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.
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