  For sharp quantum observables the following facts hold: (i) if we have a
collection of sharp observables and each pair of them is jointly measurable,
then they are jointly measurable all together; (ii) if two sharp observables
are jointly measurable, then their joint observable is unique and it gives the
greatest lower bound for the effects corresponding to the observables; (iii) if
we have two sharp observables and their every possible two outcome
partitionings are jointly measurable, then the observables themselves are
jointly measurable. We show that, in general, these properties do not hold.
Also some possible candidates which would accompany joint measurability and
generalize these apparently useful properties are discussed.
