[EM] Score Voting and Approval Voting not practically substantially different from Plurality?

[Kristofer Munsterhjelm]

On 06/24/2013 03:06 PM, Benjamin Grant wrote:
> Hi guys, I’m still here, still pondering, but now I have another
> question. I’ve been thinking about score voting, approval voting, and
> plurality (FPTP) voting, and I have a concern.
>
> Say we have a situation where we have three candidates, say Gore, Nader,
> and Bush. Say we have a voter, Abe whose greatest concern is that Bush
> NOT win. His second priority is that Nader win over Gore – but this
> priority is a distant second. He *really* doesn’t want Bush to win. He
> would prefer Nader over Gore, but he *hates* Bush.
>
> Let’s also say that Abe is intelligent, and he is committed to using his
> vote to maximize his happiness – in other words, rather than vote
> sincerely and cause his preferences harm, he will always vote
> strategically where it is to his benefit to do so.
>
> If Score Voting was in place, and he were to vote sincerely, Abe
> probably would vote something like ‘Gore:75, Nader: 100, Bush: 0’.
> However, he’s no fool, and he knows that while it is theoretically
> possibly that Nader *might* win, Gore is his best chance to stopping
> Bush, and that withholding score from Gore might (if all Nader
> supporters did it) result in Gore not getting enough of a score,
> therefor Bush could win.
>
> So strategically speaking, Abe reasons that although he supports a less
> likely candidate more, he strategically should score the front-runner
> Gore at full strength, so long as keeping Bush out is the greatest need
> – and so long as Nader’s win is unlikely.
>
> So, as far as *I* can see, this converts Score Voting into Approval
> voting.

You're generally right. There are some very particular situations with 
incomplete information where it makes the most sense to use partial 
ballots, but those happen way too rarely to make a difference.

You can see this from the other end, too: say you're in an Approval 
election and want to vote 0-10-range style. You want to give X a rating 
of 4, but it's an Approval election. To do this, you generate a random 
number on 0...10. If it is lower or equal to the rating (in this case 
4), you approve of X, otherwise, you don't. If everybody did that, the 
Range and Approval results would give the same winner (with high 
probability). So in a real sense, Range is Approval with fractional 
votes permitted.

Also, Range could possibly give different results than Approval voting. 
Consider an election where 99% of the voters are strategic. The vote 
comes out to a tie between Nader and Gore, according to these 99%. Then 
the remaining 1%, voting sincerely, vote something like [Nader: 90%, 
Gore: 70%, Bush: 10%] (strategic would be [Nader: 100%, Gore: 100%, 
Bush: 0%]). Then those votes break the tie and Nader wins.
For reasons like this, a mix of strategic and honest voters give better 
results than just having strategic ones.

> And say what you want about intelligence being a bar to entry, you can
> bet that the smart people behind ALL candidates will make sure that
> everyone gets the message, so we can largely ignore #3.  Most people I
> imagine would be pragmatic enough to worry more about the end result and
> less about sincere vs. strategic, so we ignore #2. And #1 people are
> going to vote the same way anways, so they may as well use Approval voting.
>
> OK, so let’s throw out Score Voting and use Approval voting. Gore v
> Nader V Bush.  Abe (who hates Bush but prefers Nader) gives an approval
> vote to Nader, his top-most preference, but knowing that withholding
> approval from Gore could elect Bush (and not wanting to play the
> spoiler) he also gives an approval vote to Gore. Since Gore in this
> example is far and away receiving much more support than Nader, Gore now
> beats Bush.
>
> Let’s call the party that put Nader on the ballot the Green party, and
> that they continue to field candidates in further elections that use the
> Approval voting system.  Abe notices the following pattern: when the
> Green party fields a candidate that doesn’t even have a glimmer of hope
> winning the election (like the Gore/Nader/Bush one) that people that
> support the Green party candidate also approve the Democrat candidate as
> a bulwark against the Republican. And since in those elections the Green
> party never really had a hope of winning, the Green approval vote is
> ultimately irrelevant – those elections would have proceeded no
> differently than if the Green supporters had simply voted Democrat.
>
> But much worse yet, Abe notices that in *some* election, the Green party
> actually gets a chunk of people thinking that Green could actually win.
> And emboldened by their hopes, many Green supporters decide to go for
> it, approve of the Green candidate, but *not* the Democrat one. Result:
> in elections where more voters think more favorably towards Green’s
> chances, their least preferred choice (the Republican) tends to win more!
>
> This are my two thoughts:
>
> a)Intelligent use of Score Voting becomes Approval Voting, and the harm
> in unwise use of Score voting means that Approval Voting is superior to
> (and simpler than) Score voting pragmatically.
>
> b)Approval Voting tends to result in irrelevant approval votes being
> given to weak candidates – which is pointless, or slightly stronger (but
> still losing) candidates can once again present a spoiler effect where a
> person’s least preferred choice is elected because they cast their
> approval only toward their most preferred choice, who was nowhere near
> supported enough to stop their least preferred choice.
>
> Am I substantially wrong about any of this? Ultimately, in real and
> practical terms, it seems that done intelligently, Score Voting devolves
> into Approval Voting, and Approval Voting devolves into Plurality Voting.
>
> How is this not so?

I would much prefer a good ranked balloting system to Approval, but let 
me try to explain the other side as well.

Your observation is right in that there's obvious tension between 
approving of only Nader (so Nader will win) and of both Nader and Gore 
(so Bush won't win). This is one of the reasons I dont like Approval all 
that much: I think it burdens the voter with having to convert an 
internal preference into an Approval-style ballot in what I call "manual 
DSV". DSV is Designated Strategy Voting, a meta-system where one has a 
computer find out the optimal strategic vote for some given honest vote. 
The implication of having to engage in manual DSV is rather like having 
to do a mathematical task in your head before voting: we'd rather not 
and it makes the system more unwieldy.

So there are really three stages to a prospective new party or candidate 
(like the Greens or Nader):

1. the candidate is not competitive (e.g. fringe candidate).
2. the candidate is competitive but either not strong enough to win, or 
there's been a miscalculation by the voters.
3. the candidate has taken over the position that would belong to a 
competitor (e.g. Nader becomes the new Gore).

I think Approval advocates argue that the relative share of approvals 
will inform the voters of where they are. So the progression goes 
something like:

In stage one, everybody who approves of Nader also approves of Gore.
In stage three, the tables are turned: everybody who approves of Gore 
also approves of Nader, but Nader still wins.

Stage two and the transition to three is the tricky part. In rounds of 
repeated polling, the voters start off cautious (approving both Nader 
and Gore). Then they see that Nader has approval close to Gore's level, 
so some start approving of Nader alone. This then reinforces the 
perception that Nader is winning, so more voters approve of Nader alone. 
And so it goes until Nader is slightly ahead of Gore and wins.

So, the way I see it: Approval is very simple on the front end. It's 
just "count all the votes". Back end is a completely different matter, 
as you see above. I think Approval pushes a lot of the oddities of 
voting into the "back-end" - the space in which the elections happen, as 
it were. The method itself appears to be very good (pass FBC, etc), but 
that's because the calculations happen in the minds of the voters before 
they submit their ballots and the criterion failures are therefore 
"hidden". If one were to make a computerized system that took 
preferences as inputs and then directly produced the output that the 
voters would be thought to reach through repeated polling, that system 
would probably fail quite a number of criteria.

But it is better than Plurality. It is nowhere as complex as IRV, it is 
just "count all the votes". As a compromise, it's better than not 
reaching any compromise at all.

> If it *is* so, then as much as I abhor Plurality Voting, I must now
> likewise abhor Score and Approval Voting.  But that shoves me back at
> the Bucklin, IRV, and other system that have one of my least favorite
> flaws – that ranking X higher than Y can cause Y to beat X.
>
> It’s days like these that I feel that there *is* no way to elect people
> that is fair and right.

Remember that criterion compliances are absolute. So a method may fail a 
criterion yet be perfectly acceptable in real elections. Being able to 
say that a method passes a criterion, though, helps a lot in that you 
now don't have to consider the possibility that the criterion might 
actually intrude upon real settings.

Still, there are results that are valid within certain domains. For 
instance, Black's single-peakedness theorem says that if all voters have 
preference functions that are highest at some point on a line and 
decrease from there (without increasing again), and the voters rank the 
candidates in order of preference, then any Condorcet method picks the 
candidate closest to the median voter. Also, IIA holds in such a 
situation because there are never any Condorcet cycles.