFTA, try to fast track the MAI, send political refugee boat people back
to torture in China and Haiti, bomb civilian targets without apology,
de-rail the international land mine ban, scatter depleted uranium armor
piercing rounds all over the place, up the ante in Colombia, etc.

Maybe the Democrats will put up at least token resistance to Bush when he
tries similar shenanigans, instead of rubber-stamping everything.  (Don't
count on it; most of them are loyal servants of Mammon, now.)

How would the Sally and John example change under Approval?  Well Sally
could (by slightly diluting the value of her sure two cents) add the
slight chance of being pivotal against Bush at the risk of regret of
showing support for Gore in the (highly probable) case that her vote turns
out to be non-pivotal. But, in my opinion, if Sally voted Nader under
plurality, she would probably vote only Nader under Approval.

On the other hand, under Approval, John would be very happy for the
opportunity to reduce his risk of total regret. He would almost surely
vote both Nader and Gore.  Approval eases the tension, increasing voter
sanity, etc.

So usually, under Approval, we vote the way we would under single mark
plurality, plus any and all we prefer over that plurality choice.

Thanks for reading my tirade.

And thanks to Craig for the stimulating example.

Forest


On Thu, 15 Feb 2001, LAYTON Craig wrote:

> 
> This question is open to all the strategically minded posters; Say with the
> above utilities (100, 25, 20, 0 - assign A,B,C,D respectively).  One opinion
> poll shows (and, being an approval election, these are approval polls so
> they show the predicted winner), that A will get 36 percent of the vote, B
> will get 40, C will get 45 and D will get 44.  
> 
> You even have information about the accuracy of the polls; accuracy within
> 5% of the predicted outcome is 90% (that is, 90% chance that A will get
> between 31 and 41%), and, our general understanding of such polls claiming
> this kind of accuracy is that it is more likely to be closer to the
> predicted outcome than further away.  How should you vote?
> 
> Craig Layton
> 


P.S.  All externalities being typical, I would approve A only, even if my
utility for her were only 90 (or even lower, though how much lower it
would be hard to say).