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

[Daniel LaLiberte]

Hi Kristofer,

Thanks for your message responding to the more neglected aspects of what I
wanted to discuss, not that any of the other subjects are uninteresting.

On Sat, Nov 26, 2016 at 9:27 AM, Kristofer Munsterhjelm <
km_elmet at t-online.de> wrote:

> On 11/21/2016 07:08 AM, Daniel LaLiberte wrote:
> > This message is about two related subjects:
> >
> > 1. Factoring in the long-term emergent effects of each voting system.
> > 2. An example of how Approval Voting results in better long-term effects.
> >
> > Among the many criteria for evaluating voting systems
> > (https://en.wikipedia.org/wiki/Voting_system#Evaluating_
> voting_systems_using_criteria)
> > I don't see any that address the long-term effects of using each voting
> > system.  In other words, the effect on one election is certainly
> > important, regarding the satisfaction of the election results by voters
> > and candidates.  But I would argue that it is even more important to
> > consider the long-term effects that emerge when applying a voting system
> > repeatedly over many elections.  A small bias one way or another may not
> > be very apparent if you only look at one election, but over may
> > elections, they can add up and perhaps compound the bias exponentially.
>
> There are basically two ways of doing this, as far as I can see, without
> actually running experiments.
>
> The first one is to use game theory. Determine what the strong Nash
> equilibrium is for the method in question, and if honesty is an
> evolutionarily stable strategy.
>

Do you mean to suggest that honesty (i.e. sincere voting?) is necessary in
order to possibly achieve stability?

But an election method might not result in stability and could still be a
good method, depending on the nature of the instability.   It could
oscillate between different states quickly, slowly, mildly or wildly, or
perhaps it will grow in some direction possibly toward an inevitable
catastrophic collapse, and maybe that pattern of gradual growth followed by
sudden collapse will be repeated over a longer cycle.

Stability or various kinds of instability is one class of long-term,
emergent effects, concerned with how the state of things changes over time.


Another important class of emergent effects should be about how well the
voters are represented through party organizations or otherwise.  It might
be, for example, that only half the voters are represented very well while
the other half is represented very poorly.  Or it might be that most of the
voters are represented very well to moderately well, as in homing in on the
median, with a smaller number on the fringes being less well represented.

And another important class that I mentioned previously is how vulnerable a
government is to a growing concentration of power leading to self-serving
corruption.  This is somewhat in conflict with the stability effect since
increased stability, which might otherwise be a good thing, allows a
concentration of power to remain in power and find ways to gradually
increase its power.

What other emergent effects should we be aware of that we have a chance
understanding and linking back to the election methods and other
governmental structures that affected them?

The hard part about this is that Nash might be too strong: it assumes
> that the voters know everybody else's honest votes and have unlimited
> communication. That's something that sounds more appropriate for a
> parliamentary setting than for large scale voting. An ESS can be more
> appropriate: all we then need is that there's no "slippery slope" from
> honesty down to some kind of strategy, but calculating it is hard, in
> particular given that voting is a multiplayer game with a very large
> number of players.
>

If determining a stable point is difficult, then a varying pattern is
likely to be much harder to figure out in this way.


> The second is to assume the worst and use properties as defenses against
> strategy. For instance, if a single-winner method passes monotonicity,
> there's no point in attempting pushover strategy because it won't work
> (although I'd say that's not the main point of the monotonicity
> criterion). Similarly, if a multiwinner method is weakly invulnerable to
> Hylland free riding, there's very little point in trying to tempt fate
> by voting E>F when your honest preference is X>Y>E>F, even if you think
> X and Y are sure to win.
>
> The logic is like that of an upper bound: if the method is completely
> invulnerable to some kind of strategy, it'll also be invulnerable to
> that strategy for the kind of ballots that appear in the real world.
>

This seems closer to what I was hoping for in terms of finding way to
determine the likely bounds of emergent behaviors based on the underlying
properties of election methods.  How bad or good could it get?


> The reason there's so little consideration of long term effect is that
> they're hard to model, and getting any definite answers from game theory
> is also hard. The closest you get are, I think, arguments of the form
> that "method X passes criterion Y which is very important to deter the
> kind of strategy that would render the method useless in practice, in
> the long run". Different people disagree about which criteria are most
> important, and there we are.
>

I would expect people to disagree about which criteria are most important,
but I suspect that is largely because each criteria is relevant to varying
degrees and in different ways for each emergent effect, and we haven't
agreed on what emergent effects we want in the first place.  I suspect it
might actually be easier to agree on the emergent effects, however, and
then we may have a better chance of determining which election methods
could work, or which criteria are most relevant for affecting the emergent
effects.


For instance, I think clone independence is important (to the degree it
> generalizes to near clone situations) because parties could always run
> multiple candidates instead of one, or third parties could be deterred
> if there's a vote-splitting incentive. Others think the favorite
> betrayal criterion is very important - possibly due to Plurality
> elections forcing voters to choose between the lesser evil whereas a
> method that passes the FBC would not.


Whether a criterion is more or less important relative to an election
method depends on the desired emergent effects. For Approval Voting, where
the likely emergent effect is homing in on the median, I would think clone
independence is going to be very low, but it won't matter at all because it
is actually desirable (at least in my view) to have most winning candidates
be fairly close to that median.  But for Plurality, where two party
dominance should be an expected emergent effect, high clone independence is
very desirable, especially in primary elections, to avoid vote-splitting.



> > There are many long-term effects to consider, but in particular, I am
> > thinking of one pernicious problem: the tendency for two major parties
> > to emerge and dominate all politics which results from the repeated
> > application of plurality voting.  This problem is fairly easy for most
> > people to understand, although I am surprised to see that there seems to
> > be a lot of denial about this effect as well.  Some would even defend
> > having only two major parties, or very few parties.  That is an
> > interesting subject to discuss, but regardless, I believe we should be
> > aware of how our choice of a voting system will affect things over time,
> > how society is likely to evolve based on the rules we lay down, and in
> > fact, how it is actually very likely that the dominant forces in society
> > will quickly and vociferously defend whatever rules resulted in their
> > rise to dominance.
>
> I would be in favor of multiple parties. An analogy I heard somewhere is
> that in two-party systems, the "parties" are factions inside the two
> parties, and negotiation about what factions get to govern is made
> inside that party; and in multiparty systems, the parties/factions are
> visible to the public as formally separate parties, and the negotiation
> about what factions get to govern is made after the election, based on
> electoral support.
>
> So two-party systems has negotiation, then election; multiparty ones
> have election, then negotiation. The latter seems much better to me,
> since the voters have greater influence.
>

Multiple parties seems much closer to what I would like to see, at least
compared to only two parties, but there are several other things going on
that should be considered.  I think one thing that may be missed in the
self-sorting by voters into parties is that there are really many issues,
and while each voter has a mix of positions on the issues that make hir
(gack) a relatively unique individual, each party tends to adopt a
particular set of positions.  There may be some reasonable correlation
between the positions, but more often than not, fit is uncomfortable.  And
then we may get various awkward and temporary coalitions between parties
(or factions) based on some arbitrary subset of common positions while
other positions remain in conflict.

I think it would be much better if we could avoid the exclusive boundaries
of hierarchical parties based on arbitrary bundles of positions, and
instead actively support a much more natural collection (or web) of
overlapping groups where each group focuses on just one issue or one
position.  This would be a rather messy thing but it would correspond more
directly to the true nature of collections of voters.

This organization, by the way, corresponds to what I am thinking of as a
House of Delegates where each voter can select a different delegate for
each issue.


> > But back to this one question, studies and long-term experience have
> > shown that other voting systems besides plurality, in particular IRV,
> > also result in the dominance of two major parties.  This may be more
> > surprising to people, but looking at the underlying cause, it seems we
> > can make a rather important simplifying argument about most voting
> > systems regarding this problem. I would assert that the underlying cause
> > of this problem of two-party dominance in any voting system is that it
> > gives voters the ability to rank or order at least one candidate higher
> > than the rest.
>
> I agree that IRV leads to two party domination. Well, not quite. It
> leads to "two and a half" party domination. Consider Australia: you have
> Labour as the first party and LibNats as the other "one and a half"
> party: they're technically two parties, but they coordinate among each
> other how to act.
>
> I would suggest a different effect for IRV leading to that sort of
> problem, and that is center squeeze. IRV works fine under Plurality's
> situations where you have two parties and a bunch of fringe ones, where
> IRV easily excludes "noise" fringe parties. But, to use your phrase,
> IRV's design misses the long term implications. As a third party grows
> larger, it ceases to be a noise/fringe party and IRV gets confused.
> Usually, IRV handles this confusion by eliminating the party with the
> least intense support, i.e. the broad support compromise gets eliminated
> early.
>
> That's center squeeze, and it encourages voters to focus on first
> preferences. That's a property of IRV, but not of, say, MAM or MJ.
>
> > The reason this ability to rank candidates becomes a problem is the
> > spoiler effect, where voters will have a strong motivation to give their
> > highest rank to one of the leading candidates. If they don't, then they
> > weaken the chance of that candidate winning and therefore strengthen the
> > chance of the less preferred leading candidate.  Because one of the
> > leading candidates is likely to win, all the rest of the rankings of
> > non-leading candidates hardly matter at all.
>
> Right. You've identified the spoiler effect as a problem. But you seem
> to have drawn the conclusion that *all* ranked methods suffer from the
> spoiler effect, and that in every method it must be true that "if [the
> voters] don't, then they [...] strengthen the chance of the less
> preferred leading candidate".
>

Yes, I have been saying that.  It reflects my intuition, but I am trying to
provoke a clear counter-argument. So far, it sounds like it may be mostly
true, but not so clear on the edges.



> Consider Condorcet methods, for instance, where the winner is the
> candidate who beats every other candidate one-on-one according to the
> ballots. Suppose for the sake of the argument that such a winning
> candidate exists. Then if some voters vote
>
> very good > good > bad
>
> or
>
> good > bad,
>
> there's no difference as far as the "good" vs "bad" contest goes.


But would you actually vote that way if only one of "good" or "bad" is
likely to win. Wouldn't you want to insincerely vote "good" > "very good"
to give "good" a slightly better chance, and also rank "good" better than
any other candidates you might prefer as long as they are not too bad?   I
honestly don't know enough details about any of the Condorcet methods to
say for sure, but my intuition is that this is true.  I would tend to vote
this insincere way, at least as long as my preferred "very good" candidate
is not very likely to win.

If the only cases where this is not true are rather obscure and difficult
to determine from the naive voter's perspective, then it hardly matters
anyway.

The only benefit I can see for a ranking system is if, despite the
drawbacks, when repeatedly applied overtime, it actually improves the
degree of representation by homing in on the median, just as Approval
Voting does.  But then why not just use Approval?

That is, even though a ranking system may have a spoiler effect or other
similar effects that tend to result in two parties (maybe plus some
change), this can still work out well if subsequent elections attract more
candidates who more voters would like to rank higher on the scale.

But I think that if there is still a tendency to separate candidates and
policies into a few parties, and if only one party wins, we will never
satisfy more than about half the people at a time, at best.  We will never
get very close to any kind of unity that crosses party boundaries that most
people will be happy with.  And we will still tend to flip-flop between
parties and deadlock in the meantime.

If many smaller parties can cooperate, then they could add up to more than
half the voters, but how many parties and individuals outside of this
cooperative would still be excluded entirely?  Is that really what we want,
or is it just what we have ended up with because we couldn't anticipate it
and we didn't have any better ideas?



> Hence there's no spoiler effect. The spoiler effect only comes into play
> when there's a Condorcet cycle, or if the votes lead to (or break) a
> Condorcet cycle.
>


Now, since no ranked method passes IIA, it is of course possible that
> the long term effects of every ranked method would be to push it towards
> the type of elections it handles badly.


That would be an interesting and useful result, if it is true and could be
proven.


> If that were to happen,
> Duverger's law could be reestablished. But there are a lot of "coulds"
> here, and there's no evidence that every ranked method would be pushed
> towards its vulnerable region in that manner, or that even if they were
> to be, that it would lead to two-party hegemony.
>

The "vulnerable region" of an election method sounds like something
unexpected could emerge that we don't like, whatever it is, though there is
a chance it could be better.  If we can't anticipate where a voting system
is going to evolve toward, there is at least a risk that we won't like
where it takes us. What we should prefer instead is a voting system that
tends to evolve to a known good place.


As an analogy, two round runoff doesn't seem to lead to two-party rule.
> See http://rangevoting.org/HonestRunoff.html. Yet delayed runoff
> definitely fails IIA.


Delayed runoff strikes me as very much like a two-vote Approval since you
always get a chance to vote for one of the leading candidates in the second
round, so you can safely vote for your preferred candidate in the first
round.  If the first round used normal Approval, I think it would be even
better in terms of not rewarding parties, and maybe it would help mitigate
the underdog effect, and moreover, it would completely negate the main
argument of approval-opponents that you would feel obligated to approve one
of the likely winners.

So how about this as a compromise: The first round would be a primary
election using Approval Voting with all candidates regardless of party on
one ballot.  The second round, general election will be between the top two
most approved candidates from the primary.   Each state could have a
primary, but the approval votes would be totaled across all states.



> > In any election, there will be two candidates who are the strongest in
> > terms of popular support, and thus the most likely to win. Consequently
> > (to grossly over-simplify the process) with any voting system that
> > permits ranking, groups of voters will tend to coalesce around support
> > for these two leading candidates to encourage everyone to support their
> > preferred leading candidate. Eventually two major parties arise, and
> > everyone who doesn't join one of these two major parties is excluded.
> >
> > So once voters and candidates figure this out, any such voting system
> > ends up devolving into the dominance of two major parties that we get
> > with simple plurality voting.  In fact, one might argue that plurality
> > voting is better just because it is simpler.
>
> That happens if the voting method punishes not voting for the main two
> to such an extent that the voters feel they're making the main party
> they didn't vote for win. But it remains to be shown that all ranked
> methods do punish voters that harshly.


Would be interesting to see this investigation.

I am tempted, as a matter of fact, to build an election simulator using
neural nets to model voters who would learn how to vote to get their
preferred outcome.  Has anyone done anything like that?



> > But Approval Voting avoids this problem. Equal-rank approval votes mean
> > voters don't get the option to express their preferred ranking, but
> > because of that, they aren't at all motivated to bias their ranking
> > dishonestly.  They only have to decide which candidates to approve, or
> > where the cut-off is between approval and disapproval.
> >
> > Given that there are, as before, two leading candidates, how does
> > Approval Voting affect whether one of those two leading candidates will
> > win?  One of the two leading candidates is likely to win even with
> > Approval Voting, so it would appear there is no benefit, but that would
> > be a short-sighted way to judge a voting system.  In subsequent
> > elections, it would seem likely that more candidates will run who have
> > broader appeal to ALL voters, not just a majority or plurality. Because
> > the winning candidates will be those who are most approved of by the
> > most voters, there will be no value in parties that typically focus on
> > appealing to no more than half of the voters.
>
> I don't see why, on the other hand, the above won't apply to voting
> methods that don't punish voters harshly, and on the other, the above
> necessarily applies to Approval.
>

By "the above" I assume you mean that one of the leading candidates will
likely win. And that is almost always the case for any half-way decent
voting system, depending on how "leading candidates" are determined.  Any
poll uses some voting system while sampling the population, so which voting
system is used makes all the difference, assuming they do the sampling and
reweighting in statistically reasonable ways.

And as I said, I don't think it is fair to judge Approval Voting or any
voting system based on running candidates who would do badly. The simple
reason is that candidates who would likely do badly will tend to not run at
all. We should be looking at who the likely candidates are who believe they
have a chance of winning.

(more a ways down...)

Consider a country that changes from Plurality to Approval. There are
> two strong parties (call them X and Y) and a lot of smaller ones. The
> smaller parties' supporters could easily be imagined to say:
>
> I despise Y. I like small party W, but if I vote only for W, Y might
> win. So I'll vote for W and X.
>
> If everybody does that, then (surprise, surprise) X or Y likely still
> wins. The only situation where some W would win is if W really had the
> greatest support but everybody had an illusion that X or Y had the
> greatest support; but such a situation would also lead W to win in a
> reasonable ranked method.
>
> So now suppose that, either through polling or throughout the course of
> many elections, W becomes a contender at about the same support level of
> X. Now X's supporters have a problem: they can either play it safe by
> voting for both X and W, or risk it by voting for W alone. But they
> can't know which it is, and if they get it wrong, they may be
> (understandably) annoyed afterwards.
>
> In contrast, in a reasonable ranked method, these voters can rank W>X>Y.
>
> > So I suspect the long-term use of Approval Voting would be
> > self-correcting toward better and better representation of ALL voters,
> > not just half the voters, because in each election, almost all of the
> > voters contribute to choosing the winning candidates, and that only gets
> > better over time as the candidates who decide to run get closer to
> > receiving the approval of all voters.
> >
> > Can any other voting system claim a similar long-term effect?  Even a
> > voting system with three ranks, e.g. Approve, Neutral, Disapprove, would
> > encourage voters to approve one of the leading candidates, and give
> > neutral or disapprove votes to the rest.  I wonder if Approval Voting
> > might be the ONLY system that has this long-term effect.
> >
> > What I am aiming for is a voting system that self-corrects over time.
> > No matter what voting system we choose, there is probably always going
> > to be at least some small bias, some inequities or incompleteness.  So
> > we need to understand this and deal with it.
>
> I think it would have to have two properties. First, what bias exists
> mustn't lead too strongly in either small-party or large-party bias. If
> you have large-party bias, you get two party rule. If you have
> small-party bias, you get centralized party management like in Hong Kong
> as every party splits into a miniparty that is coordinated from larger
> party bases.
>
> Second, it has to give generally good results. Random ballot is
> strategyproof but doesn't give good results. IMHO, IRV's failure is
> moreso this than that it's easy to strategize: it behaves erratically
> and the voters compensate by playing it safe.
>
> > But one important question should not be overlooked: What do we want to
> > self-correct toward? That is, what is the long-term goal? I believe we
> > should want to move toward a closer or better representation of society
> > as a whole, but there are other ways to look at that.
>
> If you take a very long perspective, it might be the case that party
> democracy itself can be improved upon, in which case what election
> method we use is irrelevant.


I strongly doubt that we can rely on parties to improve democracy.  They
tend to be anti-democratic if the power structure of the parties allows it,
and there is no reason they would give up control unless required to do so.
So if we have to live with parties, we have to impose democracy on them, in
which case they effectively become proper institutionalized bodies of the
government itself.

And even if they can be made to function democratically, then there are all
the other problems with parties I mentioned above in this message and in a
couple others.  I remain strongly anti-party.


> If something like Gohlke's recursive
> democracy is better, then that sidesteps direct elections altogether. Of
> course, one can ask similar mechanism design questions of the system
> that ends up being better. For instance, I discussed the need for
> minority representation in Gohlke's method, where I thought requiring a
> supermajority for the lower levels to support a higher level (and/or
> having larger groups than three) could help with this, and where Gohlke
> settled on a party declaration mechanism.
>

I like the direct democracy aspect of Gohlke's recursive democracy.  But I
think its structure is wrong for proportionally representing all the
positions on issues.  It is a people organization first, and that may have
some benefits for cross-fertilization of ideas, but I would suspect that
widely dispersed minority opinions will tend to be slighted.


-- 
Daniel LaLiberte
daniel.laliberte at gmail.com
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