  Basu's via media is what he referred to as the middle road between the
Bayesian and frequentist poles. He seemed skeptical that a suitable via media
could be found, but I disagree. My basic claim is that the likelihood alone
can't reliably support probabilistic inference, and I justify this by
considering a technical trap that Basu stepped in concerning interpretation of
the likelihood. While reliable probabilistic inference is out of reach, it
turns out that reliable possibilistic inference is not. I lay out my proposed
possibility-theoretic solution to Basu's via media and I investigate how the
flexibility afforded by my imprecise-probabilistic solution can be leveraged to
achieve the likelihood principle (or something close to it).
