Probabilistic Choice Induced by Strength of Preference

Just as we formulate detailed theories of utility or preference, so too should we theorize carefully about strength of preference. Likewise, because behavior is inherently uncertain, we need a theoretical framework for understanding choice probabilities. This paper fleshes out the simple premise that more strongly preferred options are more likely to be chosen. The resulting distribution-free Fechnerian models (DFMs) eschew convenience assumptions underlying popular models like the logit and probit, revealing which aspects of a core decision theory do or do not remain invariant across different ways of constructing strengths of preference, as well as across different monotonic links between those strengths of preference and choice probabilities. We formulate DFMs in a unifying polyhedral geometric space that allows for direct comparisons of theories that can be as categorically different as, say, regret theory, expected utility theory, and lexicographic semiorders. The geometric representation also provides a nuanced perspective on theoretical parsimony beyond parameter counting. Through a series of examples, we demonstrate the derivation and mathematical characterization of DFMs for decision theories with and without utilities and the inferences one can draw from data. We show how DFMs provide a multi-layered quantitative approach to the identifiability of hypothetical constructs. We highlight specific cases where DFMs protect the researcher against mistaken conclusions caused by overspecified models.