[EM] Thoughts on Burial

[fsimmons at pcc.edu]

You guys have come up with some interesting ideas about the likelihood of sincere cycles, but my idea 
is not that complicated:

Usually in the high stakes elections that I have witnessed there are just a few issues that most voters 
feel strongly about, and opinions on these issues are highly correlated (or anti-correlated) so that the 
voter distribution in issue space is basically cigar shaped.

Perpendicular to the long axis of that cigar find a plane that divides the voters into two equal subsets 
(plus or minus one).  The candidate closest to that plane is very likely a Condorcet candidate.

But this Condorcet candidate can be buried as easily as a Condorcet candidate can be buried in a 
precisely one dimensional issue space.

I like Condorcet methods that discourage burial in one dimensional cases.  I don't care so much about 
the case where the candidates are distributed on the vertices of an acute triangle, i.e. the triangle is 
close to equilateral.  In that case burial may serve a useful purpose of decreasing the probability of 
winning for a low utility Condorcet candidate.

In particular, the sincere profile

40 A>C>>B
30 B>C>A
30 C>A>>B

could easily come from a one dim or cigar shaped issue space.  Any condorcet method that doesn't 
make burial of C risky for the A faction in this context is going to end up with more artificial cycles than 
real ones.

Note that random ballot on Smith is adequate for preventing the burial without any defensive strategy on 
the part of the C supporters.

On the other hand the profile

40 A>>C>B
30 B>>C>A
30 C>>A>B

could not arise from a one dimensional or cigar shaped issue space.  And candidate C has such low 
uility, it wouldn't be bad if A got a share of the probability through a burial of C.  

Random Ballot Smith doesn't discourage burial in this case, in which C retains only 30% of the 
probability. Without more detailed information it would be impossible to prove that C deserved more than 
that amount.