paradox of preference:
Empirical finding that people's preferences are often not
transitive: While one prefers A over B and one prefers B over C,
one also prefers C over A.
How paradoxical this seems is up to
the reader's preferences. In any case, it makes reasoning about human
actions and values more complicated than it would be if preference were
a transitive relation, for then it could be treated in analogy with the
mathematical notions of "smaller than" and "equal".
As it is in fact, it makes it difficult or impossible to compare the
judgments of value people make as if they are made in one single scale
of judgments where
items are linearly ordered as if they are numbers.
Part of the explanation for the paradox is that people often use
different standards for preferences, and may do so without being
conscious of it. Thus, one may prefer Anna over Bertha, since Anna is
sexier, and prefer Bertha over Cherry, since Bertha is more intelligent,
but prefer Cherry over Anna when considering both intelligence and
sexyness - or more generally, find when comparing A and B one does so in
terms of standards S1; when comparing B and C one does so in
terms of standards S2; and when comparing A and C one does so
in terms of standards S3.
Of course, when one's preferences involve several standards or
metrics at the same time - as seems to be the case when judging most
things - things get still more complicated.
The paradox of preference makes it difficult to work out adequate
mathematical theories of utility or value, that conform to how people
really make these kinds of judgments.
Incidentally, Richard Jeffrey, in "The Logic of Decisions 2nd
Edition" works around it by simply insisting that the preferences he
uses in his system are and must be transitive. This makes sense in so
far as one needs and wants and has preferences that are comparable in
some simple scale, but then it still seems examples like given above (in
brief: different standards for comparing different pairs, rather
intuitively from the properties of the items in the pairs) are quite
normal, quite human, and not transitive for obvious reasons.
Another thing it makes most doubtful are human scales of judgment in which all
things are measured and ordered from most excellent to worst possible,
and everything gets a rank and degree in the scale. Such scales are
quite common, acceptable and indeed mandatory in all manner of
totalitarian contexts, but they
cannot hold true for humans whose preferences are not always transitive.