  Universal dimensionless quantities, such as Binder ratios and wrapping
probabilities, play an important role in the study of critical phenomena. We
study the finite-size scaling behavior of the wrapping probability for the
Potts model in the random-cluster representation, under the constraint that the
total number of occupied bonds is fixed, so that the canonical ensemble
applies. We derive that, in the limit $L \rightarrow \infty$, the critical
values of the wrapping probability are different from those of the
unconstrained model, i.e. the model in the grand-canonical ensemble, but still
universal, for systems with $2y_t - d > 0$ where $y_t = 1/\nu$ is the thermal
renormalization exponent and $d$ is the spatial dimension. Similar
modifications apply to other dimensionless quantities, such as Binder ratios.
For systems with $2y_t-d \le 0$, these quantities share same critical universal
values in the two ensembles. It is also derived that new finite-size
corrections are induced. These findings apply more generally to systems in the
canonical ensemble, e.g. the dilute Potts model with a fixed total number of
vacancies. Finally, we formulate an efficient cluster-type algorithm for the
canonical ensemble, and confirm these predictions by extensive simulations.
