[EM] Monroe article online, and Monroe's math

[James Green-Armytage]

Mr. Loring has put the Monroe article on his Accurate Democracy site, at
[http://AccurateDemocracy.com/archive/condorcet/Monroe/004004MonroeBurt.pdf],
in case anyone has become curious. Although the strategy issues it raises
are legitimate, I am starting to think that Monroe's mathematical argument
may be flawed in itself.

Specifically, I'm not sure about his critique of Simpson (the closest
thing to the Condorcet methods we discuss), which is much too brief
considering the value of that method. I don't really understand
Meyerson-Weber equilibria, but it seems like a voter would want to find
the probability of a certain pivot outcome occuring, decide which outcome
they prefer and the marginal utility of this outcome, and multiply the
probability by the marginal utility. The sum of these numbers for each
relevant pair ordering should determine which pair ordering they choose.

My suspicion is that a pivotal outcome where a B voter can help elect
candidate 2 by insincerely voting 2>3>1 is far less likely than a pivotal
outcome where the 2>3>1 vote will resolve a pivot towards the outright
election of candidate 3, because the former requires a cycle. Therefore,
if the voters were relatively blind about what the other voters were
doing, it seems that a sincere 2>1>3 vote would make more sense by
Monroe's measure, unless the 1>3 preference was amazingly marginal.