[EM] First Condorcet cycle ever spotted in a national presidential election (!?! apparently)

[Juho Laatu]

It is also interesting to separate different types of cycles.
I'll assume that the number of voters is high.

1) Weak cycle (random cycle, noise level cycle, or noise generated  
cycle)
- the looped candidates are almost tied
- can be a result of some almost random variation in the votes
- one could say that this kind of a loop is one special version of a tie
- any of the looped candidates could be the winner (no big violation  
against any of the majority opinions)
- the expected winner may change from day to day (in the polls)

2) Strong cycle (stable cycle, rational cycle, cycle with a stable  
identifiable reason)
- there is some specific reason that has led to the formation of this  
loop (not random variation in the votes)
- the reason behind the cycle can be described (maybe multiple theories)
- the cycle / opinions are strong enough to carry over daily/weekly  
fluctuation in the opinions

3) Strategic cycle
- a special case
- artificially generated (result of strategies that some voters have  
applied)
- not based on sincere opinions

Weak cycles may well exist when we have candidates that are close to  
tied. Strong cycles are more interesting since then we must have some  
specific reason behind them and the opinion is stable and clear. There  
are such situations but I believe they are not too common in real life.

One example of a strong cycle is a situation where candidate A  
promotes strongly topic T1 and slightly T2, candidate B promotes  
strongly T2 and slightly T3, and candidate C promotes strongly T3 and  
slightly T1. Many of the voters are mainly interested in one topic  
only (T1, T2 or T3). Each topic has about as many supporters. As a  
result a stable rational cycle is may well emerge. (This example is  
based on having a special set of candidates with "looped" opinions or  
campaigns. Do you have also some other kind of potential (real-life,  
rational, large election) strong cycles in mind?)

Juho



On Dec 10, 2009, at 1:31 AM, Jameson Quinn wrote:

> 2009/12/9 seppley <seppley at alumni.caltech.edu>
> Without studying details of the three Romanian candidates and the  
> voters'
> preferences, the explanation of this majority cycle cannot be known  
> for
> sure.
>
> However, consider a case of three very similar candidates. The voters'
> preferences in each of the three possible pairings would be nearly  
> tied
> (approximately 50% preferring each candidate over each other  
> candidate).
> In such a case, a cycle involving three small majorities would not be
> rare. Almost an even bet?
>
> Not rare, you're right. However, what you are describing is  
> essentially something like a "random elections model" or perhaps a  
> "Dirchlet model", which, according to WDS's table of calculations,  
> for 3 or 4 serious candidates, have probabilities of Condorcet  
> cycles somewhere in the range of 6-18% - which is certainly nothing  
> to be shocked about when it happens by chance, but also a good deal  
> less than an even bet.
>
>
> --Steve
> --------------------------
> Jameson Quinn wrote:
> > This is good math, and very interesting, but it doesn't speak at  
> all about
> > the politics of the matter. Have you figured out any tentative  
> explanation
> > for the Condorcet cycles you postulate? Why would, for instance,  
> O>B>G
> > voters be more common than O>G>B voters, yet in the mirror-image  
> votes,
> > B>G>O voters more common than G>B>O ones? (I realize that the  
> Condorcet
> > cycle does not require exactly that circumstance, but it suggests
> > something
> > of the kind).
> >
> > I understand that any such explanation would be post-hoc and  
> speculative,
> > yet it is still worthwhile to make the attempt.
> >
> > Jameson
> >
> > 2009/12/8 Warren Smith <warren.wds at gmail.com>
> >
> >> preliminary page on Romania 2009 election now available here
> >>
> >> http://rangevoting.org/Romania2009.html
> >>
> >> The results are not as impressive as I originally thought they were
> >> going to be.
> >> --
> >> Warren D. Smith
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