How we measure efficiency affects our efficiency

Jun 21 JDN 2459022

Suppose we are trying to minimize carbon emissions, and we can afford one of the two following policies to improve fuel efficiency:

  1. Policy A will replace 10,000 cars that average 25 MPG with hybrid cars that average 100 MPG.
  2. Policy B will replace 5,000 diesel trucks that average 5 MPG with turbocharged, aerodynamic diesel trucks that average 10 MPG.

Assume that both cars and trucks last about 100,000 miles (in reality this of course depends on a lot of factors), and diesel and gas pollute about the same amount per gallon (this isn’t quite true, but it’s close). Which policy should we choose?

It seems obvious: Policy A, right? 10,000 vehicles, each increasing efficiency by 75 MPG or a factor of 4, instead of 5,000 vehicles, each increasing efficiency by only 5 MPG or a factor of 2.

And yet—in fact the correct answer is definitely policy B, because the use of MPG has distorted our perception of what constitutes efficiency. We should have been using the inverse: gallons per hundred miles.

  1. Policy A will replace 10,000 cars that average 4 GPHM with cars that average 1 GPHM.
  2. Policy B will replace 5,000 trucks that average 20 GPHM with trucks that average 10 GPHM.

This means that policy A will save (10,000)(100,000/100)(4-1) = 30 million gallons, while policy B will save (5,000)(100,000/100)(20-10) = 50 million gallons.

A gallon of gasoline produces about 9 kg of CO2 when burned. This means that by choosing the right policy here, we’ll have saved 450,000 tons of CO2—or by choosing the wrong one we would only have saved 270,000.

The simple choice of which efficiency measure to use when making our judgment—GPHM versus MPG—has had a profound effect on the real impact of our choices.

Let’s try applying the same reasoning to charities. Again suppose we can choose one of two policies.

  1. Policy C will move $10 million that currently goes to local community charities which can save one QALY for $1 million to medical-research charities that can save one QALY for $50,000.
  2. Policy D will move $10 million that currently goes to direct-transfer charities which can save one QALY for $1000 to anti-malaria net charities that can save one QALY for $800.

Policy C means moving funds from charities that are almost useless ($1 million per QALY!?) to charities that meet a basic notion of cost-effectiveness (most public health agencies in the First World have a standard threshold of about $50,000 or $100,000 per QALY).

Policy D means moving funds from charities that are already highly cost-effective to other charities that are only a bit more cost-effective. It almost seems pedantic to even concern ourselves with the difference between $1000 per QALY and $800 per QALY.

It’s the same $10 million either way. So, which policy should we pick?

If the lesson you took from the MPG example is that we should always be focused on increasing the efficiency of the least efficient, you’ll get the wrong answer. The correct answer is based on actually using the right measure of efficiency.

Here, it’s not dollars per QALY we should care about; it’s QALY per million dollars.

  1. Policy C will move $10 million from charities which get 1 QALY per million dollars to charities which get 20 QALY per million dollars.
  2. Policy D will move $10 million from charities which get 1000 QALY per million dollars to charities which get 1250 QALY per million dollars.

Multiply that out, and policy C will gain (10)(20-1) = 190 QALY, while policy D will gain (10)(1250-1000) = 2500 QALY. Assuming that “saving a life” means about 50 QALY, this is the difference between saving 4 lives and saving 50 lives.

My intuition actually failed me on this one; before I actually did the math, I had assumed that it would be far more important to move funds from utterly useless charities to ones that meet a basic standard. But it turns out that it’s actually far more important to make sure that the funds being targeted at the most efficient charities are really the most efficient—even apparently tiny differences matter a great deal.

Of course, if we can move that $10 million from the useless charities to the very best charities, that’s the best of all; it would save (10)(1250-1) = 12,490 QALY. This is nearly 250 lives.

In the fuel economy example, there’s no feasible way to upgrade a semitrailer to get 100 MPG. If we could, we totally should; but nobody has any idea how to do that. Even an electric semi probably won’t be that efficient, depending on how the grid produces electricity. (Obviously if the grid were all nuclear, wind, and solar, it would be; but very few places are like that.)

But when we’re talking about charities, this is just money; it is by definition fungible. So it is absolutely feasible in an economic sense to get all the money currently going towards nearly-useless charities like churches and museums and move that money directly toward high-impact charities like anti-malaria nets and vaccines.

Then again, it may not be feasible in a practical or political sense. Someone who currently donates to their local church may simply not be motivated by the same kind of cosmopolitan humanitarianism that motivates Effective Altruism. They may care more about supporting their local community, or be motivated by genuine religious devotion. This isn’t even inherently a bad thing; nobody is a cosmopolitan in everything they do, nor should we be—we have good reasons to care more about our own friends, family, and community than we do about random strangers in foreign countries thousands of miles away. (And while I’m fairly sure Jesus himself would have been an Effective Altruist if he’d been alive today, I’m well aware that most Christians aren’t—and this doesn’t make them “false Christians”.) There might be some broader social or cultural change that could make this happen—but it’s not something any particular person can expect to accomplish.

Whereas, getting people who are already Effective Altruists giving to efficient charities to give to a slightly more efficient charity is relatively easy: Indeed, it’s basically the whole purpose for which GiveWell exists. And there are analysts working at GiveWell right now whose job it is to figure out exactly which charities yield the most QALY per dollar and publish that information. One person doing that job even slightly better can save hundreds or even thousands of lives.

Indeed, I’m seriously considering applying to be one myself—it sounds both more pleasant and more important than anything I’d be likely to get in academia.

2 thoughts on “How we measure efficiency affects our efficiency

  1. Absent explanation, comprehension of this post is limited to those who already understand that QALY refers to the change in utility value induced by the treatment multiplied by the duration of the treatment

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    • I think you can actually get the main point as long as you think of QALY as “something good that can be sensibly added up and is worth maximizing”. But in the future I’ll include a brief reminder of what QALY are as well as a link to posts that explain it in more detail.

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