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Show Chapter IV. The Utility-Maximizing Model of Rationality: Formal Interpretations 168 Now suppose a series of contiguous moments in time during which Winifred is to rank F, G, and H. At t1 she is presented with alternative F and G and selects F. At t2 she is presented with G and H and selects G. At t3 she is presented with alternative F and H. Now assume she already has the concept of something's ranking superiority, i.e. has ranked alternatives on previous occasions and learned to conceptualize her behavior in the usual way (a), and remembers the rankings she has already given to F relative to G and G relative to H (b). Then Winifred can conclude that F is superior in ranking not only to G, but to H as well. Her memory of her earlier rankings in effect establishes her third. So selection behavior that satisfies conditions (a) and (b) for intentionally ranking alternatives thereby satisfies (T). Winifred has at least one relatively long-term priority throughout each of three ranking trials. This establishes her as minimally psychologically consistent and her preference ranking as therefore transitive. Although we have already seen that having transitive preferences is compatible with psychological inconsistency, an agent who is minimally psychological consistent will have at least one transitive preference ranking. Contrast Winifred with Rex, who has and at t3 applies the concept of ranking superiority (a) to H, because he has thoroughly forgotten the relation of F and H to G established by his two previous rankings. That is, Rex's selection behavior satisfies (a) and violates (b). Then he can, contra hypothesi, draw no conclusions as to the ranking superiority of any one of the three alternatives to any of the others. That is, if (1) t1: F>G (2) t2: G>H (3) t3: H>F, then by transitivity, (4) G>F (on (2) and (3)) (5) H>G (on (3) and (1)) (6) F>H (on (1) and (2)). So Rex must conclude that everything is preferred to everything else, hence that none of the three alternatives is superior in ranking to any of the others. So, in particular, it is not superior in ranking to F. So his application of the concept of something's ranking superiority to H at t3 has involved him in a the three and you cannot make an optimal choice without paying as much or more" (109). I have more to say about this below. © Adrian Piper Research Archive Foundation Berlin |
