On the non-equivalence of weak and strict preference

Rechenauer (2008) claims that weak preference is a better starting point for preference relations than strict preferences. This contention is challenged. Definitional connections between weak and strict preference are suggested that lead to the opposite conclusion. This is not taken as a justification of the superiority of strict over weak preference as the primitive preference relation, but just as evidence that the given connections make a structure richer than the other. It is also make precise the sense in which weak and strict preference can be considered equivalent. The idea just consists of taking into account the other two implicit binary relations, indifference and non-comparability.