ALTERNATIVES TO THE
TWO-STAGE MODEL
Choice Probabilities
Some early models of the primate choice system
proposed that when choosing between two actions
a choice probability was computed directly from the
identity of the option pair, rather than by comparing
something like the utilities of the two options under
consideration. This choice probability was then proposed
to stochastically direct action. When these models
were introduced, some argued that they could
serve as an alternative to preference-based models.
Two factors argue against models of this type.
The first is axiomatic. Consider an agent who has
been asked repeatedly to choose between chocolate
and apples. Then she is asked to choose repeatedly
between apples and crackers. We can, of course,
represent the behavior of the agent with two choice
probabilities. If we begin, however, with the assumption
that the chooser represents only choice probabilities,
then we must necessarily remain agnostic about
what the agent will select if we offer her a choice
between chocolate and crackers. If, on the other hand,
we hold a belief that knowing her choices under these
first two conditions reveals her likely choice under
the third condition, then we are basically assuming
complete and transitive preferences that invoke a
utility-like representation. In other words, we invoke
a system which behaves “ as if ” abstract valuations,
subjective values, are represented.