  Recently, the partial information decomposition emerged as a promising
framework for identifying the meaningful components of the information
contained in a joint distribution. Its adoption and practical application,
however, have been stymied by the lack of a generally-accepted method of
quantifying its components. Here, we briefly discuss the bivariate (two-source)
partial information decomposition and two implicitly directional
interpretations used to intuitively motivate alternative component definitions.
Drawing parallels with secret key agreement rates from information-theoretic
cryptography, we demonstrate that these intuitions are mutually incompatible
and suggest that this underlies the persistence of competing definitions and
interpretations. Having highlighted this hitherto unacknowledged issue, we
outline several possible solutions.
