When you’re buying a gift for someone or cooking a meal for someone, it’s important to know what they like and dislike — their preferences. The obvious way to learn someone’s preferences is to ask them. But we sometimes infer people’s preferences without them telling us.
For example, if you have lunch with someone at a steakhouse and they order a salad, you might infer that they don’t eat meat. We do this in other situations too. By looking at the books on someone’s bookshelf or the albums in their music collection, you can infer something about their general tastes. These inferences seem natural — maybe even commonsense — but how do people make them?
In a paper with Chris Lucas and Charles Kemp published in Cogntion, we proposed that people make inferences like these by a process we called inverse decision-making. Basically, people have a mental model of how people make decisions and they invert that model to reason backward from a choice someone has made to the preferences that likely motivated the choice.
For example, here’s a simple decision-making model: when given a choice between two options, a person will choose the option they like more. Now suppose you see someone choose a red candy over a blue candy. Reasoning backward using the model, you can conclude that the person likes red candy more than blue candy. Our paper describes a mathematical formulation of this basic idea.
We tested this idea by running an experiment in which subjects saw many different choices that people had made between different bags of different candy. The choices were printed on cards and looked like this:
Each card represented one choice that someone had made. The different rectangles were different candies and the colors were different flavors of candies. Each column was one bag, and the column on the far right was the one the person chose. So, for example, in choice represented by the card on the lower left, someone could have had one piece of yellow candy; or one piece of brown candy; or one piece of red candy, one piece of blue candy, and one piece of black candy. That person chose the third option.
We gave people 47 different cards like these. Here’s the full set:
This representation uses colored letters instead of rectangles, and the chosen options are shaded on the left instead of the right. (The card I described appears as Choice 17 here.)
In every choice in the experiment, the chosen option included a piece of red candy. We asked subjects to sort the cards from weakest to strongest evidence that the person likes red candy. Using our inverse decision-making model, we made predictions about the order in which people would sort the cards. Our model predicted that out of these 47 choices, the choice that provided the best evidence was Choice 47: one in which the person chose a bag with a single piece of red candy over a bag with four candies of other flavors. Intuitively, this is a choice someone who loves red candies much more than other flavors would make. So seeing someone make this choice should cause you to strongly infer that they like red candies.
We compared people’s mean rankings to the inverse decision-making model’s rankings. The model predicted people’s rankings quite well:
The numbers on the plot refer to the choices in the previous picture.
We were actually a little surprised at how well the model performed. In the paper, we also show that the model predictions are pretty insensitive to specific assumptions or settings of parameter values. The rest of the paper also describes results from another condition in which the model didn’t perform quite as well and two additional experiments that test other aspects of the model. Check out the paper to see the details.
Economists sometimes talk of “revealed preferences” in which people’s preferences are revealed by the choices they make. Revealed preference theory is a way to estimate people’s preferences by analyzing their consumer behavior. Although our experiments only focused on fairly simple choices, the results suggest that people might sometimes rely on a similar kind of revealed preference theory when thinking about the choices that other people make. Our work is also consistent with a lot of other recent research on how people use inverse reasoning to infer properties about others, like their emotions, or their beliefs and goals.