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15 preferences ability to handle additional error additive model additive utility function average ability average intelligence Bl imply cardinal utility function comparisons components consider contains decision procedure discussion Doctor of Philosophy Eliminating empirical consequences ences equations and inequalities example follows hence high ability High intelligence independence condition independence model independent preferences interval model linear programming low ability Low intelligence means of transitivity minimizes errors minimum number model i.e. necessary and sufficient number of preferences observed systems ordered metric scale ordinal model partial dominance perfectly satisfied predict unobserved preferences predictive strength preferences are predictable preferences independent present model relation satisfied the additive Section set of alternatives solution stronger models structural condition three structural model subject number subset of preferences sufficient conditions sufficient to characterize Suppes system of observed system of preferences Table theorem three preferences tion tives utility differences utility function exists utility values variables violation weak ordering weaker model