The Parable of the Vases

Ann Coulter tweeted a bunch of praise for A Review of Hive Mind: How Your Nation’s IQ Matters So Much More Than Your Own today. She told people to buy the book. And she indicated her agreement with the "parable of the vases" .

I disagree with the parable. Here it is:

The parable begins with a simplifying assumption. This is that it takes exactly two workers to make a vase: one to blow it from molten glass and another to pack it for delivery. Now suppose that two workers, A1 and A2, are highly skilled—if they are assigned to either task they are guaranteed not to break the vase. Suppose two other workers, B1 and B2, are less skilled—specifically, for either task each has a 50% probability of breaking the vase.

Now suppose you are worker A1. If you team up with A2, you produce a vase every attempt. However, if you team up with B1 or B2, then only 50% of your attempts will produce a vase. Thus, your productivity is higher when you team up with A2 than with one of the B workers. Something similar happens with the B workers. They are more productive when they are paired with an A worker than with a fellow B worker.

So far, everything I’ve said is probably pretty intuitive. But here’s what’s not so intuitive. Suppose you’re the manager of the vase company and you want to produce as many vases as possible. Are you better off by (i) pairing A1 with A2 and B1 with B2, or (ii) pairing A1 with one of the B workers and A2 with the other B worker?

If you do the math, it’s clear that the first strategy works best. Here, the team with two A workers produces a vase with 100% probability, and the team with the two B workers produces a vase with 25% probability. Thus, in expectation, the company produces 1.25 vases per time period. With the second strategy, both teams produce a vase with 50% probability. Thus, in expectation, the company produces only one vase per time period.

The example illustrates how workers’ productivity is often interdependent—specifically, how your own productivity increases when your co-workers are skilled.

This is a dirty math trick (using the prestige and authority of math to trick people about a non-math issue) and the author doesn't explain what's going on. The different results are due to different amounts of idle vase-packing labor. In one scenario, A2 sits around doing nothing half the time (a loss of .5). In the other, B2 sits around doing nothing half the time (a loss of .25). A2 sitting idle is a bigger loss. That's all it is. Both potential pairings have a total of 1.5 value. They come out to 1 or 1.25 simply based on whether .25 or .5 value is sitting idle.

This can easily be fixed by hiring more appropriate labor ratios. If you have vase packers sitting idle, hire more vase blowers. You basically want two B workers doing vase blowing for each vase packer, not 1-to-1. They will on average produce one vase per vase-blowing cycle for the packer to work on. Then everything works out OK and, basically, you get the expected results: that 50% efficient workers are worth half as much as 100% efficient workers. (That's ignoring cost of materials, transaction costs to hire more people, needing a bigger factory to fit more workers, etc. When you factor all that stuff in, then yes one 100% efficient worker is better than 2 50% efficient workers. That's not what this parable is about, though).

(This is all on the assumption that people are simply assigned one job and stick to it, and that A1 and B1 do the vase blowing and A2 and B2 do the vase packing. If the packers would simply do some extra blowing when there's nothing to pack, that would also solve the problem and ruin the parable in the same way that hiring more blowers than packers would ruin the intended result.)

It's not efficient workers working with inefficient workers that's wasteful in general. It's people sitting around doing nothing that's wasteful. The parable hides people having time spent idle which is where the entire mathematical difference is coming from.

The book reviewer is very impressed with his bad parable:

To illustrate the latter effect, Jones’s constructs an example, which I call “the parable of the vases.” In a moment I’ll explain the details of the example, but first let me briefly discuss its importance. The example has significantly affected my thinking, and it is one of the highlights of the book. I do not think it is an exaggeration to say that the parable ranks as one of the all-time great examples in economics. Although it is not quite as insightful and important as Ronald Coase’s crops-near-the-train-track example (which illustrates the efficiency of property rights), I believe it is approximately as insightful and important as: (i) Adam Smith’s pin-factory example (which illustrates the benefits of division of labor) and (ii) Friedrich Hayek’s example of an entrepreneur knowing about an unused ship (which illustrates the value of particular, versus general, knowledge).

This kind of bragging about something that's wrong and misleading is not very notable. What was notable to me was that Ann Coulter was fooled and thought it was a good point.

The example generates an even more remarkable implication. It says that, if you are a manager of a company (or the central planner of an entire economy), then your optimal strategy is to clump your best workers together on the same project rather than spreading them out amongst your less-able workers.

I actually do agree with something like this conclusion, although I don't consider it remarkable at all. But the parable of the vases is a bad argument. A good argument covering part of this issue is The Mythical Man-Month.

I'd add that this point about mixing workers applies to peers. Putting a better worker in a leadership and management role interacting with inferior workers does make sense.

So I propose that instead of bringing in lots of low skill workers here, we should encourage a few top quality Americans to emmigrate and be leaders that run the governments and major businesses of other countries.