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 preferencesactuallyconform to such axioms as transitivity. There are manycomplications 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 anyapparenttransitivity failures that arise.

Most transitivity failures, it seems, will be merelyapparent. 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 bookTalking to the Enemy.

Atran在心理学和人类学方面做了大量的工作。出于了解宗教恐怖分子的动机的兴趣，他在21世纪初(9/11之后)前往印度尼西亚，研究那里的伊斯兰原教旨主义恐怖分子，他们与基督教社区进行宗教战争。令人惊讶的是，恐怖组织让他进去了，甚至给了他一个他们成员的向导。

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.

这是他给他的线人的问题，这些人都认为圣战和麦加朝圣都是神圣的。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. 成功完成一次有效的非自杀式炸弹袭击
3. Complete a holy, once-in-a-lifetime pilgrimage to Mecca.

结果是令人惊讶的:这些选择都是不及物的——至少表面上是这样。

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.

当让他们在2和3之间选择时，他们倾向于选择3。这就不奇怪了，去麦加朝圣应该比非自杀式袭击更重要。

到目前为止，有3个>2和2个>1。传递性因此使我们认为在这个例子中是3>1。

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.

但他的结论是否如他所言，“神圣的价值是不可传递的”?

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 ismerelyapparent, 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 whatyouthink.

那么，这是第一种选择吗(神圣的价值是不可传递的和神秘的)?或者第二种选择(游戏邦注:在某一场景中有一种默认的选择，乍一看并不明显，并且能够避免违背传递性)?

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?