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

[James Green-Armytage]

Dear election methods fans,

I recently completed a much higher-quality version of my 2008 election  
strategy paper. I'm using this as an academic job market paper, so if  
you do see an error in it, I'd definitely like to know. Here is a link:
http://www.econ.ucsb.edu/~armytage/svn2010.pdf

I'd also love it if one or two people would take a look at the codes  
for the primary voting strategy analysis, which can be found at  
http://www.econ.ucsb.edu/~armytage/codes.pdf They're for matlab, and  
they should start to make sense if you read section 4.1. of the paper.

A quick summary:
I focus primarily on 9 methods: plurality, runoff, Hare (IRV), minimax  
('plain Condorcet'), Borda, approval, range, Bucklin, and Coombs.
In my computer simulations, I find that Hare and runoff are least  
frequently vulnerable to strategic voting, and that Borda, approval,  
Coombs, and range are most frequently vulnerable to strategic voting.
I find that plurality is most vulnerable to strategic exit, and that  
Borda and Bucklin are most vulnerable to strategic entry. I assume  
that approval and range are minimally vulnerable to strategic  
nomination, and aside from these two methods I find that minimax is  
the next least vulnerable.

In addition to the computer simulations, I construct 22 relevant  
proofs, some of which may be of interest to some of you. For example,  
leaving aside the possibility of pairwise ties, I find that the  
existence of a sincere Condorcet winner is a necessary and sufficient  
condition for the existence of a core equilibrium in 8 of these 9  
methods, but that in the Borda count, it is necessary but not  
sufficient. The sufficient condition is for the Condorcet winner to  
have supermajority beats against all candidates, with sizes of at  
least [(2C-2)/(3C-2)]*V, where C is the number of candidates, and V is  
the number of voters.

In addition to the nine methods listed above, I tried some of my  
analyses with six other Condorcet methods: beatpath, ranked pairs,  
Smith/Hare, alternative Smith, and two versions of cardinal pairwise.  
Beatpath and ranked pairs generally seem to perform like minimax, and  
cardinal pairwise usually but not always performs somewhat better than  
these, but the really striking news in my opinion is how well the  
Hare-Condorcet hybrids perform.

That is, given a preliminary analysis, they seem to be as resistant to  
strategic voting as Hare (and possibly slightly more resistant), and  
they are distinctly less vulnerable to strategic nomination (because  
they are Smith efficient, and therefore only vulnerable to strategic  
nomination when there is a majority rule cycle). So, for single-winner  
public elections, alternative Smith and Smith/Hare seem to have a lot  
to recommend them, i.e. the combination of Smith efficiency with  
strong resistance to both types of election strategy.

I should define these methods here, for clarity. Smith/Hare eliminates  
all candidates not in the Smith set (minimal dominant set, i.e. the  
smallest set of candidates such that all members in the set pairwise  
beat all members outside the set), and then holds an IRV tally among  
remaining candidates. This method has been floating around this list  
for a while, yes? Does anyone know of an academic publication that  
mentions it? I seem to remember reading something that said that it  
had been named after a person at some point, but I no longer know  
where I read that.

Alternative Smith is a closely related method, which Nic Tideman made  
up when he was writing Collective Decisions and Voting. It (1)  
eliminates all candidates not in the Smith set, then (2) eliminates  
the candidate with the fewest top-choice votes. Steps 1 and 2  
alternate until only one candidate remains. (See page 232 of the  
book.) I focus on this rule rather than Smith/Hare in the paper,  
because I find it marginally more elegant, but the difference between  
the two is very minor.

my best,
James

P.S. My web site is back, mostly. The Antioch address got unplugged  
because of the split between Antioch College and Antioch University,  
so I've set up a new version of the site at  
http://www.econ.ucsb.edu/~armytage/voting/
I've taken down several of the peripheral articles, though if anyone  
wants to see them (unlikely, I assume), I still have them on my  
computer. Comments on my most recent proxy voting paper (which is on  
the site) are still quite welcome, by the way.