Buridan’s Donkey: How to Use Randomness to Break Stalemates

The other night my girlfriend asked me, “What do you want to have for dinner, rice or chapati?”

It was a simple question, but I had a hard time answering it. In my head rice and chapati had equal weight, and I had no plausible reason to choose one over the other.

Choice is perceived as freedom, but sometimes between a rock and a hard place, or between two roads—both well treaded, there’s no good way to choose one with proper rationale. Either there are strong reasons to choose either. Or like my case, no particularly strong reason to choose rice over chapati, or vice-versa.

I was stuck. I didn’t know it at that time, but my decision needed a small dosage of randomness to break my indecision.

Let’s take a thought experiment not unlike my situation. Only here, instead of me, there’ll be a donkey.

Imagine a donkey, equally hungry and thirsty placed at exactly equal distance from sources of food and water. In theory, it would die of both thirst and hunger as it would be unable to decide which one to get to first — kind of similar to choosing between rice and chapati for me.

But instead of rationale, if we take help from randomness to make a decision here, things can become much simpler.

We can flip a coin and randomly nudge the donkey thereby causing it to get closer to one source, either water or food, and accordingly away from the other. This way the impasse would be instantly broken, and the donkey will be either well fed then well hydrated, or well hydrated then well fed.

The paradox is named after the 14th-century French philosopher Jean Buridan, whose philosophy of moral determinism it satirises. Although the illustration is named after Buridan, others have discussed the concept before him, notably Aristotle who used the example of a man equally hungry and thirsty, and Al-Ghazali who used a man faced with the choice of equally good dates with girls.

Randomness to make a decision may seem like the opposite of reason or rationale—a form of giving up on a problem, a last resort. But random outcomes can sometimes be used as a tool to break stalemates. A man (or a donkey) who sees two options as truly equally compelling cannot be expected to be fully rational. Sometimes the best solution to a problem is to turn to chance rather than trying to fully reason out an answer.

In cricket, flipping a coin to help with the decision process of who should bat first is an example of using randomness usefully. This is efficient as long as a coin toss doesn’t influence who would win or lose a match.

Next time my girlfriend puts me in a situation like this, all I gotta do it flip a coin.