The Impossibility of Democracy II(a): Arrow’s Impossibility Theorem

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.


About J@m3z Aitch

J@m3z Aitch is a two-bit college professor who'd rather be canoeing.
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10 Responses to The Impossibility of Democracy II(a): Arrow’s Impossibility Theorem

  1. thoreau says:

    A couple years ago, I attempted to explain Arrow’s Theorem to the layman. Warning: It’s a bit long.

    However, in keeping with what you said, I view Arrow’s Theorem as more of a political science and math topic than an economics topic. I realize that Arrow is an economist, but people with some intellectual breadth can contribute to more than one field. If you wanted to view his theorem as an economics topic, I guess you could apply it to the question of whether a central planner could ever find a plan that is unambiguously the most broadly acceptable. Failure of IIA would call into question whether it makes sense to refer to a unique “most broadly acceptable” social plan. However, I think there’s better work on that topic. (Doesn’t Sen’s Theorem address it? I’ve never really studied it in detail, so I don’t know.)

    If we’re going to go down the road of applying voting theory to central planning, the Gibbard-Satterthwaite Theorem would have a more interesting implication: People will have incentives to lie to the central planners.

  2. AMW says:

    I started Lansburg’s version and found it impenetrable in the first couple paragraphs, so I stopped reading.

  3. boccioni says:

    Almost all economists study something besides economics to get started. Even in the first half of the 20th century, economists usually drifted into it from other fields like math, history, or physics. And now, to get into grad school, you can’t major JUST in econ, you need a ton of math or physics classes to show you can hack it. It’s silly to call this a mathematician’s idea. Have you read any Econometrica?

  4. thoreau says:

    For me the issue is not how Arrow was trained or what he calls himself, but rather whether the theorem is really addressing economic questions. Does Arrow’s Theorem address questions in political science, or questions in economics?

    I’m a physicist who’s working on a paper on the mathematics of voting, and while I wouldn’t call myself a political scientist (because I’m not) I would say that my paper addresses questions in political science.

  5. James Hanley says:


    Cowen and Kling called it an economic idea. I was questioning that.

    Yes, I’ve read some of the econometric approach, or tried to. There’s a reason why I stuck to public choice theory, particularly of the Richmond School (a phrase that seems to be disappearing since the death of William Riker).

  6. Matty says:

    particularly of the Richmond School (a phrase that seems to be disappearing since the death of William Riker).

    Amazing all that time on the starship Enterprise and he found time to set up a school in Richmond as well.

  7. James Hanley says:

    I’ve always assumed that Commander Riker is his great-great-great-great grandson.

  8. James K says:

    I started straight into economics as an undergrad, but there was a lot of math bound up in my economics papers. For instance, I had to learn Lagrange multiplier calculus in my high level theory papers, I’m guessing most social scientists don’t have to do that.

    FWIW I learned Arrow in my policy economics classes as an undergrad. Economists think of Social Choice Theories like Arrow as being a part of “government failure economics”, a branch of the discipline that acts as a reality check on “market failure economics”.

    James Hanley:
    So does the Richmond School concern its self with the political implications of bald anglo-french leadership or the merits of seducing alien women?

  9. James Hanley says:

    James K–They do public choice theory, so I think the answer to your question should be fairly self-evident.

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