  Ray Solomonoff invented the notion of universal induction featuring an aptly
termed "universal" prior probability function over all possible computable
environments. The essential property of this prior was its ability to dominate
all other such priors. Later, Levin introduced another construction --- a
mixture of all possible priors or `universal mixture'. These priors are well
known to be equivalent up to multiplicative constants. Here, we seek to clarify
further the relationships between these three characterisations of a universal
prior (Solomonoff's, universal mixtures, and universally dominant priors). We
see that the the constructions of Solomonoff and Levin define an identical
class of priors, while the class of universally dominant priors is strictly
larger. We provide some characterisation of the discrepancy.
