Bastiat on Tabarrok on Cost-Benefit

Over at Marginal Revolution, Alex Tabarrok writes:

Tyler asks, following philosopher Alastair Norcross, whether it could ever satisfy a cost-benefit test for one person to die a terrible and tortured death in order to alleviate the headaches of billions of others by one second. Tyler begs off with “a mushy mish-mash of philosophic pluralism, quasi-lexical values” and moral conceit. I will have none of this. The answer, is yes.

Bastiat presciently commented:

The plans differ; the planners are all alike.

Ditto for “libertarian” planners.

10 thoughts on “Bastiat on Tabarrok on Cost-Benefit”

  1. Costs and benefits to whom? When miners, employers and consumers all freely do their own individual cost-benefit analysis we see coal being mined. But miners aren’t trading their labor and heath to make others better off, they do it to make themselves better off.

    In a comment Taborrok writes:

    Most people suggest that rights or voluntarism makes the difference but that’s simply a rejection of cost/benefit analysis. I’m fine with that but note that it takes all the air out of the example since from the rights perspective the size of the benefits and costs is irrelevant.

    Fair enough as stated, but tis he really all right with that? What I’ve seen from him leads me to believe not.

  2. Tabarrok should not defile the term philosopher by attributing it to this creature Norcross. Ralph Waldo Emerson, a real philosopher, said that

    Today, there are many professors of philosophy and no philosophers.

  3. I would imagine that if the name of the person condemned to “die a terrible and tortured death” were “Alex Tabarrok”, Mr. Tabarrok might suddenly discover a few “moral conceits” of his own. It’s good fun to be skeptical and utilitarian and clear-thinking about other people’s rights after all.

  4. I think you are taking out of context the words of Tabarrok or, at least, interpreting them in a definitely non-charitable way. His example, I think, doesn’t imply any trade-off of the kind that libertarians would object:

    Coal miners, for example, risk their lives to heat our homes and to generate the electricity that drives this blog. We know that some of them will die horrible deaths but few of us think that we are morally required to give up electricity.

    May be the voluntary nature of such example begs the real question: it could ever satisfy a cost-benefit test for one person to die a terrible and tortured death imposed aggressively on him in order to alleviate the headaches of billions of others by one second? That would be another type of trade-off, I think. Thus, Tabarrok may be is begging that question, but he is not (by his very own example) endorsing an aggressive trade-off.

    Besides, he is judging the trade-off exclusively from a cost/benefit point of view, like a mental exercise. He hasn’t said that this is the correct point of view or that you can not judge the trade-off from other (more relevant) points of view. In fact, he has explicitly said that he is fine with an ethical / rights approach, but that would evade the cost/benefit analysis, which is the aim of the post:

    Most people suggest that rights or voluntarism makes the difference but that’s simply a rejection of cost/benefit analysis. I’m fine with that but note that it takes all the air out of the example since from the rights perspective the size of the benefits and costs is irrelevant.

    In other words, he is not saying that cost/benefit analysis entails normative prescriptions, or that he rejects the ethical / rights approach, he has only said what the conclusions of this analysis are.

  5. Well, some of us choose to be coal miners, right? The point is not that they consciously choose do so for the benefit of everyone else; even if they’re only doing it for themselves the market still does the rest and makes it for the benefit of everyone else.

  6. The problem with the coal miner example is partly a mathematical one.

    People will accept small risks to their life or liberty/livelihood for a payment, but rarely will they accept near certain death for any cost. It’s instructive to consider why in mathematical and economic terms, rather than in instinctual terms.

    One way to discount a benefit if I’m being completely self-interested is to consider that the money I recieve is worthless to me in the event that I die.

    So let’s say I put an economic value on my life of X. This means that in the event that I could enjoy the payment 100% of the time, I would accept X*p as a premium payment in order to accept death with probability p.

    But I can’t enjoy that payment 100% of the time. If I accept the exchange, then p of the time, the payment will be worthless to me. So the payment I actually require to make this devil’s bargain is X*p/(1-p). Note that as p gets close to 1, 1-p gets close to zero and this expression increases without bound. Any high number for p makes a huge difference in the expected compensation. If my X is 10 million dollars, I’ll accept something like a coal mining job with a 30 in 100,000 chance of dying in a year for a $3001 premium to a similar job. (and the discounting factor adds only $1 to my desired payment).

    If someone asks me to take a job with a 50% risk of death, on the other hand, I’m going to require not just a 5million dollar premium, but a 10 million dollar premium. And to take a job with a 90% risk of death, I’m going to require a 90million premium.

    And even this analysis doesn’t get to the heart of the true cost because very few people have a linear utility of money curve. If we use logarithmic utility of money, then it becomes increasingly hard to pay off that discount as p gets higher, and it’s practically impossible to compensate people for accepting very large risks of death unless the value they place on their life is especially low. For an example if my u(x) = ln(x):

    Then a 10% p of death with X=10million would require paying me 4.6 million, rather than the 1.11 million that a linear analysis would show.

    At very low risks of death, the log analysis adds little (I need 3007 to take a coal mining job rather than 3001). But as risks go up, the costs required to compensate shoot up *dramatically*. At a 20% risk of death, I need 75million to compensate me, despite my putative life value being only 10 million. To get me to accept a 50% chance of death would require 25 trillion dollars, or twice the 2005 US GDP. I can’t seem to find a figure for total world wealth, but I’d bet it’s less than the 88 quadrillion my model suggests is required to pay for a 60% chance of death. Even if I set the value for my life absurdly low, very high risks still result in absurdly high payments. If X=$100 but p = 80%, then the fair compensation is over 3 billion dollars.

    And of course, certain death would require infinite compensation under this model for anyone with a positive X.

    Realistically, most people’s utility curve is not pure log. I see effectively no difference between getting paid 100 billion and 25 trillion personally and very little between 50 million and 50 billion), so the risk of death I’d be willing to accept personally for any amount of money is going to max out in the 20-25% range.

    That looks about right, doesn’t it? I don’t know many happy middle-class people who would play russian roulette – a pure 16% risk of death gamble – for a mere $1,500,000, but everytime we drive a car or partake in extreme sports we demonstrate the willingness to accept minuscule risk that trades life at similar linear rates.

  7. Anybody arguing for “cost/benefit analysis” needs to first address the inconvenient fact that we’re living in the a world with quite arguably the highest ratio of benefits to costs of all time, and that arguing for change is risking changing that ratio for the worse.

    Of course that link contains a trap: you can’t refute the argument without refuting all cost/benefit libertarian wonkery, and you can’t accept the argument without refuting all cost/benefit libertarian wonkery.

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