[EM] Approval Voting and Long-term effects of voting systems

[Kristofer Munsterhjelm]

On 11/27/2016 09:10 PM, Daniel LaLiberte wrote:

> I agree that we should probably prefer to use a voting system in which
> it is safest to avoid using predictive information about likely winners.
>    I say
> "probably" because I don't think that should be the highest criteria,
> depending on how unreliable the predictive information is, and moreover,
> because of what should be the highest weighed criteria.  
> 
> But another important point is that, just as there is no perfect voting
> system, I suspect there is NO voting system for which it can be
> considered completely safe to ignore all predictive information all the
> time.   That is, we ALWAYS need to consider predictive information to
> some degree at least some of the time no matter which voting system we
> use.  Is this claim correct?  Does "tactical" or "strategic" voting
> always involve this predictive information?

I can think of two voting methods that cheat and thus (mostly) avoid the
need for strategy.

1. Random pair: pick two candidates at random, and whoever the majority
prefers to the other wins. Alternatively: hold a runoff between them. Or
choose a random voter and whoever he ranks first wins.

2. Asset: you name an elector. Every elector named by at least one voter
meets in a room and they all discuss whom to elect, then decide by
weighted majority vote. That they have weighted votes means that each
elector has a weight proportional to the number of people who named him,
and a majority of the weight wins.

Even Plurality Asset has some strategy if you're not sure about the
skill of the elector; but if not, you can imagine that the elector you
name will do the strategy for you.

For most practical methods, strategy seems to benefit from knowing
predictive information. It's certainly possible to construct methods
where the voters would benefit very little, but I can't think of any
good methods that work that way.

But just as there's a difference between ranked voting methods' quality
even though Arrow's theorem says none of them can be perfect, there's
also a difference between how well the methods resist strategy. Say
there are four broad types of strategy:

- Compromise (voting one of the major candidates higher than you would
if you were honest so that he wins instead of the greater evil)

- Burial (voting one of the major candidates lower so that he loses)

- Pushover (voting some candidate Z higher so Z loses).

- Strategic nomination (for parties: adding or removing candidates to
shift the result in their favor).

Then it'd be possible to consider various criterion compliances as ways
of saying that the method resists a particular form of strategy.

For instance, all other things equal, a method that passes the favorite
betrayal criterion would resist compromise more strongly than one that
doesn't; while a method that passes, say, mutual dominant third burial
resistance would resist burial more strongly than one that doesn't; and
methods that pass various monotonicity criteria would not be vulnerable
to pushover.

But I don't think you can get invulnerability to all of them at once, so
to some extent, you have to "pick your poison". Approval seems to do the
impossible, but on a second look, even it has strategy: it consists of
having to decide which particular sincere vote you should submit.

> If it is true that there is always going to be some tactical aspect to
> voting for any voting system, then we should try to minimize the
> negative aspects of when it needs to be applied.

Yes, subject to that the cure shouldn't be worse than the disease. Take
again random ballot. It's strategy proof: if your ballot is chosen, you
get to choose who the winner is, so it's in your best interest to put
your favorite first. If you don't get picked, you have no say either
way, so you're never harmed by voting sincerely. But the performance is
awful. It's too high a price to pay.

> In the case of all ranking systems, I claimed that it is necessary to
> rank one of the frontrunners highest, or you risk a win by one of your
> less favored frontrunners. I'm not sure I got an affirmative answer to
> this broad claim.  In which ranking systems would it be completely safe
> for voters to ignore who the frontrunners are?

Those claims aren't quite the same. Your first claim is that every
method is susceptible to compromise strategy, but your later question is
about whether there's a method that doesn't require frontrunner strategy
at all.

Consider Antiplurality: voters submit ranked ballots, and each candidate
gets a penalty according to how many ballots he's ranked last on. The
candidate with the lowest penalty wins.

Here there's no need to put the lesser evil first because the method
doesn't care at all about who you put first. So the method is immune to
compromise strategy. However, you may strategically decide to put the
worse frontrunner last, even if there're some awful minor candidates you
think even worse of. That's burial strategy.

Antiplurality shows that there are some methods that are completely
immune to compromise strategy. (Antiplurality is not a particular good
method, however.) And there are restricted domains where better methods
are strategy-proof, e.g. Condorcet methods when there's no cycle. But I
don't know to what degree FBC methods in general are immune to
compromise - it's not my area, so to speak.

> But as Michael says, and I agree, this one tactical decision is not as
> much of an issue once elections have evolved to the point where the most
> likely winning candidates are also the most approved by voters.  And
> that is an overriding factor in my mind.

"The most likely winning candidates are also the most approved by
voters" is true by definition for Approval voting if you mean "approved"
in the sense of "has the most Approval votes". But if you mean really
approved (in the sense of "liked by the voters"), then that seems to
assume two things about Approval voting:

- First, it must lead to a state where the most likely winning
candidates are the ones most approved/liked by the voters, and do so
stably enough that it doesn't get repealed, and

- second, it must be able to stay in that state. This is related to the
stability you mentioned, I'd think.

Neither of these seem completely evident.

> In contrast to the criterion of having to be strategic (in any way that
> might be required), I believe that the most important criteria should be
> the "fairness" of the outcome.  And by "fairness" I mean in the sense of
> how well the election represents the will of the people, at least in the
> short-term.  But since that word is probably fairly (heh) subjective and
> overloaded because different people will have different conflicting
> views of what is "fair", I am fine with replacing it with something more
> specific.  
> 
> Stability in the long-term is another criterion that, when combined with
> "my fairness", I would tend to prefer.  However, the chicken dilemma
> adds a bit of instability, which, if it is not to shocking and
> destabilizing, might actually be a benefit to a system that could
> otherwise become too entrenched.

It might be pretty destabilizing in a contentious election. Suppose you
had a situation like the last election, but a third party was also
pretty strong, and the voters of that third party mostly preferred
Clinton to Trump. The vast majority of polls showed that Clinton was
going to win. So a third party voter might have reasoned: "I can take
the chance of voting for third party alone". Now, as we know, the polls
were wrong. The voters would not be amused.

The problem here is that (in my opinion) while a good ranked voting
method like the advanced Condorcet methods are safe in a bunch of
situations (no cycle, singlepeaked preferences, etc), and in such a
situation, only voters who want to squeeze something extra from their
votes need to think of strategy, in Approval *every voter* needs to
consider strategy. As long as you don't have an inherently binary
preference ("I like these candidates, I don't like those candidates, and
there's nothing in between"), there's no obvious way of picking your
cutoff. The closer the election, the more important polls become. And if
the polls are wrong, Approval goes wrong too.

Approval passes many criteria and seems to do the impossible in many
ways. But to quote Forest Simmons:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-October/000717.html

> In particular he [Kristofer] pointed out how certain procedural
> rules
> can externalize the paradoxes of voting. To a certain extent Approval
> avoids bad properties by externalizing them. The cost is the "burden" of
> the voter deciding whom to approve. As Ron LeGrand has so amply
> demonstrated, any time you try to automate approval strategy in a
> semi-optimal way, you end up with a non-monotone method. By the same
> token IRV can be thought of as a rudimentary DSV approach to plurality
> voting, so it should be no surprise that IRV/STV is non-monotone.

This is to say that, suppose you try to create an algorithm where you
input your sincere (ranked) vote into the computer and it uses all the
data it can get to make the optimal Approval vote for you. Now suppose
every voter uses this algorithm. Then you could consider that the
country is essentially running another voting method. Then LeGrand
showed that such a method is nonmonotone, i.e. sometimes ranking a
candidate higher makes him lose. Approval hides this by moving the
"algorithm" into the voters' heads, but the voters still have to do what
the algorithm would have done in the hypothetical setting above.