Observers saw 234 different pairs of stochastically organized dot patterns and indicated which of the two patterns appeared to be more numerous. All of the data can be accounted for by supposing that the choice of the more numerous pattern is based on the determination of the occupancy indices of both patterns. Each dot is posited to have an impact upon its neighborhood in a constant occupancy radius R. The area of the stimulus plane occupied collectively by all dots provides a basis for judging relative numerosity; the pattern with the larger occupancy value is chosen as more numerous. The occupancy model, besides providing a general explanation of known numerosity illusions in strictly quantitative terms, can explain some puzzling aspects of numerosity perception.