The role played by gauge fixing in the description of superselection s
ectors for a simple quantum mechanical system is analysed. By viewing
this as a theory with constraints, it is shown that the possibility of
having inequivalent gauge fixing conditions (Gribov's ambiguity) sign
als the existence of inequivalent reductions to a physical quantum the
ory, and hence superselection sectors. This point of view is contraste
d with the more traditional one that identifies superselection sectors
with inequivalent quantisations. It is argued that emphasising the ro
le of gauge fixing (along with the Gribov problem) will allow for a mo
re direct extension of these ideas to quantum field theory and, in par
ticular, gauge theories.