Wednesday, March 19, 2014

Innumeracy and Immorality

Is it immoral to trade with someone who doesn't know how to count to ten?

For members of the Pirahã tribe, this isn't an idle thought experiment. The Pirahã language lacks words for numbers (Wiki page here). They have vague words for "few" and "many", but this does not allow them to add two and two.

An oddity, this lil' Amazonian tribe is a trove for linguists. But it also challenges moral intuitions about the gains from trade. Everything else is there: there appears to be no evidence that the linguistic quirks reduces their ability to adjudge subjective value. But can prices do that voodoo what they do do so well if they're effectively written in alien Futurama scrawl? Is there a conventional capacity to exchange if there's no meeting of the minds on the terms of trade? Pirahã is monolinguistic, the numeracy problem appears to be intractable.

This question might seem like navel-fluff-rolling armchair moral economics, but consider that the US's own Uniform Commercial Code (which is actually not Federal law, but rather 50 separate state laws, plus similar codes for DC and the territories, and also some [all?] of the Indian Nations) treats minors as non-contracting entities. With a few exceptions, a contract with a minor is avoidable. If you sign up for a lifetime membership with a record club when you're sixteen and decide the following year you've had enough, you're protected under the UCC from civil penalties (nb, this is NOT legal advice, it's my murky lower-division recollections of my undergraduate business law class. For actual legal advice, contact an attorney). But the same elementary intuition applies: kids are too dumb to make decisions they'll have to carry around for the rest of their lives, so we don't make them accountable until a "reasonable" age.

Does any of this mean that the axiom of exchange is violated when trading with kids or the Pirahã? Does the willingness to trade no longer signal economic efficiency in these cases? And if so, what is the appropriate remedy? Thanks to the evident impossibility of Pirahã tribe members gaining numeracy, what does this imply about their market autonomy?

And if basic numeracy is declining in the bottom quintile, what does this imply about marginal autonomy in the secular West? What alternative institutions are available to address these issues?

As usual, there are no solutions, only tradeoffs. How much coercion is appropriate to ensure individual autonomy?


  1. So, is barter euvoluntary? This many in exchange for that many?

    1. The counting ability tests were interesting. The experimenters used piles of batteries to determine what the words for "few" and "many" meant. The tribe members were able to easily judge relative quantities, but had a hard time recalling what was there once it was removed from view. It's as if they never developed the ability to abstract, which is, evidently, an important part of being able to do arithmetic.

      I suppose spot trades would be more euvoluntary if it was "these things for those things" with both piles of things in plain view.

      Hard to know without more field experimentation though.

    2. Have you ever read the book Number by Tobias Dantzig? He goes through the history of the concept and talks about how before we had numbers, we had a lot of words for specific numbers of specific things. Do you know if these guys have that? Or do they not even have that level of specificity?

    3. The paper I linked seems to suggest two things: a) they have an idea of relative quantities and b) it doesn't appear to be abstract at all.

      My hunch: quantitative thinking is just not salient for them, so they don't bother ever developing those cognitive faculties.

      But like I said, more research is probably a good idea.


Do you have suggestions on where we could find more examples of this phenomenon?