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).