On 06/25/2013 12:53 AM, Benjamin Grant wrote:
On Mon, Jun 24, 2013 at 6:06 PM, Kristofer Munsterhjelm
<km_el...@lavabit.com <mailto:km_el...@lavabit.com>> wrote:
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.
Of course, there are (in the circumstance where Gore is the better
chance to beat Bush than Nader) likely more Gore:100 Nader:0 Bush) votes
than Nader: 90 Gore:70 Bush 10 ones.
In fact, given that we *are* talking about an election with two strong
front running candidates and one "spoiler" weaker one, isn't it *far*
more likely that Gore is far in front of Nader and the only real unknown
is if Gore will beat Bush or not? Which leads right back to the entire
scenario of issues I began with.
The thing is, whenever we have more than two parties running, I think we
will always have weaker "spoiler" parties that cannot really win, but
that can, if the system allows or encourages people to vote against
their best interest, cause people to get a much lower ranked choice,
possibly their least preferred choice - this is my whole concern.
But here's a thing also to note. Nader voters are never worse off by
voting [Nader: 100, Gore: 100, Bush: 0] than by voting [Nader: 0, Gore:
100, Bush: 0]. Because of this, a simple Approval strategy goes: "Vote
for the frontrunner if you prefer him to the second-place candidate.
Then vote for everybody you like more than the candidate you approved in
the first step".
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.
Aha! But what if what is likely happens in stage two: People get ahead
of themselves and give their full support to Nader and less support to
Gore *before* Nader is strong enough to beat Bush? Then Bush wins, both
the Nader and Gore voters freak out, and now Nader people go back to
voting Gore with full support, because now they've been burned!
The only way to avoid this, I *think*, is with a system in which
expressing a preference of A over B doesn't let C win - and such a
system may well have worse flaws, possibly.
Yep. That's a very definite risk, and one of the reasons I don't think
Approval is a good method "in a vacuum". I'd support Approval as a
compromise more because it gives a lot of benefit for a very small tweak
to Plurality, than that it is good in itself: a value/cost consideration
rather than a raw value consideration.
But you're right, the problem there is very real (unless somehow the
voters only think of candidates as "people I can accept" and "people I
definitely don't want to see in office"). And the burn, as you put it,
could not just harm Nader, but it could harm Approval itself -- just
like I've argued that the weird way IRV acts can backfire.
So, for rated methods, I suggest Majority Judgement. It's more resistant
to strategy, the ballots are set up so as to encourage comparisons to a
common standard (the grades) rather than comparisons between candidates,
and the method passes IIA. There's also experimental data from its use
in France. The proposers found out that IIA is too weak when the voters
compare candidates to each other, because the addition or removal of
candidates may lead the voters to change what they put on the ballots.
Thus, they emphasize the importance of having the voter evaluate the
candidates against a common standard rather than against each other:
because otherwise, IIA doesn't amount to much.
For ranked methods, I support Condorcet methods, particularly the
advanced ones like Ranked Pairs and Schulze.
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.
Well, to be fair, just about anything is better than plurality. However,
what I meant is that functionally Approval (when each voter acts to
their best (or least bad) outcome) seems not that different from
Plurality Voting. We still top vote the front runner that has the best
chance to defeat our abhorred candidate. If we have a candidate we
prefer more than the palatable front runner, we can top vote him too,
but that won't help Nader beat Gore. It seems irreconcilable in this
context.
In Approval, you can choose between helping Nader beat Gore, or helping
{Nader, Gore} beat Bush. In Plurality, you can choose between helping
Nader beat Gore or helping Gore beat Bush. The whole dynamic of the
readjustment in stage 2 depends on the voters being able to tell others,
through the poll results, that they prefer *both* Nader and Gore to Bush.
As such, Approval is better than Plurality. If the tricky part between
stages two and three go off well, then Nader wins. In contrast, in
Plurality, there's no way to get to stage two itself because signaling
that you like Nader carries such a high cost of potentially making Bush
win.
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.
Yup, that's where I will begin making charts! ;) (Seriously.)
I just have to find the time and focus to bring my endeavor with this to
that level.
You might be interested in Ka-Ping Yee's work. I've linked to some of
it, but here it is again, along with some other stuff:
http://zesty.ca/voting/voteline/
http://zesty.ca/voting/sim/
Also, there's Brian Olson's page with some more Yee diagrams as well as
some graphs of the performance of various methods as the number of
candidates increase:
http://bolson.org/voting/
Myself, I originally investigated the tradeoff between representation
accuracy and majoritarian appeal of assemblies elected by various PR
methods, and I made something like this:
http://munsterhjelm.no/km/elections/multiwinner_tradeoffs/
I also made some multiwinner Yee maps, way back:
http://munsterhjelm.no/km/elections/multiwinner_yee/
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