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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.

Elliot Temple on November 19, 2015

Messages (13)

I tweeted Ann about this 6 times, tagged her on Facebook, and posted at her forum ( http://chat.anncoulter.com/viewtopic.php?f=46&t=127654 ). I made every reasonable effort to contact her and inform her, given her choices about how open to feedback she is. Let's see if there's any results.

Anonymous at 11:54 AM on November 19, 2015 | #4449 | reply | quote

compare A1/A2 pair and B1/B1/B2 triple. OR, alternatively, A1/B2 pair and B1/B1/A2 triple. according to parable, boss keeping A1/A2 together should come out ahead, rather than having mixed labor.

but the parable thing is wrong. u get avg 1.5 vases per cycle in both of those cases.

another way to look at it: would you rather have A2 or B2 spend half his time napping? if you're the factory boss who answers "A2" and doesn't give him enough vases to pack to keep busy, then your factory produces less. this has nothing to do with what the parable is supposedly about.

Anonymous at 12:49 PM on November 19, 2015 | #4450 | reply | quote

suppose u have a guys who write and review code. code must be written and reviewed, then can be used.

A1 writes 100 code lines per hour. A2 reviews 100 code lines per hour. B1 and B2 do 50.

A1 B2 etc are types of ppl. u have dozens of all types.

as boss, do u make teams of only A ppl and other teams of only B ppl. do u get a better result that way?

parable of vases CLEARLY is claiming yes.

answer is NO. you can easily make mixed teams and come out with the same total code production.

to maximize this kinda toy scenario, make teams without idle time. don't have a team that writes 150 lines of code per hour and has 200 lines of code per hour of code review. that's wasteful.

Anonymous at 1:04 PM on November 19, 2015 | #4451 | reply | quote

if you have both 100% ppl do vase blowing, and both 50% ppl do packing, u get 1 vase per cycle with the mixed teams, and no one sits idle.

regardless, some vaguely brought up aspects of multiplication of fractions, plus an unargued idea that this apply to tons of actual real life cases, does not make for some great economics parable.

Anonymous at 4:45 PM on November 19, 2015 | #4452 | reply | quote

a different way to phrase the "parable of vases" is: it's better to spread out your quality people.

instead of having all your quality people on the blowing vases team, and none on the packing vase team (so you get something like 1 * 0.5), it's better to have more even quality between different teams (like 0.75 * 0.75)

which is the opposite of the conclusion they reached, while talking about the same math of how multiplication works

Anonymous at 6:35 PM on November 19, 2015 | #4453 | reply | quote

whether to have the good ppl on the same team, or spread out, simply depends on what you define as a team.

i think if u look at it more objectively, the multiplication math says to spread good ppl out. u will get the highest multiplication result if ur multiplying the same fraction over and over, rather than some other fractions with the same mean.

if the mean of your people is .5 and you have 10 teams or assembly line stations or whatever, and you then get a final product with quality proportional to multiplying the mean of each team, then you should organize your people into the teams to best equalize them (have each team's mean as close to the overall mean as possible), NOT by grouping your best people together (which would result in a WORSE score).

Anonymous at 6:39 PM on November 19, 2015 | #4454 | reply | quote

the scenario is really bad because it's much more costly to break vases later in the process than earlier (more work has gone into them). this adds a large distortion.

Anonymous at 7:11 PM on November 19, 2015 | #4455 | reply | quote

I read some and I don't get what the point of the parable is. What's the lesson it's supposed to teach?

Anonymous at 3:19 AM on November 20, 2015 | #4456 | reply | quote

It's explicit about the lesson, and this is quoted, e.g.

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


> 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.

Anonymous at 10:01 AM on November 20, 2015 | #4457 | reply | quote

the best way to do it is b1 and b2 both make vases, a1 packs the vases, and a2 does else extra or is fired to save money. as one option, A2 can make and then pack his own vases,for a total of 1.5 vases per cycle, which beats the other groupings using the same 4 people.

Anonymous at 10:06 AM on November 20, 2015 | #4458 | reply | quote

Thanks for discussing my model. All I'm doing in the Parable of the Vases is trying simplify Michael Kremer's excellent O-Ring theory. His theory is a big part of the strategic complementarity literature. Jason Collins summed up the story in a blog post on the O-Ring theory, it's also in my Palgrave essay on my homepage. The first section of Kremer's original paper is also well worth reading IMO.

Alas I'm on a plane just now, so regrettably can't provide links, but the strategic complementarity literature is quite helpful for thinking about endogenous sorting on worker skill.

Thanks again.

Garett Jones at 5:31 PM on November 20, 2015 | #4459 | reply | quote


> Workers performing the same task earn higher wages in a high-skill firm than in a low-skill firm;

This conclusion seems to suggest wages are not set by supply and demand in this model.

I also noticed the assumptions:

> workers are imperfect substitutes for one another

This doesn't fit the vase example in which A1 and A2, or B1 and B2, are perfect substitutes for each other (they have identical properties, if the firm fired one or the other it'd make no difference which).

> and there is a sufficient complementarity of tasks.

i wonder how much is sufficient.

Overall the theory appears to say something like, "if you have a list of numbers which you are going to multiply together in fixed size groups, group up the top ones, then the next highest, and so on". True, but quite far from directly applicable to real life scenarios.

That's wikipedia though. Looking at this next:


The first page says:

> I assume that it is not possible to substitute several low-skill workers for one high-skill worker, where skill refers to the probability a worker will successfully complete a task.

This is incompatible with the parable of the vases scenario where one would straightforwardly expect that it'd be possible to have a larger number of low skill workers making vases to be sent over to a smaller packing department.

> There is a fixed supply of capital

> Workers face no labor-leisure choice and supply labor inelastically.

The paper makes unrealistic assumptions. Why? To get conclusions about the real world from the simple truth about multiplying groups of numbers to get a higher sum.

In real life there isn't a fixed supply of capital and workers do have a labor-leisure choice (that is, they value days off work above zero).

> For example, it assumes that it is impossible to substitute two mediocre advertising copywriters, chefs, or quarterbacks for one good one.

This assumption makes sense in those 3 examples (though not in various other parts of the economy – in many, many cases you can make substitutions like that with just a bit of inefficiency), but not in the parable example of creating vases with outcomes of either broken or perfect.

> 0-ring production functions are consistent with a series of stylized facts in development and labor economics. While each of these stylized facts may be due to a variety of different factors, taken together, they suggest that 0-ring production functions are empirically relevant.

This is a bad method. It's trivial to construct hundreds of false economics theories, each of which fit a handful of stylized facts of your choice. Being able to fit your theory to several facts does NOT suggest it's empirically (real world) relevant.

All 5 stylized facts are things I already know how to explain in other ways. They aren't surprising to me, and don't require a new explanation. I don't count that as a strike against his O-ring theory, but it's also not suggestive evidence for it.

> Consider a firm using a production process consisting of n tasks. For example, in an automobile factory one task might be installing the brakes, and in a restaurant one task might be waiting on tables. For simplicity of exposition, I assume that each task requires a single worker,

This is another simplifying assumption that's a big problem. If you have teams working on a task, then the basic concept of "group up the better workers together" falls apart.

Say you have an automobile factory where there are assembly lines with 5 different tasks to create a car, and each task is performed by a team of 3 people (with results at their average quality). Do you take your best 15 people and put them all together on the first assembly line? Yes. But how do you divide them up into the 5 teams of 3? You do NOT put your best people together. You spread them out in such a way that each team is as close to the mean quality as possible.

This is a simple way you can end up doing something rather different than the parable suggested – spreading out some good workers to different stations instead of grouping them together more.

Another way you can do something different than the parable is by spreading out your best people in leadership, training or management positions.

Overall, the parable of vases is not accurate in a broad general way like the blog post suggested, and the blog post has several major deviations from the O-ring paper. And to get from the underlying math to real world conclusions involves unrealistic simplifying assumptions and still has gaps (hence things like the compatibility with stylized facts, which was only done because no more rigorous method was known for that part).

Elliot Temple at 9:28 PM on November 20, 2015 | #4460 | reply | quote

note for clarity that i have not read your book. i'm commenting on parable of vases from this review: https://ricochet.com/review-hive-mind-nations-iq-matters-much/

plus commenting on wikipedia and Kremer's paper as quoted from.

Elliot Temple at 9:33 PM on November 20, 2015 | #4461 | reply | quote

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