Another way to remove the dependence of selection on an offset is to take the exponential of fitness where s controls the strength of selection. Although this removes the dependence of selection on an offset it does not remove the dependence on a multiplicative function. This can, however, be removed by making the selection strength inversely proportional to the standard deviation of the distribution of fitnesses.
Boltzmann selection has at least two practical benefits.
Secondly it typically produces a larger ratio of gain in the fitness to loss of variance in the fitness than other selection procedures.