Testing Transitivity (and other Properties) Using a True and Error Model. Michael H. Birnbaum. Testing Algebraic Models with Error-Filled Data. Algebraic models assume or imply formal properties such as stochastic dominance, coalescing, transitivity, gain-loss separability, etc.
Michael H. Birnbaum
122 Undergrads: 59% repeated viols (BB)
28% Preference Reversals (AB or BA)
Estimates: e = 0.19; p = 0.85
170 Experts: 35% repeated violations
Estimates: e = 0.196; p = 0.50
Chi-Squared test reject H0: p < 0.4
A similar expression is written for the
other seven probabilities. These can in turn be expanded to predict the probabilities of showing each pattern repeatedly.
Full model is underdetermined. One error
Fixed to zero; but other errors not equal.
Most people recognized dominance.