Pair Comparison, with and without Ties

A probabilistic model for pair comparison, in various experimental settings, and with and without admission of ties, is described. When discrimination is the objective, admission of tied decisions theoretically increases the power of the test of the null hypothesis, but in practice this may be offset by a decrease in the subject's efficiency of decision, and in these circumstances it is better to prohibit ties. When preference is the objective, ties should be admitted as they add information.