Decision-Time for the Donkey6 May 2013
Yester-day, I finished reading the 1969 version of
Choice without Preference: A Study of the History and of the Logic of the Problem of by Nicholas Rescher, which version appears in his Essays in Philosophical Analysis. An earlier version appeared in Kantstudien volume 51 (1959/60), and some version has or versions have appeared in later collections. I have only read the 1969 version, and some of the objections that I raise here may have been addressed by a revision.
The problem of Buridan's ass may not be familiar by name to all of my readers, but I imagine that all of them have encountered some form of it. A creature is given a choice between two options neither of which seems more desirable than the other. The question then is of how, if at all, the creature can make a choice. In the classical presentation, the creature is a donkey or some other member of the sub-genus Asinus of Equus, the choice is between food sources, and a failure to make a choice will result in death by starvation. The problem was not first presented by the Fourteenth-Century cleric and philosopher Jean Buridan, but it has come to be associated with his name. (Unsurprisingly, my paper on indifference and indecision makes mention of Buridan's ass.)
Rescher explores the history of the problem, in terms of the forms that it took, the ultimate purposes for which a principle were sought from its consideration, and the principles that were claimed to be found. Then he presents his own ostensible resolution, and examines how that might be applied to those ultimate purposes.
One of the immediate problems that I have with the essay is that nowhere does Rescher actually define what he means by
preference. I feel this absence most keenly when Rescher objects that there is no preference where some author and I think there to be a preference.
As it happens, in my paper on indifference and indecision, I actually gave a definition of
strict preference: which is to say that X1 is strictly preferred to X2 if X2 is not in the choice made from the two of them. So, in that paper,
strict preference really just refers to a pattern of choice. I didn't in fact define
choice, and I'll return to that issue later.
The Merriam-Webster Dictionary essentially identifies
preference as a gerund of
prefer, and offers two potentially relevant definitions of
- to promote or advance to a rank or position
- to like better or best
like, I'm still wondering what sense I might make of it other than an inclination to choose.
I'm not claiming that Rescher is necessarily caught-up in an illusion. Rather, I'm claiming, first, that he hasn't explained something that is both essential to his position and far from evident; and, second, that his criticism of some authors is based upon confusing their definitions with his own.
When I used the notion of a choice function C( ) in my paper, my conception of choice was no more than one of selection, and that's what I was unconsciously taking Rescher to mean until, towards the end of his essay, speaking of decisions made by flips of coins (and the like), he writes
In either event, we can be said to have "made a choice" purely by courtesty. It would be more rigorously correct to say that we have effected a selection.
Well, no. This isn't a matter of rigor, whatever it might be. The word
choice can rigorously refer to selection of any sort. It can also refer to selection with some sort of care, which seems to be what he had in mind.
Some of the authors whom Rescher cites, and Rescher himself, assert that when a choice is to be made in the face of indifference, it may be done by
random means. Indeed, Rescher argues that it must be done by such means. But he waits rather a long time before he provides any explicit definition of what he means by
random, and he involves two notions without explaining why one must invoke the other, and indeed seemingly without seeing that he would involve two distinct notions. When he finally gives an explicit notion, it to characterize a choice to be made as
random when there is equal weight of evidence in favor of each option. However, when earlier writing of the device by which the selection is to be made, he insists
The randomness of any selection process is a matter which in cases of importance, shall be checked by empirical means.
Now, one does not test the previously mentioned equal weight of the evidence by empirical means. An empirical test, instead,
Rescher makes a somewhat naïve claim just before that insistence on empirical testing. For less critical choices, he declares
This randomizing instrument may, however, be the human mind, since men are capable of making arbitrary selections, with respect to which they can be adequately certain in their own mind that the choice was made haphazardly, and without anyreasonswhatsoever. This process is, it is true, open to possible intrusions of unrecognized biases, but then so are physical randomizers such as coins.
Actually, empirical testing of attempts by people to generate random numbers internally show very marked biases, such that it's fairly easy to find much less predictable
Rescher's confusion of notions of randomness is entangled with a confounding taxonomy of choice which is perhaps the biggest problem with Rescher's analysis. The options that he allows are
- decision paralysis
- selection favoring the first option
- selection favoring the second option
randomselection, in which
randomentails a lack of bias
Another term that Rescher uses without definition is
fair and its coördinates, as when he writes
Random selection, it is clear, constitutes the sole wholly satisfactory manner of resolving exclusive choice between equivalent claims in a wholly fair and unobjectionable manner.
I certainly don't see that random selection should be seen as wholly satisfactory (though I believe it to often be the least unsatisfying manner), and I don't know what Rescher imagines by
fair. My experience is that when the word
fair is used, it is typically for something more appealing than justice to those inclined to envy. In the case of allotments by coin-flip, there may be no motivation for envy ex ante, but things will be different ex post. People do a great deal of railing against the ostensible
unfairness of their luck or of that of another.
I recall one final objection, which moves us quite out of the realm of economics, but which I have none-the-less. One of the applications of these questions of choice without preference (or, at least, without preference except stemming from meta-preference) has been to choices made by G_d. In looking at these problems, Rescher insists that G_d's knowledge must be timeless; I think that he ought to allow for the possibility that it were not.
 That might seem an awkward way of saying that X1 is strictly preferred to X2 if only X1 is in the choice from the two of them, but it actually made the proofs less awkward to define
strict preference in this odd manner.
 Even if one insists that the selection device must be characterized by equal propensity, there is in fact little need for empirical testing, if one accepts the presumptions that a coin may be considered to have unchanging bias and that flips of a coin may be independent one from another. Implicitly making these assumptions, my father proposes a method for the construction of a coin where the chances of heads and of tails would be exactly equal. One starts with an ordinary coin; it comes-up heads sometimes, and tails others. Its bias is unknown; at best approximated. But, whatever the bias may be, says my father, in any pair of flips, the chances of heads-followed-by-tails are exactly equal to the chances of tails-followed-by-heads. So a pair of flips of the ordinary coin that comes-up heads-tails is heads for the constructed coin; a pair of flips of the ordinary coin that comes-up tails-heads is tails for the constructed coin; any other pair for the ordinary coin (heads-heads, tails-tails, or one or both flips on edge) is discarded.
 I don't know that my father could explain his solution to a donkey. I've had trouble explaining it to human beings.