A collisional radiative model for the argon ion system has been set up. In this model collisional data of Zapesochnyi et al. for the 4p group and of Rubin and Sobolev for the other groups have been used. Absorption of resonance radiation has been included in the model. The population densities of the 4p group with upper laser levels and the 4s group with lower laser levels have been calculated with this model as functions of the elecron temperature and density. We also measured these group densities and the electron temperature and density in a continous hollow cathode are discharge and compared them with the model data at the relevant temperature and density. This method may be qualified as a direct comparison between model and experiment by excluding an indirect determination of the electron temperature and density by a calculation. We found over three decades of excited level densities that the model predicts densities which are a factor 3 too large for the 4p group and a factor 3-8 for the 4s group. Possible reasons for this discrepancy are discussed.