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

[Kristofer Munsterhjelm]

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.

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.

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.

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.

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.

> 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.

> 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".

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.
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. 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.

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.

> 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.

> 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.

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. 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.