Methods and apparatus to determine characteristics of media audiences are disclosed. An example method includes creating a constraint matrix based on a first activity associated with a first characteristic of a population, the first activity associated with a second characteristic of the population, and a first combination associated with at least one of the first activity, the first characteristic, and the second characteristic. The example method includes creating a combination total set based on a first measurement for the first activity associated with the first characteristic and a second measurement for the first activity associated with the second characteristic. The example method includes computing a first entropy probability based on the constraint matrix and the combination total set. The example method includes estimating a first portion of the population that matches the first combination based on the first entropy probability.