Friday, December 03, 2004

Buridan's Ass Takes a Random Walk

Despite my best efforts not to, I've been thinking a bit about Buridan's Ass over the last couple weeks. At first, I saw it as a complete non-problem, and said so in this post. Now, I see it as a problem, but wonder if the human brain has a way around this sort of problem. The issue seems to be whether there is some randomness in choice, and where that randomness comes from. Neurath's solution is to flip a coin, or use some other random decision-making process. However, this external randomness has its problems. An ass, for instance, is not going to flip a coin, and therefore, according to the way the problem is formulated, should still starve to death. Also, as Joe at Third Floor notes, the coin-flip solution just raises another Buridan's ass problem. He writes:
One argument that seems like a good one for undermining choice without preference is the solution of Otto Neurath article by Michael Stoltzner Chris suggested in his post. In the article (p. 12ff), Stoltzner suggests that an auxiliary motive - drawing lots, flipping a coin - is a way around the problem. But Stoltzner has not considered the new problem that results from introducing the auxiliary motive. If two different auxiliary motives leave things completely to chance, then which of the many different auxiliary motives should I use to determine my choice. For example, S seems to have no preference about auxiliary motives - flipping a coin is just as good as drawing lots. If S has his choice between drawing lots and flipping a coin and he has no preference about which he should use, then we have a new problem of choice without preference. So, Neurath's suggested conclusion seems to fail too.
Still, if the brain itself imputes some randomness into the decision-making process, then the second Buridan's ass problem, the problem of which random method to use, wouldn't arise. In other words, what we need is some internal, rather than external randomness. Here's an analogous problem to illustrate how the brain might have its own randomness. Imagine we are presented with an exemplar that fits our criteria for classification into two categories equally, but we have to classify it into only one category (this is the sort of task that experimenters use all the time in concept research). In most cases, humans will eventually classify the exemplar as being a member of one of the two categories, but how? One answer is that classification uses a random-walk procedure (a procedure present in several current models of categorization and decision making, as well as neuroscientific models of neuron firings). With this procedure, only one option can reach the threshold first, even when two classifications are equally likely to reach the threshold. Thus, the exemplar can be classified in only one category if that's the task at hand.

The same could work in a choice without preference situation. Even if both potential options are equally attractive, if we are motivated to choose only one, then using a random-walk model, only one of the options will be chosen. The random-walk procedure (which, as I've said, is common in cognitive models, as well as neuroscientific ones) thus imputes randomness into the decision making context without having to use an external source (e.g., a dice throw).


Anonymous said...

"In other words, what we need is some internal, rather than external randomness."

Yeah, I'd agree with that. My attempted answer was to appeal to the idea of cognitive 'fluctuations'. If the state of our judgements/preferences are constantly in flux, then at some moments we might find ourselves with a (random) preference for one choice over the other. We could then act, without having to appeal to any sort of external procedure to make the decision for us. Since we don't ourselves choose the fluctuations, we avoid any second-order problems here.

I'm not sure whether this picture is neurologically plausible, however. (What do you think?) 

Posted by Richard

Anonymous said...

I agree. That's what I tried to in my original post, too, though in a much more convoluted way. In this post, I just wanted to use a specific way of getting that randomness, one that's used a lot in cognitive modeling. In reality, there's all sorts of randomness or semi-randomness involved in cognition and perception, in the form of different kinds of noise (1/f, for instance). 

Posted by Chris

Anonymous said...

I like the move from external to internal randomness, but I am not clear on how this works yet. (This is another way of saying I'm ignorant of the stuff you mention. My apologies.) So, I have a few clarificatory questions.

First, if humans categorize the exemplar by using the random walk procedure, then does this presume that the category chosen is the correct one for the exemplar?

Second, if both options are equally likely to reach the threshold and both options are equal in every way (my assumption if consistent with Buridan's Ass type problems), then why would we expect that one option would reach the threshold first?

I guess that's all for now. I've meant to comment here b/f, but never got around to it. Great blog, and I'm very interested in your newest blog on reasoning! Also, how did you get the bloggerhack comments to say "proofread" and not "preview?"

Posted by Joe

Anonymous said...

Random walks don't have to exclude the possibility that both (or all) possibile choices could arrive at the same time, but they could. Of course, a coin could land on its edge. Finding something that is completely random is one of those things mathematicians struggle with (if you add white noise, which looks completely random, to white noise, you get brown noise, which isn't random at all, for instance). If it is equally possible for two solutions to reach a threshold, what you would get, in most models, is one or the other solution reaching the threshold first almost every time, and once in a million blue moons, both reaching at the same time. 

Posted by Chris

Anonymous said...

Oh, and on the comments thing, you just mess with the html for the preview button. The code looks like this:

var previewButtonText = "Proofread"; 

Posted by Chris

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