Unfortunately, physicists and philosophers disagree on what exactly the preferred basis problem is, what would constitute a solution, and how this relates (or subsumes) “the measurement problem” more generally. In my opinion, the most general version of the preferred basis problem was best articulated by Adrian Kent and Fey Dowker near the end their 1996 article “On the Consistent Histories Approach to Quantum Mechanics” in the *Journal of Statistical Physics*. Unfortunately, this article is long so I will try to quickly summarize the idea.

Kent and Dowker analyzed the question of whether the consistent histories formalism provided a satisfactory and complete account of quantum mechanics (QM). Contrary to what is often said, consistent histories and many-worlds need not be opposing interpretations of quantum mechanics ^{ a }. Instead, consistent histories is a good mathematical framework for rigorously identifying the branch structure of the wavefunction of the universe ^{ b }. Most many-world’ers would agree that unambiguously describing this branch structure would be very nice (although they might disagree on whether this is “necessary” for QM to be a complete theory).… [continue reading]