  Two particles are identical if all their intrinsic properties, such as spin
and charge, are the same, meaning that no quantum experiment can distinguish
them. In addition to the well known principles of quantum mechanics,
understanding systems of identical particles requires a new postulate, the so
called symmetrization postulate. In this work, we show that the postulate
corresponds to exchangeability assessments for sets of observables (gambles) in
a quantum experiment, when quantum mechanics is seen as a normative and
algorithmic theory guiding an agent to assess her subjective beliefs
represented as (coherent) sets of gambles. Finally, we show how sets of
exchangeable observables (gambles) may be updated after a measurement and
discuss the issue of defining entanglement for indistinguishable particle
systems.
