[EM] The worst about each system; Approval Preferential Voting (new name for an MCA-like system)

[Jameson Quinn]

>
>  This method is very simple. I think that the description above, without
>> the parentheses, is simple and intuitive; it uses only concrete terms. It is
>> also very easy for a voter to sort candidates into three rankings; I'd argue
>> that this is the easiest possible ballot task, easier in general than either
>> two or four ranking categories. (Two means too many compromises, and four
>> means too many fine distinctions.)
>>
>
> The voters can easily not use them. Many didn't. This is overprotecting
> voters, taking facility away from them in the name of .... what?
>
> In the name of reducing turkey-raising strategy to an absolute minimum.

First, I'd love to take full range data on the first election, defaulting to
100/75/0 for preferred/approved/unapproved, to be analyzed by Range,
Condorcet, and Bucklin standards and published before the runoff. And the
runoff should allow approval-style write-ins, in case that analysis shows
that my method got it wrong somehow. So it's not about reducing
expressivity.

But let's look at the *overall strategy for APV*:

First off, if nobody ever uses the middle rank, it's just approval with a
runoff if there's no majority. That's a good system. It would, for instance,
have handled Clinton/Bush/Perot or Bush/Gore/Nader with nary a hiccup. But
in the recent Hawaii election, with two 30% clones who hate each other
against a 40% other, it would have gone into a runoff.

The basic strategies in approval/runoff are standard approval strategy (vote
for one of the two frontrunners and anybody better than them), plus
turkey-raising. I'll look at turkey-raising later, but let's assume for the
moment that it's not a big factor. So, we have standard approval strategy
for the top rank. That means that if there's a clear CW and a clear
Condorcet 2nd place, then the CW will have the only majority. If that
happens, great; you're done.

Of course, that condition held in HI and there was no majority. That's
because if the two frontrunners are clones, supporters of other candidates
will see no reason to waste voting power choosing between two equal-utility
options, and so will consider them as effectively being just one of the
frontrunners. So that's the other possibility: a HI-like majority failure.
Call the clones A and B, and the third candidate opposing both C. (In HI, C
was Djou, who won.)

At that point, standard approval with no runoffs just falls down and gives
the election to the true third-place winner. One big yuck. Approval with
runoffs needs a runoff to decide, and the true Condorcet winner might not
actually be in the runoff, so the election might go to the true second-place
winner. Two small yucks.

How do you encourage voters to include additional rankings so as to avoid a
runoff in this situation? *Standard Bucklin certainly does not do the trick*;
the same
damned-if-I'll-cancel-out-my-own-vote-by-also-voting-for-the-second-frontrunner
logic applies exactly as much in the second ranking as it did in the first!
My later-minimum harm takes away this strong reason for A and B voters not
to extend their approval. But they still have no particular positive reason
to do so.

What carrot can you offer two allied subfactions to get them to cooperate? A
better chance to defeat their common enemy, of course. Presumably, they both
want to be the bigger subfaction, but they also both agree that whichever
one is bigger, is the best one to face C in the runoff. This is exactly the
promise that my system gives: if two factions mutually extend approval to
each other, they're helping each other climb the condorcet matrix against
all other candidates to get into the runoff. But if it comes down to just
one of them making it into the runoff - as it very likely will - the one
with the strongest "competitive advantage" (first preferences, plus second
preferences from third-candidate voters) will be the one. That's something
that benefits both sides.

Should they be afraid of overshooting and giving the other faction a
majority? No, because if one side overshoots, the other side probably will
too, so both will have a majority. And then the winner is... the one with
the strongest first preferences, probably** the very same as the one who
would have made it into the runoff.  So extending approval hasn't hurt them
at all, it's just let them avoid the work of voting again, exactly as
designed.

There is of course a middle case, where they "overshoot" the cooperation by
enough to both make it into the runoff, but not by enough to both have a
majority. Voters for the candidate with the stronger first preferences -
say, A - if they are being selfishly rational, probably want to avoid this.
So, if A is clearly beating B, A voters might not approve B. But it would
make no sense for B voters to retaliate; they were approving A as having a
better chance against C, and that still holds.

If the two are not clones with respect to C, but one is actually closer,
that logic for the "middle case" is different. The more "centrist" candidate
- say, B - should easily get enough approval from C to make up for the lack
of it from A. That's because C voters probably know they have a good chance
of losing the runoff, and would rather do so to B.

...

That brings us, finally, to the issue of turkey-raising. That is the reason
for restricting to three ranks. If you let people make fine distinctions
"for free", that is, with essentially no effect on a first-round winner and
only affecting who makes it into the runoff, then that's basically begging
people to think about turkey-raising. (BTW, Abd, that's the problem with
your idea of having distinctions among unapproved candidates on a Bucklin
ballot.)

In my system, however, where would people raise a turkey? By voting for them
as favorites? Besides going against human nature, this is extremely
dangerous; it is likely to elect the turkey outright or to knock your
favored candidate out of the runoff. By approving them? Again, this is a
self-limiting strategy. For it to matter, it must mean that there is a
runoff; but then, the more it's used, the more likely it is to simply elect
the turkey outright. (It would be safe if there were expected to be one or
more majorities and no runoff; but then it would be irrelevant.)

**Yes, I could have used a Condorcet logic to resolve the multiple majority,
as I did to decide who goes to the runoff. It would even have made this
method satisfy the Condorcet criterion for honest voters. But I think that
multiple majorities will be rare, and that when they happen, top preferences
and Condorcet will give the same answer, so I went with the option that
simplifies explanations and rapid counts.


>  It's not quite the same as MCA or any other Bucklin system, since if there
>> are two approval majorities, the preferences, not the approvals, break the
>> tie. This makes APV more lesser-no-harm-like than Bucklin, encouraging
>> voters not to truncate.
>>
>
> Not a tie, Jameson. Multiple majorities, quite a different things.


How do you say it, then? "Break the multiple majority"? "Decide the multiple
majority"? "Decide the issue"? "Resolve the multiple majority"? I guess the
latter, but we should agree on terminology. I was trying to use "tiebreak"
as the right verb here, but you're right, it's imprecise.

As was pointed out, this rule (if multiple majority, the highest
> first-preference vote prevails) leads to proposterous conclusions, i.e, to
> make it completely extreme, one candidate has 51% approval, but leads in
> first preferences (say it's a plurality, and this can be quite small,
> overall), and the other has 100% approval, but the 51% candidate wins,
> through the rule about first preferences.


Yes but:


> In reality, multiple majorities were rare with Bucklin, the problem tends
> to be in the reverse direction, no majority even after all rounds are
> collapsed.


Exactly! This system is designed to best resolve the common case - encourage
majorities by not encouraging truncation - and not the rare case of multiple
majorities. It's a trade-off.

As mentioned above, using a condorcet analysis of the three-rank ballots to
resolve majorities, with first preferences only as a fallback, would resolve
your issue. I like that system; it's better theoretically than the one I
proposed. But while you can hide the rules for getting into a runoff in
parentheses, you can't hide the rules for an outright win there. Basically,
I came down on the side of having a simple three-sentence description, with
all concrete terms; and of making the one-round-win calculable with any
vote-counting technology on the planet. (On the other hand, an
election-night announcement that "there will be a runoff, it will probably
be between X and Y but we'll tell you for sure who's in it in two days" is
something most people could live with.)


> My own solution to the multiple majority problem is different and more
> comprehensive, without creating this preposterous conclusion of rejecting a
> candidate clearly approved by all the voters, in favor of one who might be
> quite divisive.


Your solution also requires a course in voting theory to even explain, much
less understand. I support it nonetheless. Do you support mine?
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20100526/c15a7e69/attachment-0004.htm>