Classification of local realistic theories

Recently, it has been shown that an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment (two-setting model), works only for the specific set of settings in the given experiment, but cannot construct a local realistic model for the values of a correlation function, given in a continuous-infinite settings Bell experiment (infinite-setting model), even though there exist two-setting models for all directions in space. Hence, the two-setting model does not have the property which the infinite-setting model has. Here, we show that an explicit two-setting model cannot construct a local realistic model for the values of a correlation function, given in an only discrete-three settings Bell experiment (three-setting model), even though there exist two-setting models for the three measurement directions chosen in the given three-setting experiment. Hence, the two-setting model does not have the property which the three-setting model has.