[EM] election strategy paper, alternative Smith, web site relaunch

[James Green-Armytage]

quoting Jameson Quinn:
"These two facts seem somewhat contradictory, since in order for Hare to
elect the Condorcet winner, voters must frequently use strategy. Are you
saying that strategy is even more frequent in other methods?"

My reply:

You're correct that if the sincere Condorcet winner is not also the  
sincere Hare winner, then sincere voting will not be a core  
equilibrium in Hare. However, I find that the sincere Condorcet winner  
usually is the sincere Hare winner, in most of my specifications.  
Further, when the two sincere winners are the same, the result is  
highly unlikely to be manipulable in Hare.

quoting Jameson Quinn:
"Also, what's your voter model? All possible sets of voter preferences? Real
elections, of course, frequently have much lower entropy than such a model;
but any other model involves questionable assumptions."

My reply:

Right. Well, the simplest and most complete answer to your question is  
to refer you to section 3 of my paper, but I don't see the harm in  
giving a short explanation here as well.

First, for any of this to make sense, I should mention that my measure  
of 'how vulnerable' a method is to manipulation is just the fraction  
of trials in which manipulation that benefits all manipulators is  
logically possible. Of course there are other ways to measure it, but  
this method requires the fewest assumptions, so I think that it's a  
good place to start. (Also, it's the most common approach used in the  
literature, as I discuss briefly in the introduction.)

Now, about the models. I actually use three distinct models, and  
several specifications within each of these. The first is a spatial  
model, in which both candidates and voters are randomly placed in an  
S-dimensional issue space according to a multivariate normal  
distribution, with variances of 1 and covariances of 0. Voters prefer  
candidates who are closer to them in this space.

The second is an impartial culture model, in which each voter's  
utility from each candidate is an independent random variable. (I use  
a uniform distribution for this, but this is irrelevant where  
ranking-based methods are concerned, because only the preference  
ordering matters to the analysis.)

My third data generating process is derived from political survey  
data, specifically the American National Election Studies. You can  
download the data set for free at
http://www.electionstudies.org/studypages/download/datacenter_all.htm
(I used the June 2010 time series cumulative data file.) Since the  
60's, this survey has been asking people to rate various politicians  
on a scale from 0 to 100; since there's no actual election attached to  
this, it seems fair to treat these as sincere cardinal ratings. For a  
given number of candidates C, and a given year, I find all the  
C-candidate subsets of the rated candidates for that year, and analyze  
them as separate elections. I take a simple average over the years to  
get an overall percentage for each given number of candidates.

Actually, the idea to use the ANES data in this way comes from Nic  
Tideman and Florenz Plassman, who do something pretty similar in an  
as-yet unpublished paper called "The Structure of the  
Election-Generating Universe."
You can find their working draft of that paper at
http://bingweb.binghamton.edu/~fplass/papers/ElectionGeneratingUniverse.pdf

So, there are three models. One of the things that makes this paper  
relatively strong, in my opinion, is that it produces a set of results  
that are supported by all three models, which is cool, because they're  
really very different from each other.

For example, have a look at the graphs in section 6 (which are between  
pages 23 and 28 of the current version). I show results from the three  
models side by side, and although of course they're not identical,  
there are very strong patterns that are immediately apparent. The raw  
percentage of elections in which manipulation is possible is of course  
highly sensitive to the specification used, but there are a set of  
comparative relationships between the voting rules that seem to be  
remarkably stable across models and specifications.

In terms of overall strategic voting vulnerability, as I said, Hare  
and runoff are usually the least manipulable in general, minimax,  
plurality, and Bucklin are usually intermediate (and minimax is  
usually best among these), and range, approval, Borda, and Coombs are  
generally most manipulable. Also, these differences tend to be quite  
large -- not just a matter of a few percentage points here and there.

When we look at just compromising strategies, plurality is the most  
vulnerable in just about every specification, minimax is consistently  
second-best (after Coombs, which is immune), and Borda, range,  
Bucklin, and approval are generally worse than runoff and Hare. When  
it comes to burying, the plurality-based methods (plurality, runoff,  
and Hare) are immune, and range, approval, and Coombs are consistently  
worse than the remaining methods.

As for the strategic nomination simulations, I only used the spatial  
model, because it allows us to generate candidates' preferences over  
other candidates using the same proximity method. I've played around  
with imputing candidate preferences in the impartial culture model by  
using the correlations between voters ratings of the candidates, but  
I'm not sure that that makes quite as much sense. (The problem with  
using the ANES data set for this is that it can't generate elections  
with all that many candidates.)

So, the nomination results are a little less robust, but many of them  
seem pretty intuitive. For example, it makes perfect sense to me that  
plurality would be most vulnerable to strategic exit, and that minimax  
would be minimally vulnerable to strategic nomination. It also makes  
sense that Borda would be highly vulnerable to strategic entry (I give  
some intuition for this in proposition 21), but I'm not as yet able to  
give a good explanation for why Bucklin seems to be even more  
vulnerable to strategic entry. Does anyone here want to try their hand  
at that? I added Bucklin and Coombs to the paper at kind of the last  
minute (September), so there's at least some possibility of a  
programming glitch, but I've checked through several examples, and it  
seems to be working properly, as far as I can tell.

my best,
James