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

[Daniel LaLiberte]

On Wed, Nov 30, 2016 at 5:51 AM, Kristofer Munsterhjelm <
km_elmet at t-online.de> wrote:

> 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.
>

By "cheating", it looks like these systems avoid having voters do much
decision making at all, and thus there is no place for strategy either.


>
> 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.
>

With any random decision making, the voters get no decision at that point,
and but then later may be given a choice among two, where honesty prevails.


> 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.
>

With asset voting, voters choose honestly among electors to find one who
best represents them, and then leave subsequent decision making up to those
electors.  But then how those decisions are made, which voting system the
electors use, could make a lot of difference in what strategies they use.

So in this "cheat", the decision making and strategizing still exist among
the electors, so it is not really any different regarding the kind of
strategizing that is necessary based on the voting system the electors are
inclined to use.

And therefore, we should expect to get some of the same kind of effects
with asset voting as with direct voting.  One important difference is that
with asset voting, the assets are transferable, which would be similar to a
series of run-off elections.  More below.

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.
>

So with Plurality Asset, if I understand (or even if I misunderstand, this
sounds interesting), voters would vote for only one candidate, and the
candidates with the lowest votes would then transfer their votes, as
assets, to another candidate, until there is only one left.  I can see that
this would avoid the spoiler effect by original voters since votes are
never wasted in the same way as direct plurality voting.  But the
candidates who are eliminated would then vote for, presumably, another
candidate who the voters should probably have voted for initially, if they
could.  But the same strategizing these eliminated candidates might do is
also avoided for the same reason since their votes are also not wasted.

Would we still end up with two dominant parties?  I think so, at least as
long as the eliminated candidates transfer *all* of their votes to one
other candidate.  Any third parties would tend to fall under the umbrella
of one of the two dominant parties.

But if eliminated candidates could split their asset votes by some means
(either arbitrarily or evenly) among other candidates that changes things,
but perhaps not enough.

Letting the original voters essentially say, if my preferred candidate is
eliminated, then here is my second choice, etc, gives us an instant run-off.

IRV is Borda with instant run-off, correct?  Does IRV amplify or ameliorate
the many problems with Borda?

But the process of conducting an instant run-off could apply to many other
voting systems, just as asset transference could apply to many other voting
systems.  Is there some reason it is not considered for other voting
systems, and has become associated with IRV?

Is there a Range Voting with instant run-off?  Range Voting with assets?
Is there Approval Voting with instant run-off?  Approval Voting with assets?

Is there a breakdown all voting systems into a set of steps, each step
being done in one of a variety of ways, some steps repeated?  There might
be many more interesting and useful combinations that could be discovered
by using such a matrix of options.

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).
>

The wikipedia page https://en.wikipedia.org/wiki/Tactical_voting lists
Compromose, Burial, Pushover, and one other, Bullet voting (voting for just
one candidate, not to be confused with Bullet Voting).  It doesn't list
strategic nomination, but at a party level, nominating just one candidate
is analogous to the Bullet voting strategy.

I'd like to see something more convincingly comprehensive about the
possible strategies, but perhaps that is similar to asking for a list of
all possible emergent effects, when we rarely have any way to predict
emergent effects just looking at the components of a system.  Or perhaps
our differential equations are just not up to the task yet.



> 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".


Yes, I wasn't expecting to be invulnerable to all strategies, or even to
any of them.  In fact, as long as the strategies are not to obscure and
counter-intuitive, I find it much more important to focus on the emergent
effects that despite the strategies applied, or perhaps because of them,
affect how the democracy functions and changes over the long-haul.


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.
>

Yes, but I find that the strategy required for Approval is in your face, up
front and honest about it.  Meanwhile, you don't get to strategize about
which ordering of weightings or preferences might work out better.  And for
many ranking systems, you might not even be aware that there are many
strategic decisions you ought to make, and maybe many voters default to
being honest just because it is too complex to be strategic.

With Approval Voting, there is really only one bit of strategy, where to
draw the line between approval and disapproval, and you have no choice but
to make that decision.  The complexity comes in deciding among several
candidates who are close to that dividing line between approval and
disapproval, and also factor in the chances that some are more likely to
win than others.

But I am not too concerned about that fuzzy gray dividing line between
approval and disapproval once most of the candidates in elections are much
more likely to be liked by many more voters.  Different voters will chose
where to draw the line differently, and a reasonable gradient will result,
keeping the least approved candidates further away from the top end.



> > 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.
>

Yes, they are different, and I am interested in both.  But if there is a
ranking system in which it is safe to ignore who the frontrunners are, then
I was assuming that voters would not have to consider ranking one of the
frontrunners highest.

But given your example of Antiplurality, I would have to expand that to
say: If there is a ranking system in which it is safe to ignore who the
frontrunners are, *then voters wouldn't have to do anything special with
the frontrunners*, for example, vote for the lesser evil highest or the
worser evil lowest.


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.


Not completely evident, I agree, though my growing intuition is that they
are true. Hence I am still seeking confirmation or refutation.

I think both points depend on having a large predominance of voters near
the median, as well as a smooth gradation to the extremes.  I.e. no huge
bumps or voids.  If voters tend to divide into mutually exclusive parties,
and there is no 'centralist' party such that there are relatively few
voters near the median, then I would expect to see more instability.

But I think most voters are near the median, and what we see in the US is
an artificially constructed subdivision between two dominant parties that
each appear to be more polarized in opposition to the other, but behave
more moderately when they can cooperate at all.  Lies all around and no one
is happy about it except maybe a few billionaires.


> > 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.
>

I agree that would be bad, but I don't believe it is fair to judge how
Approval would work in an election where it was known in advance that
Plurality will be used.

With Approval being used, a different set of candidates would more likely
rise to the top, and we would be unlikely to have to contend with any that
are hugely unpopular, or at least there would be less reason to fear that
they might get close to winning.

Approval Voting could be used badly, however. If Approval Voting were used
in party nominations, then the party might get a better representative of
all the voters in the party, which might be good for the party, but it
would not be good if several such candidates who were nominated separately
by their parties all ran in the general election.  Or rather, the best
outcome might be the emergence of a Centralist party that could suck the
life out of the other two dominant parties.

With Approval Voting being used in state primaries, where all candidates
for all parties are on one ballot, then parties would soon not matter at
all.  The Chicken Dilemma actually raises a possibility for when it would
still be advantageous for similar candidates to cooperate, so I am hoping
we can cut the head off that chicken before it arises.


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.
>

I don't think Approval goes wrong so badly, after it stabilizes around the
median.  With most candidates who have a chance of winning being close to
the median, it can't go far wrong when someone slightly farther away from
the median wins occasionally.

I think this stability around the median is far better than having third
parties occasionally win due to the weakness of major parties, or other
destabilizing situations and asymmetries of power.



> 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-elect
> orama.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.
>

Granted, this could occur.  But I have a couple responses.

1. Real voters will make their strategic decisions differently, not ideally
or optimally, to the extremes of approving only one, or all but one.  Does
that change the monotonicity?

2. We might model the voters probabilisticly to match what real voters do.
I'm thinking of effectively doing that with a neural net model of voters.

3. Does it matter much in the long run, when most candidates are close to
the median and the degree of disapproval is small, in comparison to the
gross disparities we have now?

-- 
Daniel LaLiberte
daniel.laliberte at gmail.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20161206/c8f0a9ab/attachment-0001.htm>