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 <sepp...@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....@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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