Classic theories of choice posit that our preferences are transitive. That sounds fancy, but the idea is straightforward. It means that if you prefer A to B and B to C, then you’ll also prefer A to C. For example, if you prefer the apple to the orange and the orange to the banana, then you’ll also prefer the apple to the banana. 

Now one interesting question in psychology is the extent to which human preferences actually conform to such axioms as transitivity. There are many complications that arise on that issue. For example, as Daniel Kahneman says, “People don’t choose between things. They choose between descriptions of things.” And this means that insofar as humans do conform to transitivity, this conformity will be complicated by psychological phenomena like frame effects, endowment effects, and many other cognitive biases. 

But it’s fair to say that, for ordinary day-to-day choices, human choice tends to be transitive to a great enough extent that it’s at least worth investigating and trying to explain any apparent transitivity failures that arise. 

Most transitivity failures, it seems, will be merely apparent. Say I offer you a choice between three pieces of cake and two, and you prefer three. Then I offer you a choice between two and one, and you prefer two. But then when I offer you a choice between one and three, you pick one.

This at first blush seems like a transitivity failure (3>2 and 2>1, but it’s not true that 3>1). But it’s easily explained by the likely social dynamics of the situation: someone faced with a choice between three and one pieces of cake may worry about appearing greedy, so when they choose the one piece of cake, it’s not just a matter of 1>3. Rather, it’s [1+not appearing greedy] > 3, which means that transitivity hasn’t strictly been violated. They probably would still prefer three pieces two one, if there were no risk of appearing greedy.

What’s interesting about all this is that apparent transitivity failures generate psychological hypotheses that can be tested empirically. Here, the hypothesis would be that the person who chose the one piece of cake is concerned about the appearance of greed, which can presumably be tested by various empirical measures, such as (surprise, surprise) simply asking the person.

With all that as background, I’d like to pose a puzzle about preferences that concern sacred values, which I first discovered when reading anthropologist Scott Atran’s astonishing 2010 book Talking to the Enemy. 

Atran does extensive work in psychology as well as anthropology. And out of interest in understanding what motivates religious terrorists, he set out to Indonesia in the early 2000s (just after 9/11) to study the Islamic fundamentalist terrorists there who were engaged in a religious war with Christian communities. Amazingly, the terror cells let him in and even gave him a guide who was one of their members. 

As you’d expect, the book that emerged is a fascinating piece of anthropological research. Atran, after all, was a protégé of Margaret Mead, and he lives up to the expectations that pedigree would set.

One of the questions Atran asked of his terrorist informants was designed to assess whether sacred values (sacred preferences, choices, etc.) operate the way ordinary utilitarian values do. And one issue he looked at was transitivity. 

Here’s the problem he gave his informants, who all regarded both jihad and pilgrimage to Mecca as sacred. In each choice presented, they would have to choose between two of the three options, which were as follows:

1. Complete a successful, effective suicide bombing attack.
2. Complete a successful, effective non-suicide bombing attack.
3. Complete a holy, once-in-a-lifetime pilgrimage to Mecca. 

The results were surprising: the choices were intransitive—or at least apparently so. 

Atran’s informants generally thought that 2 was better than 1. That is, it’s better to do an equally effective non-suicide attack than a suicide attack. 

When they were given the choice between 2 and 3, they tended to choose 3. That is—somehow not surprisingly—going on a pilgrimage to Mecca should take priority over a non-suicide attack. 

So far, we have 3>2 and 2>1. Transitivity would thus lead us to think that 3>1 in this case. 

But when given the choice between 3 and 1…they chose 1! Martyrdom, apparently, is more choiceworthy than pilgrimage.

So 3>2 and 2>1, but 1>3. Transitivity, apparently, is violated.

Atran interprets this as further evidence that sacred values don’t function like ordinary utilitarian preferences. He’s most likely right about that, and a lot of other evidence suggests the same. 

But is he licensed in his conclusion that, as he puts it, “sacred values aren’t transitive”? 

There are two options here. First, Atran is right that they’re just not transitive, which would seem to imply that sacred values—from a rational standpoint—are far more mysterious than we might have thought. But second, maybe this is somehow analogous to the cake case, where the apparent violation of transitive preferences is merely apparent, meaning there’s an implicit aspect of the choice that’s not mentioned in one of the scenarios.

I have my own solution to this problem. But for now I want to leave it as a puzzle so I can see what you think. 

So is it the first option (sacred values are intransitive and mysterious)? Or the second option (there’s a tacit aspect of the choice in one of the scenarios that’s not obvious at first glance and keeps transitivity from being violated)? 

If you go with the first option, it’s incumbent on you to say what you think the advantage is to an organism’s being designed—in Dennett’s sense of design without a designer—in a way that includes intransitive values (which seems an odd design feature to say the least). If you go with the second, it’s incumbent on you to say what the tacit feature is that saves this pattern of choices from being a violation of transitivity. 

So, what do you think?