A projection operator which maps the q-state Potts model onto an Ising model is investigated. The case of an approximate mapping between two-spin nearest-neighbour clusters on a d-dimensional hypercubic lattice is considered. In the ferromagnetic case, first-order transitions occur for q>q_c(d)=1+exp(2K_Ic(d))>or=2, where K_Ic(d) is the critical Ising coupling. Among the results are q_c(d) to exp(2/(d-1)) as d to 1⁺, q_c(2)=3.41 and q_c(3)=2.56. The antiferromagnetic Potts model has no long range order for q>2.