  The problem of measurement is often considered as an inconsistency inside the
quantum formalism. Many attempts to solve (or to dissolve) it have been made
since the inception of quantum mechanics. The form of these attempts depends on
the philosophical position that their authors endorse. I will review some of
them and analyze their relevance. The phenomenon of decoherence is often
presented as a solution lying inside the pure quantum formalism and not
demanding any particular philosophical assumption. Nevertheless, a widely
debated question is to decide between two different interpretations. The first
one is to consider that the decoherence process has the effect to actually
project a superposed state into one of its classically interpretable component,
hence doing the same job as the reduction postulate. For the second one,
decoherence is only a way to show why no macroscopic superposed state can be
observed, so explaining the classical appearance of the macroscopic world,
while the quantum entanglement between the system, the apparatus and the
environment never disappears. In this case, explaining why only one single
definite outcome is observed remains to do. In this paper, I examine the
arguments that have been given for and against both interpretations and defend
a new position, the "Convivial Solipsism" , according to which the outcome that
is observed is relative to the observer, different but in close parallel to the
Everett's interpretation and sharing also some similarities with Rovelli's
relational interpretation and quantum bayesianism. I also show how "Convivial
Solipsism" can help getting a new standpoint about the EPR paradox providing a
way out of the standard dilemma that is having to choose between abandoning
either realism or locality.
