[Election-Methods] strategic voting and strategic nomination

[James Green-Armytage]

Hello!

Really, a big hello to everyone. How long has it been? About a year and a
half since my last post, apparently, and then a while longer since I was
really a 'regular' here. If anyone feels moved to tell me what they think
the most exiting developments on the list have been in the last couple of
years, I would be quite interested to hear about it. (No pressure, though
:-)

As I've probably mentioned, I'm working on my PhD in economics, and I
estimate that about half of my dissertation will focus on voting theory.
(There is always the temptation to make it more than half, but I've been
told that it will be harder to get a job if I don't spend a bit more time
on more traditional topics.) I feel that I'm beginning to reach a stage
where I ought to start sharing my work with others a bit more, and stop
being stuck in my own head quite as much.

So, I'm writing to say that I have a voting theory paper in a kind of
advanced first-draft stage (really it's more of a tenth or twentieth
draft, but it probably still has a ways to go before it's finished), and
have made it available on the UCSB economics department web site, at: 
http://econ.ucsb.edu/graduate/PhDResearch/phdResearch.htm

Your comments, if you have any, will be greatly appreciated. 

I'll give you a quick summary here: This paper is the beginning of a
project which has the overall goal of developing measures of the
vulnerability that different voting methods have to strategic
manipulation, that is, vulnerability to strategic voting and strategic
nomination. So far, I've been using computer simulations as my primary
method of study. The paper describes simulations that I've used to measure
the relative strategic vulnerability of seven single-winner voting
methods: 

plurality 
two round runoff 
alternative vote 
minimax 
Borda 
approval
range 

The gist of my methodology is this: Using a fairly simple model, I
generate candidates and voters in S-dimensional issue space. Preferences
of the voters over the candidates are determined by relative proximity. To
measure strategic voting vulnerability for each method, I calculate
initial results based on sincere voting, and then see how often a group of
voters can get a mutually preferable outcome by voting strategically. To
measure strategic nomination vulnerability, I see how often the withdrawal
of a non-winning candidate (or group of candidates, under certain
restrictions) changes the outcome. 

Perhaps the most conceptually challenging part of this was to write
programs for each method (I've been writing my simulations in matlab, by
the way) that are able to determine, in every possible case, and for any
number of candidates, whether manipulation by strategic voting is at all
possible, without having an absurdly long runtime. (Before this, I was
completely inexperienced in computer programming, but now I'm at least
able to do simulations, if not much else.) The paper goes into some detail
about how each program works; I believe that they work correctly, but am
happy to hear from anyone who can find a hole somewhere. 

I can also tell you a little bit about my preliminary results. The
orderings of the methods are somewhat sensitive to the specifications of
the model (there are three parameters: N, the number of candidates, NV,
the number of voters, and S, the number of issue dimensions), but it is
possible to comment broadly on which methods tend to perform well or
poorly. 

With respect to strategic voting, alternative vote (IRV) is usually the
least manipulable, followed by two round runoff, then minimax, then
plurality. Approval, Borda, and range voting tend to be the most
manipulable, roughly in that order (going from best to worst).

With respect to strategic nomination, I should first say that I didn't
bother to calculate vulnerability scores for approval and range, because
they are probably very close to zero (under some assumptions, exactly
zero), that is, very resistant to strategy. Aside from those, minimax is
clearly the best, in the specifications I looked at. Alternative vote is
generally better than two round runoff, which in turn is generally better
than plurality (plurality is clearly the worst). Borda occupies different
places in the ranking, depending on various assumptions, but it is always
better than plurality and worse than minimax. However, my simulations
agree with existing intuition in finding that Borda systematically
encourages more non-winning candidates to enter (what has been called
'teaming'). By contrast, minimax gives no specific bias in either
direction, while the remaining methods have a specific bias that
discourages candidate entry (what has been called 'vote-splitting'.)

So, to sum up, speaking very, very roughly,
for strategic voting: IRV > runoffs > minimax > plurality >> approval >
Borda > range 
for strategic nomination: approval, range >> minimax >> IRV > runoffs >
Borda (varies) > plurality

Especially towards the end, the paper goes into some detail about how this
approach can be extended (e.g. more methods, more sophisticated
data-generating processes, weighting strategies inversely by how difficult
they might be to pull off, etc.), and a few other approaches that can be
tried (e.g., for voting, taking the next step beyond finding out whether
strategies are possible, and trying to get at what might happen next,
finding strategic equilibria, etc.; for nomination, finding the full set
of Nash and core equilibria)... again, this is just intended to be a first
step.

Again, the full paper (in its current draft) is available online, and
again, I'm looking forward to hearing your comments. I hope that everyone
has been well, and I hope that I won't be quite so absent from the list as
I have been over the last few years.

all my best,
James    





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