Kids fight a lot over toys. My twins are no exception. When they do, my partner sometimes try to calm them by announcing “turns” that each kid has with a toy, hoping that after a short while the kid in possession of the toy will lose interest or be willing to relinquish his claim for a short period, until it is his turn again. This works sometimes, but more often than not, both kids find it annoying–the one who waits and the one who can only use the toy for a short while.
The principle of transitivity of preferences holds that if I prefer Apple to Banana and Banana to Corn, then it must be that if offered a choice between Apple and Corn, I will opt for an Apple.
The motivation for this fundamental principle is the so-called money pump thought experiment. Suppose you have a Banana, and I offer you that in exchange for your Banana and one cent, I will give you an apple. If we suppose that you like apples more than bananas by more than the equivalent of one cent, you would take my offer. Then I come to you and offer to trade your newly acquired Apple for Corn and, again, I ask that you pay me 1 cent for this exchange. Since you prefer Corn to Apple, you take this deal as well. Then, I offer you the old Banana you had in exchange for your Corn and 1c. Again, it makes sense for you to take this offer. And then I offer you an Apple, a Corn, a Banana, an Apple… ad infinitum. So I can use your intransitive preferences to take all your money, while keeping a grin on your face.
It would be irrational to hold such preferences. But toddlers seem to exhibit some form of intransitive preferences. When they play with toys, a kid may see on the floor both a Doll and a Teddy bear, and will pick up the doll. Then another kid comes along, picks up the Teddy bear, and all of a sudden, the first kid shows interest in the Teddy bear as well. This is an instance of intransitive preferences, because the first kid had the choice of Doll and Teddy Bear and clearly preferred the former to the latter.
Is this behavior irrational? There may be a few reasons why it is not. First, sometimes we don’t know the value of the good until we use it. If the other kid seems to be really liking the doll, perhaps it is worth more than we first thought? Changing your mind on the basis of new information is not irrational. Second, sometimes the value of goods comes not from any inherent characteristic, but from the fact that many other people covet them and cannot have them. Those are called positional goods and include gold and diamond, which are inherently almost useless.
Whether this preference is irrational or whether it is rational on the basis of these two explanations, economics provides us with a good parenting tool. When my twins start fighting over toys, I announce “TRADE”, and then each kid has to give his own toy to the other kid. Both kids usually become instantly happy, and if, after a while, they start wanting the other toy, I announce “TRADE” again, keeping everybody happy. This method has clear advantages over any other system we tried, including its closest alternative, the turn system.