Author Archive for Steve Landsburg

The Rules of Excommunication

If Bernie Sanders wants to say that Fidel Castro occasionally did something good, while acknowledging that he often did things that were very bad, I think that’s a reasonable position. (It might also be reasonable to say that Adolf Hitler occasionally did something good, though offhand I can’t think of a good example.)

But surely — surely — if it’s reasonable to say this about Castro, then it’s enormously more reasonable to say that there were good people among the protestors in Charlottesville, Virginia, while acknowledging that there were also some very bad people. Because I have not the slightest shred of a doubt that the fraction of people on either side of that Charlottesville protest who were basically good is enormously greater than the fraction of Castro’s policies that were basically good.

You might want to argue that it’s not okay to acknowledge any goodness at all in a Hitler or a Castro or a large crowd of people that includes some number of violent neo-Nazis. I wouldn’t agree with you, because I think it’s always okay to acknowledge anything that happens to be true. But if that’s your position, you have to decide where to draw the line, and if you draw the line in a way that puts Trump beyond the pale, then Sanders is way beyond the pale.

In other words, I see how you can excommunicate both of them, I see how you can excommunicate just Sanders, and I see how you can excommunicate neither. My preference is neither. If your preference is otherwise, we can cheerfully disagree. But if you want to excommunicate just Trump, I’m very skeptical that you’re applying anything like a consistent standard. Feel free to prove me wrong in comments.

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Stop-And-Think

I hold these truths to be self-evident:

  1. Any law whatsoever, no matter how desirable on balance, will impose some costs on someone somewhere.
  2. In any society with more than about 12 people, it is virtually certain that those costs will be borne unequally.
  3. If the costs are borne unequally, then the costs borne by various individuals are virtually certain to be non-trivially correlated with at least one observable characteristic.

For example: A law that says you have to pick up after your dog will be costlier for dog owners than for non-dog-owners. Dog owners, depending on the community, will be either disproportionately old or disproportionately young or disproportionately rich or disproportionately poor or disproportionately ill or disproportionately healthy.

Therefore, unless you are willing to conclude that all laws are bad essentially without exception, you cannot argue that a law is bad just because it imposes individual costs in a way that is correlated with observable characteristics.

Therefore when Michael Bloomberg is criticized for supporting a stop-and-frisk policy because it caused disproportionate pain to young people with dark skin, his critics are being either disingenuous or unthoughtful.

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Swamp Creatures

Here’s what I saw on the news tonight:

1) A President exploiting the power of his office to manipulate the justice system.

2) A presidential candidate boasting about how, in her first act as a state legislator, she exploited the power of her office to manipulate the insurance market (by requiring the purchase of additional insurance to cover the cost of extended hospital stays for new mothers of hospitalized infants).

The President seeks to change judicial outcomes for the benefit of his small band of cronies. The presidential candidate sought to change market outcomes for what she portrayed as the benefit of a small number of patients.

At least the President seems to know what he’s doing. The presidential candidate seems not to have understood, and still not to understand (or at least pretends not to understand), that you don’t make people better off by forcing them to buy additional insurance after the market has already revealed that they have other priorities.

I also saw a bunch of commentators who, like me, are outraged, appalled, and frightened by the arrogance of the President. None of them offered any comment on the arrogance of the presidential candidate — who, frighteningly enough, seems to me to be probably the least dreadful of the alternatives.

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Innumeracy at CNN

At the moment (and it’s been this way for quite a while), CNN has Amy Klobuchar 84 votes behind Pete Buttigieg, and 2.1% of the vote behind Pete Buttigieg. Which should mean that the total number of votes counted is about 4000. But Klobuchar and Buttigieg have about 11,000 each, and Bernie Sanders has more than that. None of the anchors seems even slightly perturbed by this.

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Essential Reading

essential

The Essential Milton Friedman is now available from Amazon and other sellers, in an electronic edition priced — thanks to the generosity of the Fraser Institute— at an incredibly low 99 cents. I hope this is a subsidy that even Professor Friedman would approve. If you prefer an actual hardcopy book you can hold in your hands, you can request one (for roughly the price of shipping) by emailing publications@fraserinstitute.org . Either way, you’ll save so much money you can afford to pick up a copy of Can You Outsmart an Economist? while you’re shopping.

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The Value of Life — What’s Wrong With This Picture?

Trapeze Artist

Edited to add: As Salim suggests in comments, the entire problem is that I assumed an implausible value for wealth (which should be interpreted as lifetime consumption). With a more plausible number, everything makes sense. Mea culpa for not realizing this right away. I will leave this post up as a monument to my rashness, but have inserted boldfaced comments in appropriate places to update for my new understanding.

This is bugging me. It’s a perfectly simple exercise in valuing lives for the purposes of cost-benefit analysis. I would not hesitate to assign it to my undergraduates. But it leads me to a very unsettling and unexpected place, and I want to know how to avoid that place.

It’s also a little geeky, so I hope someone geeky will answer — ideally, someone geeky who thinks about this stuff for a living.

Start here: You’re a trapeze artist who currently works without a net. There’s a small probability p that you’ll fall someday, and if you fall you’ll die. You have the opportunity to buy a net that is sure to save you. What are you willing to pay for that net?

Well, let’s take U to be your utility function and W your existing wealth. If you don’t buy the net, your expected utility is

p U(death)+(1-p) U(W)

But we can simplify this by adding a constant to your utility function so that U(death)=0. So if you don’t buy the net, your expected utility is just

(1-p )U(W)

If you do buy a net at price C, then you’re sure to live, with utility

U(W-C) = U(W) – C U′ (W)

where the equal sign means “approximately equal” and the approximation is justified by the assumption that the probability of falling (p) is small, so your willingness to pay (C) is presumably also small.

Equating these two expected utilities gives me C = p U(W)/U′ (W). If we set V = U(W)/U′ (W), then C = pV. That is, you’re willing to pay pV to protect yourself from a p-chance of death. This justifies calling V the “value of your life” and using this value in cost-benefit calculatios regarding public projects that have some small chance of saving your life (guard rails, fire protection, etc.)

So far, so good, I think. But now let’s see what happens when we posit a particular utility function.

I will posit U(W) = log (W), which is a perfectly standard choice for this sort of toy exercise, though actual real-world people are probably a bit more risk-averse than this. Except I can’t just leave it at U(W) = log(W), because my analysis requires me to add some constant T to make the utility of death equal to zero.

So let’s take E to be the income-equivalent of death; that is, living with E dollars is exactly as attractive as not living at all. Then I have to choose T so that log(E) + T = 0. In other words, T = -log(E).

Now I know that, with your current wealth equal to W, the value of your life is U(W)/U'(W) = W log(W/E) .

Now as a youngish but promising trapeze artist, you’ve probably got some modest savings, so lets make your current wealth W=50,000 (with everything measured in dollars). (Edited to add: This was the source of all the difficulty. W represents something like lifetime consumption, so 50,000 is a ridiculously small number. Let’s go with 5 million instead.) Then here is the value of your life, as a function of E, the income-equivalent of death.

If E = .0001 (that is, if dying seems just as attractive to you as living with your wealth equal one-one-hundredth of a penny), then the value of your life is $1 million. (Edited to add: This should actually be E= 4.1 million dollars, which is considerably more than one-one-hundredth of a penny.)

If E = 6.92 x 10-82, then the value of your life is $10 million. (Edited to add: This should be E = $677,000 which might be a plausible figure.)

If E = 1.29 x 10-864, then the value of your life is $100 million. (Edited to add: This should be E equal to about one cent, which is of course implausible, but that’s fine, because a $100 million value of life is also implausible.)

Edited to add: I won’t continue to edit the details in the rest of this post, but I think this is all straightened out now. Thanks to those who chimed in, and sorry to have taken your time on this!

Now I am extremely skeptical that you, I, or anyone else is capable of envisioning the difference between living on 10-82 dollars and living on 10-864 dollars. Yet the decision of whether to value your life at $10 million or at $100 million hinges entirely on which of these seems more to you to be the utility-equivalent of death.

There is some purely theoretical level at which this is no problem. It is possible that you’d rather die than live on 10-864 dollars and would rather live on 10-863 dollars than die. But I am extremely skeptical of any real-world cost-benefit analysis that hinges on this distinction.

(And this is the range in which we have to be worried, since empirical estimates of the value of life tend to come in somewhere around $10 million.)

If I make you less risk-averse — say with a relative risk aversion coefficient of 4 — almost the entire problem disappears. But the tiny part that remains is still plenty disturbing. Then I get:

If E = .007 (that is, about 2/3 of a penny), the value of your life is $1 million.

If E = .003 (about 1/3 of a penny), your life is worth $10 million.

If E = .0015 (a sixth of a penny), your life is worth $100 million.

So we need to tell the folks in accounting to value your life at either $1 million or $100 million, depending on where you draw the suicide line between having two thirds of a penny and having one sixth of a penny.

This is nuts, right? And how squeamish should it make me about the whole value-of-life literature? And what, if anything, am I missing?

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Aha!

Christmas week seems like a good time to share this video of my talk on “Truth, Provability and the Fabric of the Universe” delivered in March, 2018 in Madison, Wisconsin. The venue was the Free Thought Festival sponsored by a student group that goes by the umbrella title of “Atheists, Humanists and Agnostics” (AHA for short).

The video is below (or will be soon if you’re patient; it might take a minute or two to load). (Edited to add: I believe I’ve fixed things so it loads quickly now; please let me know if there are any problems.)

Or you can either:

  • click here for a larger display of the same video
  • Or:

  • click here for a (far) higher quality video that might (or might not) take a bit longer to load.

A big hat tip to Lisa Talpey for cleaning up the video and making it possible to see both my face and the slides at the same time.

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Next in Line?

trump

Let me preface this post by saying that this post is not intended as some backhanded way of suggesting that Trump supporters are disproportionately ignorant. I am pretty confident that rational ignorance (and perhaps even a dollop of irrational ignorance?) is pretty rampant among voters of all persuasions.

That having been said: I am idly curious as to what fraction of those Trump supporters who oppose impeachment/removal are guided by a belief that if Trump is removed from office, then Hillary Clinton will become president. Are there any survey data on this?

Replies that directly address the question about survey data, or that offer plausible arguments based at least partly on logic or evidence, are on-topic. Honest speculation about similar false beliefs among voters of any stripe are on-topic, especially if they come with data and/or plausible arguments. Digressions about what a hero or a villain Mr. Trump is, and what fate he does or does not deserve, are decidedly off-topic on this thread.

Edited to add: I should have added, and am adding now, that the reciprocal question is equally interesting: How many anti-Trumpers favor impeachment/removal because they believe it will make Hilary Clinton president?

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That British Election

In a showdown between nationalism and socialism, it’s hard to know who to root for. I guess we can be thankful they didn’t form a coalition and compromise on national socialism.

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Life Lessons

The Washington Post and others of that ilk have been sounding the alarm about declining life expectancy in the U.S., driven mostly by rising death rates due to opioid use and obesity among the young and middle-aged.

There’s something terribly wrong says the Post headline. Maybe. But the content of the article suggests that a better headline might have been There’s something to celebrate. Certainly the article offers no argument or evidence for the former interpretation.

There is something to celebrate if rising death rates result from voluntary, informed choices. The thing to celebrate, of course, is not the deaths themselves, but the fact that people have found something worth dying for — just as, when you buy a house, I’ll congratulate not for the expense, but for finding something that made the expense worthwhile.

You’d think (or at least I‘d think) this was entirely obvious, but apparently it’s not obvious to everyone, so maybe it’s worth offering an extreme example. Suppose we’re all tied to beds in hospital rooms, with doctors monitoring every blip in our health and attending to it immediately. As a result, we mostly live long and miserable lives. Now one day, we engineer a mass escape. Life expectancy goes down for reasons that call for a celebration.

Opioids offer escape from miserable lives. They also offer enhancement of non-miserable lives. The decision to be obese comes with a great many perks — you can spend a lot more time eating M&M’s and a lot less on the treadmill. (I myself spend much of my treadmill time wondering whether I’ve made the wrong choice.) Like all good things, these come with costs. In this case, the cost is in the form of increased mortality. Apparently, people think that’s a cost worth paying. We should be glad for them.

Now you can certainly tell a story in which mortality due to opioid use is up because the world has gotten so much worse that there’s more demand for escape. That would be a bad trend (though even then, we’d want to celebrate the ability of opioids to mitigate some of that misery). Or you can tell a story in which mortality due to opioid use is up because people have gotten so much richer they can afford to be opioid addicts, or because opioids have gotten better, or because they’ve become more readily available. That would be a good trend. The Washington Post article alludes to the former possibility, without a shred of a good reason to think it’s the right story, as opposed to one of many possible stories.

You know what else is way up over the past couple of decades? Expenditures on smartphones. That sounds really really bad if you choose to ignore the fact that the people who are spending all that money get to have smarthpones. Likewise, an upward trend in mortality from M&M consumption sounds really really bad if you choose to ignore the fact that the people who are shortening their life expectancies also get to eat a lot of M&Ms. There is more to life than life expectancy.

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Dear Google: Please Stop Trying to Kill Me

wm2

When I’m in the car, I use my phone as a music player. Sometimes a song comes on that I’m not in the mood to hear. Once upon a time — in fact, once upon a very recent time — I could say “Okay Google. Next song.” Then the current song would stop and a new song would start. It was all part of Google’s awesome — and free — service. The service was imperfect in some minor ways, but mostly it was awesome and free and I was thankful to have it.

Here’s what happens now when I say “Okay Google. Next song.” The perky Google Assistant voice comes on and says something like “Oh, you want a different song? Okay. Let me sing you one.” Then the perky assistant sings some stupid little jingle for me, and then it returns me to the song I was trying to bypass. My only options at that point are to either a) listen to the rest of the unwanted song, b) try again and have the same thing happen again, which approximately triples my frustration level with each iteration, or c) fumble with my phone, call up the music player, search for the little “next song” button, push it, and try to put the phone back down before I drive into a lamppost. The pattern I’ve developed is to do b) approximately three times, then do c). I hope I’m still alive by the time you read this blog post.

Okay, so the service is still free, and still mostly awesome, right? But I am furious and I think I have a right to be. Let’s review the bidding here. Google has deliberately done the following:

  • Disabled the good and useful “next song” feature, for no apparent reason.
  • Trained its Assistant to mock its users when they try to invoke that longtime feature.
  • Done so in a way that is sure to drive those users into a state of combined frenzy and distraction while they are driving.

Let’s be clear: Mocking users and driving them into a state of frenzy seems to me to be the only conceivable reason for the whole “Here, I’ll sing a song for you, ha ha” bit. I am willing to bet you at substantial odds that no user requested this mockery. It’s apparently put there by Google (or perhaps by a rogue programmer on his last day of work, and overlooked by a lethargic quality control team) for the sole purpose of pissing people off and giving the folks at Google a good chuckle, without regard for possible deadly consequences. It seems to me to be roughly the moral equivalent of throwing watermelons off overpasses.

And just to make that analogy fair: If someone, through sheer technical brilliance and the goodness of his heart, ever designs the world’s most awesome overpass, builds it at his own expense, offers it to the world for free, maintains it for years, and then one day starts throwing watermelons off it — the main thing I’m going to remember is the watermelons.

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Where I’ll Be

kennesaw.small

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Current Events

Congratulations to the winners of this morning’s exceptionally well-deserved Nobel Prize.

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Wild Surmise

This is pure wild speculation, which should put it squarely in the mainstream of commentary on the death of Jeffrey Epstein.

But: Here’s a guy with a notoriously voracious and exotic sexual appetite, deprived of his customary means of achieving three orgasms per day.

Is it so far-fetched to speculate that his death-by-hanging was a case of autoerotic asphyxiation?

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Slips and Lies

One winter day in the midst of her husband’s 1980 presidential campaign, Nancy Reagan told a crowd at the Heritage Foundation that she was happy to see “all this beautiful white snow and all these beautiful white people” — which she instantly corrected to “all these beautiful people”. I happened to be standing no more than a few yards from her at the time, and it was crystal clear from her speech pattern, her demeanor, and her facial expression that her slip of the tongue conveyed no deeper meaning (conscious or otherwise). I am quite sure that if snow had been green, she’d have referred to “all this beautiful green snow and all these beautiful green people”.

Much of the press, of course, thought otherwise, or pretended to, leading to a brief contretemps that fortunately blew over.

I was not present at Joe Biden’s recent speech, and I have not seen the video, but I am essentially certain that the phrase “Poor kids are just as bright as white kids” — which Biden, like Mrs. Reagan, instantly corrected — was an equally innocent slip of the tongue. I have little patience for those who are attempting to profit by suggesting otherwise. What Mr. Biden meant to say was that “poor kids are just as bright as wealthy kids”. And therein lies the true outrage. Because that statement is a lie.

Poor kids are not just as bright as wealthy kids. The sources for this empirical fact are easy to find, so I won’t review them here. There are several plausible explanations. First, IQ is highly correlated with wealth and IQ is heritable. Next, poverty is stressful, and stress impedes cognitive development. Et cetera.

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The Prestige Cost of Affirmative Action

I. The Issue

It’s often claimed (at least by politicians, journalists and their ilk) that affirmative action tends to “stigmatize” succcessful members of the favored group, in the sense that a Harvard professorship is less prestigious when it’s held by someone who might not have made it to Harvard without an affirmative action boost.

It’s approximately equally often claimed that this is effect is too small to worry about.

I’m not aware of anyone on either side of this argument having attempted to settle the question with arithmetic.

In their defense, the question can’t be settled by arithmetic, because it’s pretty hard to quantify the difference in “prestige” between a professorship that reveals you’re likely to be in the top one-one-hundredth of one percent of the population and a professorship that only reveals you’re likely to be in the top two-one-hundredths of one percent of the population. But we can at least give some answers contingent on different assumptions about this issue. (And contingent also, of course, on various modeling assumptions.)

II. A Model

To that end, here is a primitive first-pass model:

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Measuring Prestige

You live in a world with 1000 other people, only one of whom can beat you at chess. You can beat the other 999. This gives you great prestige, because this is a world where chess skill is exalted above all else.

Now your chess skills atrophy, and all of a sudden you find that 100 people can beat you at chess; you can beat the other 900. You’ve lost some prestige.

I want to quantify the fraction of your prestige that’s gone missing. Of course the answer could be anything at all depending on how you choose to quantify “prestige”, but I’m looking for a definition that most people will agree captures their intuitions (or at least doesn’t grate too harshly against their intuitions).

Attempt One: If N people can beat you, then your prestige is measured by 1/N. Therefore your prestige has fallen from 1/1=1 to 1/100 = .01. You’ve lost 99% of your prestige.

Attempt Two: Your prestige is measured by the number of people you can beat. Therefore your prestige has fallen from 999 to 900. You’ve lost just under 10% of your prestige.

Which of these seems more “right” to you? And do you have an “Attempt Three” that seems even better?

In a few days, I’ll tell you why I asked.

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Price Gouging at Its Best

From Frank Harris‘s first-person account of the Great Chicago Fire:

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Cultural Interlude

I’m a little surprised that this, from one of my all-time favorite bands, hasn’t been getting more airplay lately:

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Thursday Puzzle/Science Lesson

nickelEvery day, a man comes to my door with a United States nickel in his hand. He asks me whether I’d prefer to examine the heads side (which is always painted either black or white) or the tails side (which is always painted either red or green). I choose each day according to my whims.

And the same thing happens to my sister. Different man, different coin, but each day he’s there with a painted nickel, offering to let her examine either the heads side or the tails side.

Sometimes we call each other to compare notes on the colors we’ve seen. Here’s what we’ve concluded:

The Rules

  1. Our heads sides are never both white.
  2. Whenever one of our tail sides is green, the other one’s heads side is white.

We have thousands of observations to support these conclusions: On days when we both examine our heads sides, we never both see white. On days when we examine opposite sides and one sees a green tail, the other always sees a white head.

The Brain Teaser: Today we both chose Tails and both saw green. What colors were on our Heads sides?

Solution: By point 2) above, they were both white. But by point 1) above, that can’t happen. So….?

So what now?

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Oxycontin: Yea or Nay

Should oxycontin be legal? Here’s what the back of my envelope says:

oxycontinIn the U.S., there are about 50 million prescriptions a year for oxycontin, most of them legitimate and for the purpose of alleviating severe pain. I’m going to take a stab in the dark and guess that the average prescription is for a two-week supply.

There are also (at least if you believe what’s on the Internet) about 20,000 deaths a year in the U.S. related to oxycontin abuse. If we value a life at $10,000,000 (which is a standard estimate based on observed willingness-to-pay for life-preserving safety measures), that’s a cost of 200 billion dollars a year, or $4000 per prescription.

If those were all the costs and benefits, the conclusion would be that oxycontin should be legal if (and only if) the average American is willing to pay $4000 to avoid two weeks of severe pain. I’m guessing that might be true in some cases (particularly when the pain is excruciating) but not on average. So by that (incomplete) reckoning, oxycontin should either be off the market entirely or regulated in some entirely new way that will dramatically reduce those overdose deaths.

But of course what this overlooks on the benefit side is all the “abusers” whose lives have been enriched by oxycontin. This includes the vast majority who use and live to tell the tale, and also some of the OD’ers, for whom a few years of oxycontin highs might well have been preferable to a longer lifetime with no highs at all. Relatedly, what this overlooks on the cost side is that the average “abuser” is likely to value his life at considerably less than the typical $10 million — as evidenced by the fact that he’s electing to take these risks in the first place. Also relatedly, it overlooks the likelihood that many of those who overdose on oxycontin would, in its absence, be killing themselves some other way.

If the back of your envelope is larger than mine and you make those corrections, I’m reasonably confident that your bottom line will come out pro-oxycontin. (Please share that bottom line!) I am however, mildly surprised (and — both as a blogger who prefers slam-dunk arguments and as a libertarian who prefers to come down on the side of freedom — mildly disappointed) that the first quick-and-dirty calculation comes out the other way.

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Jamie Whyte!

jamiewhyteJamie Whyte, whose has been at various times an academic philosopher (and winner of the Analysis prize for the best paper by a philosopher under 30), a consultant to the banking industry with Oliver Wyman, a foreign currency trader, the leader of New Zealand’s ACT political party, the research director at the Institute for Economic Affairs, the author of several books that every thinking person should read, a frequent contributor to the European edition of the Wall Street Journal and other publications of that ilk, the incoming editor of Standpoint Magazine, an occasional guest poster on this very blog — and the deliverer of one of the most thought-provoking and entertaining lectures I’ve ever heard when he visited Rochester a few years back — will be here again next week, with two events open to the general public. They are:

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Is American Airlines too Reckless?

aa

My return trip from Lubbock to Rochester took almost 36 hours, due to maintenance issues on three separate aircraft. This leads me to wonder whether American Airlines is erring too far in the direction of safety and too little in the direction of getting people where they want to go — perhaps even recklessly so.

Here’s what the back of my envelope shows:

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Where I’ll be

ttu

(Click picture for more info.)

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What I Get and What I Don’t Get

If you get accepted to college because you faked being a sports star, pretty much everyone is outraged. I get that.

If you get accepted at college because you are a sports star, almost nobody seems to mind. That’s what I don’t get.

Either way, you’ve climbed the ladder by prevailing in a largely meaningless zero-sum (and hence socially useless) game, thereby signalling a dollop of narcissism together with a few mostly irrelevant talents or advantages. What’s the difference?

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Where to Find Me

This week, I’ll be in Charleston, South Carolina as part of the annual Adam Smith Week celebration at the College of Charleston. You, along with the rest of the public, are invited to attend any or all of my talks:

Thursday, March 7, 1:45PM, “Is the World Overpopulated?”, Wells Fargo Auditorium

Thursday, March 7, 6:00PM, “What Do the Rich Owe to the Poor?”, Wells Fargo Auditorium

Friday, March 8, 12:00, “Why Be an Econ Major?” (discussion with Dr. Doug Walker)

If you attend, be sure to say hello!

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A Matter of Perspective

Let’s stipulate that:

A. The border wall is stupid.

B. The border wall would cost about $5 billion.

According to Democratic congressional leadership, these reasons suffice to withhold funding for the border wall.

This is a radical new stance for the congressional leadership, which last year rejected the Trump administration’s bid to cut roughly $300 million a year from the budgets of the National Endowments for the Arts and Humanities. Assuming a 3% interest rate, that’s a present value of about $10 billion — enough to fund two border walls. (Take that, you pesky Canadians!).

One could argue that a border wall is not only stupid but a grotesque symbol of xenophobia. One could equally well argue that a National Endowment for the Arts is not only stupid but a grotesque symbol of government overreach and the politicization of everything.

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Walls Versus Walls

The President of the United States tweets that his proposed border wall is essentially “the same thing” as a wall built around the Obamas’ house (or presumably anyone else’s house) to keep away intruders.

No, you idiot. There is absolutely no relevant similarity between a wall somebody builds around his own house and a wall that you build between other people’s houses. The effect of a wall around my house, if I had one (and if I controlled the gates), would be to increase my control over who enters my living room. The effect of a border wall would be to decrease my control over who enters my living room.

That doesn’t prove that the border wall is a bad idea. But if the President believes there are good arguments for his pet project, why does he resort to ridiculous analogies that have absolutely zero chance of being taken seriously by anybody on either side of the issue? I’m pretty sure Rex Tillerson had this right.

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Escalators (The Geeky Version)

I hadn’t expected this escalator business (and see also here) to go on so long, but there have been a lot of smart comments, and a lot of smart disagreements, and a lot of smart changing and re-changing of minds, some of it the unavoidable consequence of the fact that we might all be using language a little differently.

So here is the geeky (i.e. precise!) version of what I want to say.

I. Your journey consists of some time on the stairs and some time on the escalator. You rest for a total of one minute, which you can take on the stairs or on the escalator (or split it if you like).

II. Define some constants:

W = your walking speed

V = the escalator speed

L = the distance from your starting point to your destination

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Escalating Matters

There were a lot of great comments on my recent post about escalators, but none better than Bennett Haselton’s, which is so good I want to highlight here in a separate post.

I’m going to strip his argument down to make it even simpler, but this is all Bennett’s idea:

A New Puzzle: You’re boarding an escalator precisely at noon. You know that on a normal day, if you walk the entire way, the ride takes exactly ten minutes. But you also know that this is not a normal day, because the escalator is scheduled to be stopped for maintenance beginning at 12:05, and will at that point turn into the equivalent of a stairway. You’re planning to take a one-minute rest from walking at some point along your journey. Should you rest before 12:05, when the escalator is moving, or after 12:05, when the escalator is stopped?

Answer One:Of course you should rest while the escalator is moving, because that way, at least you make some progress while you rest.

Answer One, Reworded: Of course you shouldn’t rest while the escalator is stopped, because then you’ll spend an entire minute not getting anywhere.

Here’s the thing about Answer One: It’s completely wrong. It doesn’t make a bit of difference whether you rest from 12:00 to 12:01 or from 12:05 to 12:06 or for any other minute in between. If you don’t believe me, try an example: Suppose the escalator travels, oh, say, 20 yards per minute and your walking speed is 10 yards per minute. Then if you rest from 12:00 to 12:01, with the elevator moving, you’ll have traveled 160 yards by 12:07, and will continue to gain ten yards per minute after that. If instead you rest from 12:05 to 12:06 with the escalator stopped, you’ll have traveled exactly the same 160 yards by 12:07, and will continue to gain exactly the same ten yards per minute after that.

The Old Puzzle: You’re going to travel on a 100 yard staircase followed by a 100 yard escalator. You’re planning to take a one minute rest somewhere along the way. Should you take it on the stairs or on the escalator?

Answer One: You should rest on the escalator, because at least that way you make some progress while you rest. Or to put this another way, you shouldn’t rest on the stairs because then you’ll spend an entire minute not getting anywhere.

This time Answer One gives the right conclusion. But the reasoning can’t be right, because it’s the exact same reasoning that we applied to the New Puzzle, whereupon that reasoning led us totally astray.

Bennett’s lovely example illustrates as starkly as possible why we must reject Answer One even though it sometimes yields the right conclusion. The reason is that it also sometimes leads to the wrong conclusion. I’ve been trying to argue in the abstract that the logic of Answer One makes no sense; Bennett has done us the awesome service of pointing to a concrete example where that logic leads you inarguably astray.

It also illustrates my other main point: The real reason to rest on the escalator in the Old Puzzle is that resting on the escalator buys you more time on the escalator. Bennett has removed that advantage by giving you exactly five minutes on the escalator regardless of where you rest. In other words, when you cook up an example (like Bennett’s) in which resting on the escalator doesn’t buy you more time on the escalator, the argument for resting on the escalator vanishes in a puff of smoke.

This, incidentally, is related to a cryptic comment of my own on that earlier post, where I replied to an inquiry from Bob Murphy about my observation in an old Slate column that the fundamental confusion arises from measuring benefits in distance instead of time. (I claim that this is, in a sense that might not be entirely obvious, an equivalent description of the problem with Answer One.) In the Old Puzzle, you’re on the escalator for a fixed distance; in Bennett’s New Puzzle, you’re on the escalator for a fixed time. That illustrates exactly the distinction I had in mind, and if I find the time, I’ll write out the details sometime soon.

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