[EM] Approval voting under fire #3 (James)

[James Green-Armytage]

Dear Mike,

>Staying with Plurality. I'm not saying that Plurality
>is as good as IRV. It's just that adopting IRV will
>get us stuck with IRV, and prevent genuine reforms,
>such as Approval or Condorcet, from being adopted.
>People will say "You want a better voting system?
>We've adopted a new one. Do you want us to now drop
>that one and go through it all again?" No good.
>Anything worth doing is worth doing right. And, as you
>said, IRV will discredit itself, its promoters, and
>electoral reformers in general. "Yeah right, they said
>that IRV was a reform too. We've heard that one
>before." 

	This is a valid concern which I share to some degree. I would certainly
be thrilled if we were able to shoot straight to Condorcet for public
elections. 
	What I think we disagree on is whether approval voting is clearly better
than IRV, if a more gradual progression is needed.

>That example is the fortuitous situation called a
>"mutual majority". The L1 & L2 voters are a mutual
>majority. Majorities aren't always mutual. In fact
>they're probably usually not mutual. For instance, say
>a majority prefer Democrat to Republican. That
>majority consists of Greens and Democrats. But do the
>Democrats prefer the Green to the Republican? The
>Democrats & Republicans are so much more like
>eachother than the Democrat is like the Green, that
>anyone who really considers the Dem his favorite will
>like Repub better than Green.
>
>So it's a fortuitous situation.

	I don't think that you have demonstrated this. I think it is actually a
fairly straightforward situation, and in a race with more candidates this
sort of dynamic could be enfolded in other dynamics, retaining the problem
it creates in approval voting. There is no reason to assume that this is a
situation of Democrats, Greens and Republicans. I imagined it more as a
situation with a Republican and two Democrat factions, but really it could
be anything; the names are just to make it easier to imagine. The basic
point is that the two L candidates have much more in common with each
other than they do with the R candidate, and together they form a clear
majority, but neither one forms a majority on his own. The two candidates
are assumed to be not identical.

>So the R voters have reason to bury their favorite.
>That's the case in every mutual majority example. Yes,
>a mutual majority is better for one group, while being
>bad news for another group.

	An interesting point.

>Someone could say "But the R voters have no right to
>expect to win, since L has a majority". Yes, but the
>whole fundamental problem about strategy is that we
>don't have perfect information. The R voters could
>mistakenly believe that that mutual majority situation
>exists, and therefore give the election away to their
>more preferred of the L candidates, when actually R
>could have won if they'd voted sincerely. Isn't that
>the main reason why we don't like voters to be given
>incentive to bury their favorite?

	Yes, this is the reason. But doesn't it apply in a different way in the
approval example I gave? I will elaborate...

>But if there aren't such candidates, then people can
>do what they do in Plurality: Vote for their more
>preferred of the 2 expected frontrunners...except that
>with Approval they can also vote for everyone whom
>they like better.

	Let's say that people follow this strategy in my example, but without
perfect information. Let's say that L2 somehow manages to convince people
that he is more likely to win, so that the L1 voters double vote and the
L2 voters bullet vote. The perception has created the reality. No one will
ever know that L1 was the sincere Condorcet winner.

>Another way to put it: Vote for the candidates who are better
>than your expectation for the election.
>That's called the better-than-expectation strategy.  
>I'd often use it when there are no completely
>unacceptable candidates who might win.
 

	It is not clear to me how this strategy would be of help in my example.

>	The more you find out about Approval, the better it
>turns out to be. It's deceptively, elegantly simple,
>but it has a lot of unexpected desirable properties.

	I wish I could believe this, but I don't think that approval can
successfully navigate this sort of mutual majority situation.
>

23: right > left#1 > left#2
22: right > left#2 > left#1
29: left#1 > left#2 > right
26: left#2 > left#1 > right

	Basically, I just don't see how approval voting offers any way for voters
to effectively choose between these three candidates. 

	To eliminate the possibility of a solution based on anything but voter
strategy, imagine that the sincere cardinal ratings (from 1 to 100) look
something like this:

23: right 80 > left#1 40 > left#2 30
22: right 80 > left#2 40 > left#1 30
29: left#1 90 > left#2 80 > right 30
26: left#2 90 > left #1 80 > right 30

	I would say that the outcome of this election under approval is anybody's
guess, which is I think a fatal problem.
	What is it that will induce L2 voters to capitulate and double vote for
L1? What will induce L1 voters to double vote for L2? It can't possibly
have anything to do with the relative margins of preference for those
candidates, because they are approximately equal.
	It is of course not necessary for the rankings to be this similar for
this situation to be an approval voting nightmare. I am just pointing out
that there is no reason to assume that one of the two L candidates is
preferred by a substantially greater margin than the other one.
	Even if so, it will not necessarily be possible to get accurate
information on the margin of preference amongst the L voters. If they get
a chance, the L2 voters will have an interest in telling the L1 voters
that they only barely prefer L1 over R, and that they plan to single vote,
thus trying to scare the L1 voters into double voting. Meanwhile, the L1
voters will be hoping to do the same.
	It is really just nothing but a chicken game, where the winner is either
the L candidate whose voters are most willing to take the risk of a bullet
vote, or, if both groups of L voters take that risk in sufficient number,
the victory goes to R.

	Also, I should note that voters don't have to be especially devious
strategy wizards to realize to hesitate in double voting in hopes that
adherents of the other candidate will help vote in your favorite. For
example, an L2 voter doesn't have to be a genius to realize that L1 is one
of L2's main competitors, and if it comes down to L1 versus L2 then they
will have screwed up by double voting.

	The only way I can think of to avoid this sort of thing is to have
primaries. That might help to prevent this particular example from
happening, but there are not always situations where primaries are
appropriate, where they will be consented to by all the candidates, or
where the candidates who form the mutual majority will have enough in
common to consider a primary. Also, if you have more than two candidates
in the primary and you use approval for that, than you might run into
exactly the same problem again. If you use a method other than approval
then this is a cop-out as far as saying that approval works.

	In the absence of a primary or negotiated agreement (which effectively
makes a different election method), there is no civilized way for voters
to effectively choose between L1 and L2. That is, a reasonable mechanism
for such a choice simply isn't built into approval voting, because voters
cannot express such a preference while still noting that they would prefer
either candidate to R.


yours truly,
James Green-Armytage