[EM] Doubts on Approval Strategy

[Adam Tarr]

Rob L wrote:

>Let's assume a simple left-right spectrum, with candidates A, B, C, and D
>(far left to far right).  Let's also say that candidates B wins in a world
>where there's accurate data, and everyone votes according to expected
>strategy (where "B" and "C" are the only candidates who get or come close
>to getting majority approval). However, let's say that A has pretty strong
>support, with about 30% of the electorate wanting A as a first choice.

So we're saying that it's something like

30% ABCD

14% BACD
14% BCAD (middle-left supporters are split in their second preference)

14% CBDA
14% CDBA (same deal with middle-right)

14% DCBA

OK... I am with you so far.  B is the Condorcet winner, with a 58-42 
victory over C being the only remotely close contest.

>Now we've got an interesting problem.  Prior to the election, "A"
>supporters may not want to tip their hands that they'd settle for "B", in
>hopes that "A" can be considered the "front-runner" candidate that "B"
>voters should also approve.  So, when asked by the pollsters, they "lie",
>saying that they only approve "A".
>
>So, perhaps what happens at this point is now "A" pulls ahead in the
>pre-election polls, where "A" has the highest approval rating, at 30%, and
>"B" only has 28% (for instance).  Does that mean "A" voters would never
>vote for "B"?  Does that mean that "C" voters should perhaps adjust their
>strategy and "approve" B?  Would "C" voters admit this to pollsters if
>they knew?

While I fully admit that the initial conditions can be a little chaotic, 
there is a nearly inexorable pull toward the Condorcet winner in cases like 
this.  You can draw up any strategy of approvals that you like, but if 
people act rationally, then even if they don't know who is lying and who is 
telling the truth, the Condorcet winner will end up pulling ahead pretty 
quickly.

Let me provide an example.  Let's say everyone just expresses their first 
preference to start:

30 A
28 B
28 C
14 D

So now, who will adjust their strategy?  Well, let's assume all the A, B, 
and C voters are obstinate, but clearly the D voters will see the need to 
vote their second choice.

30 A
28 B
28 C
14 DC

So now C is the clear front-runner with 42% approval.  I would argue that 
both AB and BA voters would tend to scramble to support each other, but 
let's continue the hypothetical "lying" scenario as far as we can and say 
that the A voters hold back.

30 A
14 BA
14 B
28 C
14 DC

Now we have a polling-error dead heat between A and C, with B far 
behind.  The BC voters now must obviously see the need to support their 
second choice:

30 A
14 BA
14 BC
28 C
14 DC

Now C has reached his full support level of 56%, and is clearly in the 
lead.  Now, the stubborn A voters have no choice.  If they are paying 
attention, they have to approve B.

30 AB
14 BA
14 BC
28 C
14 DC

And now B and C are in a virtual dead heat.  But the B voters will quickly 
realize that they have no need to support second choices, least of all C...

30 AB
28 B
28 C
14 DC

And we have a stable result that gives a good sense of the true preferences 
of the electorate.  No faction can change it's strategy and come out 
better, so there is no incentive to lie.  Proper approval strategy does not 
depend on voters being honest or not being stubborn; it merely depends on 
them being realistic.  I could do examples like this all day.  Every so 
often, you can find a stable result where the Condorcet winner loses, but 
it's not easy.

>I think the temptation to "lie" to pollsters for strategic reasons would
>be pretty strong in a world where the polls matter so much.  What's more,
>it wouldn't be lying at all, it may actually be sincere.  The strategic
>calculus is a little too much for me, and I suspect it'd be pretty
>baffling to the public.  Just like in first-past-the-post, I think that
>some norms would evolve around Approval; what I'm not sure of is whether
>they'd be an improvement over current conditions.

Well, it's nearly impossible to argue that they would not be an 
improvement, although you might argue it would be a small one.  Surely, 
approval voting will solve the spoiler problem in the case of a marginal 
third candidate.

Your contention, as I understand it, is that there's a good chance the 
voters will get stuck at one of the intermediate stages I listed there and 
not make it all the way to the stable result.  This is possible, I 
suppose.  But I don't think this strategy is that much harder than 
plurality strategy, and the public has very little trouble playing that 
game (note how third party candidates tend to drop off in support as the 
election approaches).  Maybe this strategy takes longer to play out, but I 
don't think it is much more tricky.  Also note that it usually won't take 
five steps to reach the stable outcome; if the A voters had been a little 
quicker to support B we would have reached a stable result in two quick steps.

Look, I agree that Condorcet is better.  I definitely prefer the Condorcet, 
winning votes scenario where everyone gives one quick glance at the polls 
on election day and then generally just votes their conscience.  But I 
think Approval will lead to better results and stronger third 
parties.  It's worth fighting for.

-Adam

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