On the equivalence between elimination-by-aspects and generalised extreme value models of choice behaviour

Elimination-by-aspects and generalised extreme value offer competing paradigms for the representation of a common behaviour, that of individual discrete choice. Observing certain consistencies in their mathematical structure, several eminent authors have commented on the degree of equivalence between the two paradigms. Most contributions to this debate have, however, been less than definitive. More fundamentally, the contributions lack consensus. We advance the debate by establishing formal mathematical conditions under which three-alternative tree models from the two paradigms are exactly equivalent. We then extend our analysis to consider more general models, showing that equivalence can be established for general tree models, but not for cross-nested models.