My girlfriend and I took a weekend trip this past week, leaving our fat cat Mao behind with what should be an ample supply of food. While we were packing up and heading out the door, she asked me whether we should leave our bedroom door open or closed while we were gone.
We’ve recently begun closing our door at night to conserve the heat in our room when we go to bed. Our cat, who sleeps in the living room, has since developed the habit of meowing and scratching relentlessly at our door starting around 5AM, probably begging to be fed.
My girlfriend’s main concern was that while we were gone, Mao would finish all of her food in the first day or so, and then spend the rest of the weekend meowing herself hoarse at our bedroom door. I considered the alternative, that we leave the door open, allowing Mao to see in no uncertain terms that she was utterly abandoned and left to starve. Perhaps in her seething cat-rage, she’d take revenge in the only way she knew how: peeing and/or pooing on our bed.
I immediately thought of the minimax method. It’s a common rule used in decision making in the academic world, notably apparent in economics (specifically game theory and decision theory). Basically, the minimax method tells us to imagine the worst possible outcome for each possible decision and pick the lesser of the two evils. In other words, we are minimizing the maximum loss we can attain. It’s really simple, almost common sense, but I’m going to try my best to make it sound a little more complicated.
The Minimax Method
In almost any given problem, the decision model an individual uses can be simplified to a few basic approaches, and one of them in particular is the minimax method. The minimax method isn’t always the the best choice for every decision. I think a few key characteristics of the situation made minimax the winner here.
First, we were limited to strictly a scenario analysis. In other words, we were facing a non-probabilistic decision. It was uncertainty in its purest form. We had no assumptions about the probabilities of situations, or the expected values of decisions. If we were provided with the probabilities of each situation occurring, we would have a vastly different approach. We weren’t, and unfortunately, the human mind is terrible at calculating odds.
On top of that, our outcomes can only be ranked, as opposed to being rated “how much better is x than y.” I can tell you that having our bed being used as a litter-box is worse than some alternative, but I have no quantitative measure of how much worse it is.
With these limitations in mind, a lot of more flexible and detailed models of decision making were out the window.
The minimax model is also especially useful when the scenarios you are facing include one or more plausible “catastrophic” outcomes. However low the probability of something catastrophic happening, the damage of that event occurring is so high that it’s significance is much larger than other types of analysis may reveal. On top of that, in my mind, the “disaster” scenario had a non-trivial probability of occurring. As a matter of fact, there are several precedents. I’ve been told multiple stories of cats leaving special presents on the beds of less-than-thoughtful co-habitants. I’ve even experienced this first-hand: My old roommate’s cat has a habit of revenge peeing on the couch whenever she is slighted.
Why did I do this?
This decision has one major advantage over other decision making methods: it’s completely robust. Without additional information, any other choice leaves us in danger of being in a worse situation. Not only are we are controlling uncertainty to the extent that we can, but we are optimizing against catastrophic failure; hedging our bets, if you will. In other words, ignoring low-probability events may work to your favor in the short term, but consistently doing so only makes you more and more susceptible to the occasional catastrophe. By adopting a minimax strategy over the long term, you’re mitigating that risk.
Why did I bother making something so simple into something this complex? I don’t know. But I thought I’d share anyway, because when I first learned of it I thought it was a really ingenious way of making a decision in the face of complete uncertainty.
With all this in mind, we closed the door, packed up, and left Mao to fend for herself for the weekend.
