On October 1 I wrote about Condorcet’s Paradox, and noted that my next post on the subject of the impossibility of democracy would touch on Arrow’s Impossibility Theorem. This post isn’t quite it (hence, the (a) behind the II), but notes some others’ attempts to do so.
Tyler Cowen recently asked what economic ideas are hard to popularize, and Arnold Kling suggested Arrow’s Theorem. So of course Cowen tries. I think he fails dismally (Arnold Kling, in the comments, agrees), which is a surprise because he’s a great popular writer of economics.* So Alex Tabarrok gave it a try. His attempt makes sense if you already know Arrow’s Theorem, so I think it necessarily fails as a popularization. Steven Landsburg gives us his attempt as well. I’m tired and groggy today, so maybe that explains it, but I’m familiar with Arrow’s Theorem and I still couldn’t really follow his approach. I’m not saying he’s wrong; I’m just saying that a popularization has to be fairly easy to follow for someone who doesn’t already know it, much less for someone who does. A commenter on Tyler’s effort linked to a video of Don Boudreaux’s explanation. Boudreaux’s nothing if not a popularizer (I imagine he fancies himself a modern day Bastiat). I don’t like his explanation because he says he’s talking about Arrow’s Theorem but begins with an extended explanation of Condorcet’s Paradox without ever mentioning that he’s talking about Condorcet’s Paradox. Perhaps that’s an effort at simplification, but he begins that discussion at the three minute mark, and only at about the fourteen minutes mark does he really get to Arrow. It’s not a bad lecture, but again it fails as popularization.
So now you have a hint at why I haven’t written that post yet. I will, I promise. But I won’t promise I can be any more successful in crafting a clear explanation than these gentlemen can.
Meanwhile, I’m trying to figure out if it’s right to call the theorem an economic idea. Granted Kenneth Arrow was an economist, but his undergraduate studies were in math. Duncan Black, who also worked with the idea, had undergraduate degrees in physics and math, and his graduate degree in economics and politics. Mathematician (and author) Charles Dodgson also played around with elements of the idea. So at its core it’s a mathematicians’ idea, and it’s about politics. But economists are more familiar with it than political science, and it usually comes into political science through the influence–whether direct or indirect–of economics. Political scientists of the political economist stripe are most likely to be familiar with it. So I guess the answer to the puzzle is provided by Shakespeare’s Juliet–”What’s in a name?”
* If you haven’t read his In Praise of Commercial Culture or Creative Destruction, you’re missing out. I haven’t yet read Discover Your Inner Economist or Create Your Own Economy, but both have highly positive ratings at Amazon.