Should We Leave Tough Choices to Chance?

two asses, one choice

Source: Lauren E. Krueger

Sometimes I wish I were Buridan’s ass. — Hoca Camide

Professor Hafiz is facing a difficult choice. For his upcoming course on Kurdish Dairy Science, he has recruited two promising teaching assistants, Aysha and Zeynep. Both are equally competent and eager to do the job but the university administration informs Professor Hafiz that he can make only one job offer. What is Hafiz to do?

The short answer is that Hafiz could flip a coin. Since he cannot articulate a clear preference for either candidate, chance seems the only road to fairness (Krueger & Grüning, 2024). Neither Aysha nor Zeynep would be able to argue with the process or the result.

Yet, a feeling of discontent remains. Who wants a career built on chance? Both Aysha and Zeynep, we suspect, would like to see Professor Hafiz have a preferenc—and that Aysha and Zeynep, respectively, would turn up as the preferred candidate.

Since, however, Hafiz has no preference, can he find a way to improve on the limited happiness delivered by the chance method? Perhaps so, but he would have to massage the truth a little. His first approach would be to flip a coin, and then tell the winner that she, in fact, was his preference: a white lie. This way, the loser would attribute her loss to chance, and the winner would (falsely) attribute her win to her putative higher competence (Weiner, 1985). But clearly, this won’t do. Aysha and Zeynep would very likely talk to each other and figure out that Hafiz told them different stories. Hafiz’s credibility would be shot.

Hafiz’s second, more sophisticated, approach is to propose a two-stage game. In the first round, he will flip a coin to determine whether he will flip a coin again in the second round or whether he will reach more deeply into himself to find a preference. Now, the winner after round 2 may infer that the chance outcome of round 1 determined that the better candidate be chosen, while the loser may infer that round 1 determined that the choice in round 2 be random. The winner feels she was chosen on merit, while the loser feels she was cut because of dumb luck. There is no risk to Hafiz that Aysha and Zeynep could challenge his method—if Hafiz lies well and credibly, that is.

A risk remains, though not to Professor Hafiz: If Aysha and Zeynep think past the immediate outcome and the evident inference it suggests, the loser might still find cause for anger. Thinking back, she notes that there was a .5 probability of losing by chance and a .5 probability of losing for lack of merit. Likewise, the winner notes there was a .5 probability of winning by chance and a .5 probability of winning on merit. The only certainty is that the loser knows she did not win on merit, and the winner knows she did not lose on demerit.

Professor Hafiz can console himself knowing that he did not actively produce unhappiness and that he offered the loser a way to save face (Goffman, 1955). Where the logic of probability ends, motivated reasoning can begin.

Writing this post, I had to make a choice regarding the professor’s and the assistants’ genders. Luckily, I found a pair of dice in the cabinet.

As for Buridan’s ass from the epigraph, he or she could not make a choice between eating from a bale of hay on the right and eating from a bale of hay on the left (Rescher, 1960). So the animal starved to death. This is what a true lack of preference can do. Dice remain relevant. If the ass only had had one!

It is worth noting that the problem of choice without preference runs deep in the history of philosophy. Aristotle gave it some thought, as did the medieval Persian sage Al-Ghazali.