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

[Juho]

Here are two example situations where sincere cycles might exist.

Sincere cycles are probably not very common in real elections. There  
have already been many ranked ballot based elections with reasonably  
sincere ballots, but at least I'm not aware of any top level cycles in  
them. This is at least a weak practical proof. But still cycles could  
exist in some quite reasonable set-ups.


1) Randomness

Lets assume that all candidates are about equally good and all kind of  
preferences are well distributed among the voters. In this situation  
votes would look pretty much like random. votes, or at least not  
follow a clear linear or other simple model. All candidates would get  
about equal number of first preferences. And there would be no strong  
preferences between any two candidates. The preference matrix will  
thus be filled with more or less random values.

In this situation the probability of a top cycle increases to some  
clearly higher than zero probability. The cycle will of course be very  
weak, and small differences in voter opinions can change the  
situation. Therefore it is not probable that one could efficiently  
build any strategy on the assumption that some cycle A>B>C>A exists.

Strong left-right or other clear voting patterns and fixed and uniform  
opinions among the voters will decrease the probability of having a  
random cycle. Elections with no such strong set-up are more likely to  
lead to (random like) top level cycles.


2) Voters with simple targets + appropriate selection of candidate  
profiles

Lets assume that there are three leading candidates, and there are  
three key topics (positive targets) under discussion (e.g. lower  
taxes, better health care, some needed action in foreign policy), and  
we have a reasonably high number of voters that see one of the three  
questions as the key question in this election (reasonable number of  
voters for each question). It is quite typical that those three  
leading candidates each try to collect their support from different  
voter groups, and therefore each put more weight on one of the  
questions. (There could be also clones but let's ignore that to keep  
things simple.) Candidate C1 is thus known to promote question Q1,  
candidate C2 is associated with Q2 and C3 with Q3.

Since all candidates want to collect votes also outside their core  
support group they will say something positive also about the other  
two positive targets. Candidate C1 has to talk a lot about Q1 to  
guarantee her core support. Then she has to make a decision on how  
much effort she will put on questions Q2 vs. Q3. It is probable that  
she will consider one of these two questions to be more important than  
the other (or even if she would find them equally important or  
strategically equally profitable she probably would anyhow get better  
results in one of the two sectors (Q2, Q3)). Also C2 and C3 have to  
make similar decisions on how to run their campaign. We thus have  
three candidates that will rank three questions. Each candidate has  
different first preference. The probability of a loop in the rankings  
of the three leading candidates is now 0.25. Things might change  
dynamically during the campaign, but possibility of a loop in the  
candidate preferences or a loop as perceived by the voters remains.

The point in this scenario is thus that while strong preference loops  
in the voter opinions may be rare, in the candidate opinions/campaigns  
such loops are more likely to occur. And if such a perceived loop  
exists, and if many voters are mainly interested in one of the  
questions, then it is natural for those voters to rank the candidate  
that is strongly associated with their question first, and then rank  
second the candidate that supports this question more than the third  
candidate. And we may have a stronger than random loop (that was  
discussed above) in the results.


Juho


P.S. In general I think Condorcet methods will do quite fine in the  
elections. If we arrange an election among the EM list members, then  
we might see strategy analyses and even attempts to use some strategy.  
But in "real life" elections things might look different. It is  
difficult to reliably measure opinions and changes in the opinions,  
and regular voters can not be effectively controlled, and they will  
not make efficient strategic calculations themselves. Therefore my  
guess is that strategic voting would typically not be a major problem  
in typical public political elections, or if there are strategies they  
might well be irrational and noise in the results. We should try  
Condorcet methods in political elections of all (or many different)  
political environments to see (since political culture of each society  
is a major factor here).




On Nov 12, 2010, at 9:06 PM, fsimmons at pcc.edu wrote:

> 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
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