Posted by: captainfalcon | May 7, 2010

Completing the objections to completeness

In case any of you (Chris) get turned off by the evaluative preliminaries of Wolff’s second post on Formal Methods in Political Philosophy, I recommend persevering. He returns to a description of rational choice theory in paragraph six or seven.

I, needless to say, enjoyed his evaluation of the claim that one is rational only if one has an ordinal ordering of one’s preferences.

To see if I’ve got this right (more than anything else), as I understand it one’s preference set has an ordinal ordering just in case the ordering is complete and transitive.

  1. The ordering of a set of preferences is complete just in case for any two elements (x & y) in the set either (i) A prefers x to y (or is indifferent between them) or (ii) A prefers y to x (or is indifferent). (Does this imply that a set of preferences is actually a set of outcomes over which relation xRy is construed to mean x is preferred to y or there is indifference?) What it means for your set of preferences to be complete, then, is that (a) there are no incommensurables in it and (b) it is fully decided (that is: there is no subset of preferences x and y about which you can say; I do not prefer x to y; I don’t not prefer y to x; but nor am I indifferent between the two – I just don’t know yet).
  2. The ordering of a set of preferences is transitive just in case for any three elements (x & y & z) if A prefers x to y (or is indifferent) and A prefers y to z (or is indifferent) then A prefers x to z (or is indifferent). I would like to be able to characterize transitivity in a way analogous to how I characterized completeness, viz. what it means for your set of preferences to be transitive, then, is that there are no __________ in it, but nothing is coming to mind. For some reason “quantum jumps” strikes me as a quasi-apt metaphor, but it is, at best, only quasi-apt.

Wolff gives a dispositive confutation of the claim that you’re rational only if you have a transitive set of preferences (optometrist case). He gives a persuasive – but less dispositive – confutation of the claim that you’re rational only if there are no incommensurables in your preference set (Sophie’s choice). Here I’ll flag Hilary Putnam’s attempted confutation of the claim that you’re rational only if you have a fully decided set of preferences.[1]

Here’s a version of Putnam’s counterexample. Putnam asks us to imagine that Theresa is trying to choose between two radically different alternatives – an ascetic life or a sensual one (a or s). If Theresa’s preferences are complete then either aRs or sRa. That is, either Theresa prefers a to s (or is indifferent), or prefers s to a (or is indifferent). Ex hypothesi, Theresa hasn’t yet decided which of the two lives she prefers; hence, she doesn’t prefer s to a and she doesn’t prefer a to s. Thus, if Theresa’s preference set is complete, then she is indifferent between a and s.

Is it rational for her to be indifferent between a and s if she doesn’t prefer one to the other? Putnam imagines a decision theorist arguing that it is, as follows. Suppose I offer Theresa a choice between a and s and she declines to accept either one. Then suppose I just give her one or the other. Why she should object? She doesn’t, after all, prefer the alternative I didn’t give her. Thus, indifference in this case is rational.

Putnam’s reply is that the decision theorist has misrepresented the relevant choices. Theresa wants either (i) a sensual life chosen, after reflection, of her own free will or (ii) an ascetic life chosen, after reflection, of her own free will. She should object, then, because by giving her one of a or s the decision theorist thwarts one of her preferences though she doesn’t yet know which one. Her objection, then, doesn’t imply that she prefers the alternative the decision theorist doesn’t proffer. The decision theorist’s reply therefore fails.

My sense is that Putnam’s example shows the falsity of the claim that a preference set is rational only if it is fully decided. Thoughts?

[1] The essay from which I draw this is “On the Rationality of Preferences,” which is in this volume.

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