Although it is often assumed that a set (of goods) can be
completely ordered (priced) by the preferences of some
agent it is not possible, in general, to define on a set a real
valued order preserving function (utility or monetary price).
See, for instance, "The non-existence of a utility function
and the structure of non-representable preference relations"
(Beardon, et al, Journal of Mathematical Economics, vol.
37, pg 17, 2002) and references therein.
If you take values that are NOT representable by a scalar
(money, utility) you distort them if/when you FORCE such
a scalar representation (i.e. monetary pricing).
It is, in general, impossible to define a single common
currency with which to measure all that is valuable. There
are things whose value are orthogonal to money (the value
of your vote, a decision in a court of law, your wife's love,
etc.)
If you have any doubt that human society exhibits value
pluralism you need only observe the legal system. Upon
being found guilty of some crimes it is only required that
you pay a (monetary) fine, whereas in other cases you
must pay with your life, or at least some years worth
(jail term, probation, community service, etc.). No one
would be satisfied to see a serial killer merely pay a
fine each time he took another life. A scalar utility
(money) can not serve as a measure of the value of all
things.
In place of a scalar utility a few economists have considered
vector utilities (see, for example, Hausner,
"multidimensional utilities" chap XII in Decision Processes
R. M. Thrall, Wiley, 1960). Perhaps what we need is to
replace money with a vector currency.
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