On Dec 10, 2009, at 2:36 AM, Warren Smith wrote:
--It seems to me the Romanian O>B>G>O cycle was not "weak" in the
sense it was strong enough to be stable day to day, and there was some
nonrandom "rational"
reason behind it. However, it wasn't very strong in the sense the
margins were about
3.5%, 0.66%, and 7.7% respectively.
In a stable and "opinion conservative" society (or when at least
opinions concerning one of the topics are stable) already a 0.66%
margin may be reasonably strong and stable. People may have some very
stable opinions e.g. on religion, left vs. right, liberal vs.
conservative and ethnic questions.
- - -
Here's btw also one concrete example of a possible stable cycle. Let's
take first a traditional set-up on a one dimensional (left-right)
political space. We have three parties, left (L, 47%), centre (C, 10%)
and right (R, 43%). We may assume that C>L (since almost all R
supporters will support C). We may assume that L>R (since about 50%t
of the C supporters prefer L to R). Then we need some additional
reason why R>C. In the basic linear scenario C would win R, so there
must be some additional reason. Let that reason be that the candidate
of C party has earlier given some strong negative statements about the
leftist values of party L supporters. The candidate of party R has
been more diplomatic. This is enough to make sufficient number of
party L supporters dislike the C party candidate so much that they
will rank her last. As a result R>C. Those old statements of the C
party candidate do not change the other preferences. They may have
actually made the C>L preference even stronger. C party supporters may
still like L (as much as they like R) although their nominated
candidate maybe doesn't always feel that way.
In an opinion space that focuses on multiple separate questions strong
and stable loops may be even easier to arrange. There are three
parties, right (R), left (L) and green (G). All are about equal in
size. These parties are not on a linear spectrum but rather form a
triangle with equal distances between all parties. The R party
candidate happens to be slightly L oriented and not G oriented. Also
candidates of the other parties have been nominated in a similar way,
not from the very centre of each party but they all have similarly
somewhat biased opinions. Together these biased opinions of the
nominated candidates will form a cycle (with some not so small
probability, assuming that the leading three parties are roughly equal
in size).
In real life opinions are of course not as clear cut as in these
examples. But if there is some bias among the voters/candidates in
this kind of "cyclic direction" then the end result may well be a
stable cycle.
Now when rethinking about the definition of a strong or stable cycle,
maybe the characteristic feature is the stability. A cycle can be said
to be stable if one can collect sufficient justification that explains
why it is likely to be and stay stable (can be based e.g. on available
polls (that cover a sufficiently long time span) or a theoretical
credible model that explains why people feel this way).
Juho
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