 A further difficulty with the barebones theory of rationality concerns the individuation of the objects of preference or choice. Consider, for example, data from multistage ultimatum games. Suppose A can propose any division of $10 between A and B. B can accept or reject A’s proposal. If B rejects the proposal, then the amount of money drops to $5, and B gets to offer a division of the $5 which A can accept or reject. If A rejects B’s offer, then both players get nothing. Suppose that A proposes to divide the money with $7 for A and $3 for B. B declines and offers to split the $5 evenly, with $2.50 for each. Behavior such as this is, in fact, common (Ochs and Roth 1989, p. 362). Assuming that B prefers more money to less, these choices appear to be a violation of transitivity. B prefers $3 to $2.50, yet declines $3 for certain for $2.50 (with some slight chance of A declining and B getting nothing). But the objects of choice are not just quantities of money. B is turning down $3 as part of “a raw deal” in favor of $2.50 as part of a fair arrangement. If the objects of choice are defined in this way, there is no failure of transitivity.