[EM] Why I Think Sincere Cycles are Extremely Unlikely in Practice

[fsimmons at pcc.edu]

If sincere cycles are extremely unlikely in practice, then the best Condorcet method is the one that most 
effectively discourages artificial cycles.

Here's why I think that in practice there is almost always a sincere CW.

(1)  In most public elections there are one or two dominant issues at stake, and voters' views on these 
two issues are highly correlated (or anti correlated) so that the issue space is effectively one 
dimensional.  

In that case the candidate near the voter median in the (nearly) linear distribution will be a sincere CW.

(2) Almost all of the common examples of voter profiles given on this EM list either have a ballot CW or 
an artificial cycle, meaning that when you lay out the faction geometrically, you see that the factions can 
be distributed along a line if you switch one preference in one faction.

(3)  All of the Yee-Bolson diagrams no matter how many candidates or how they are distributed have a 
sincere CW.  The central symmetry of the voter distribution guarantees it.  Central symmetry is not 
necessary.  It is just one of many conditions that can gurantee the existence of a sincere CW, no matter 
the placement of the candidates.

(4)  You can contrive positions of candidates relative to contrived distributions of voters to bring about a 
sincere cycle, but these are not configurations that occur at random.  Furthermore, in all of these cases 
that I have seen it is easy to introduce a sincere CW by perturbing the position of one of the existing 
candidates a little or by introducing another candidate almost at random near the barycenter of the 
distribution.

For example, the standard geometric example of a Condorcet cycle is to have three factions distributed 
at 120 degree intervals on a circle, and to have three candidates on the same circle ten degrees 
(counter) clockwise from their support.  If you distrub this arrangement significantly at random, a CW will 
appear. Or if you introduce a candidate almost anywhere well inside of the circle, it will end up being a 
sincere CW.

Real candidates are savvy enough to take advantage of such an opportunity by positioning themselves 
through their PR campaigns.  That's what the big bucks are used for.

"Nature abhors a vacuum."  Politicians are sucked into these pockets of opportunity.

But we don't have to be cynical about this.  The presence of such a vacuum is a sign that their might be 
a compromise alternative on which the voters could agree.  such a compromise wouold be detected in 
the primaries if a sufficient variety of candidates entered the race.  But this is not true under plurality or 
IRV.  That's why we need Condorcet!

Forest