Revealed preference and satisficing behavior

A much discussed topic in the theory of choice is how a preference order among options can be derived from the assumption that the notion of 'choice' is primitive. Assuming a choice function that selects elements from each finite set of options, Arrow (Economica 26:121-127, 1959) already showed how we can generate a weak ordering by putting constraints on the behavior of such a function such that it reflects utility maximization. Arrow proposed that rational agents can be modeled by such choice functions. Arrow's standard model of rationality has been criticized in economics and gave rise to approaches of bounded rationality. Two standard assumptions of rationality will be given up in this paper. First, the idea that agents are utility optimizers (Simon). Second, the idea that the relation of 'indifference' gives rise to an equivalence relation. To account for the latter, Luce (Econometrica 24:178-191, 1956) introduced semi-orders. Extending some ideas of Van Benthem (Pac Philos Q 63:193-203, 1982), we will show how to derive semi-orders (and so-called interval orders) based on the idea that agents are utility satisficers rather than utility optimizers.