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Suppose 100 chickens are produced. And, suppose 100% of the population becomes vegetarian. The number of chickens produced will drop to zero.
100 fewer chickens demanded; 100 fewer produced. So, on average, between 1 and 100, the next marginal drop in chicken demand drops production by 1.
Which elicits the question: what is the pattern from 100 down to 0?
Suppose there's suddenly only one non-vegetarian left. At today's price, he would demand 1 chicken. Clearly, prices will have to rise if only 1 is produced instead of 100. He might, then, demand only half a chicken at the new, higher price.
That means: an instant drop in demand from 100 to 1 chicken leads to an eventual drop in production of 99.5 chickens. That's 99.5 fewer produced when 99 fewer are demanded.
Also, an instant drop in demand from 0.5 to 0 leads to a drop in production from 0.5 to zero.
If the function is monotonic, it must be that a drop in demand of X units must lead to an eventual drop in production of X+f(X) units, where f(X) > 0. That's the only way the math works out.
There is a drop of X chickens produced, to match the drop in quantity demanded at price X. The extra drop of f(X) reflects the fact that even fewer chickens are demanded at the new, higher price that must result.
I don't think there's anything special about the tails.
Take a sheet of paper, and cover up the left 9/10 of the high-correlation graph. That leaves the right tail of the X variable. The remaining datapoints have a much less linear shape.
But: take two sheets of paper, and cover up (say) the left 4/10, and the right 5/10. You get the same shape left over! It has nothing to do with the tail -- it just has to do with compressing the range of X values.
The correlation, roughly speaking, tells you what percentage of the variation is not caused by random error. When you compress the X, you compress the "real" variation, but leave the "error" variation as is. So the correlation drops.
I read the "heretical" statements as talking about truth replacing falsehood. I read the non-heretical statements as talking about truth replacing ignorance. If you reword the "truth" statements to make it clear that the alternative is not falsehood, they would sound much less heretical to me.
One factoid says that your chance of death doubles for each 5 km/h above the limit you are. Another says that speeding factors into 40% of crashes.
Suppose the average speeder's risk is equivalent to 5 km/h over the limit (which seems low). Then only 25% of drivers must be speeding. Those 25% of drivers make up 40% of deaths, and the other 75% of drivers make up 60% of deaths. This keeps the ratio at 2.0, as required.
But non-speeders die too, when hit by speeders. The "40% of deaths had speeding as a factor" includes those non-speeders. Therefore, speeders have to be fewer than 25% of drivers. Call it 20%, for the sake of argument.
It's hard for me to believe that only 20% of drivers are doing 65 or more in a 60 km/h zone. And, remember: we made the conservative assumption that the average effect is 5 km/h. If you keep in mind that some drivers do 10 km/h over the limit, and have four times the risk, and some do 15 km/h over the limit, and have eight times the risk ... well, now, you're WAY below 20% of drivers speeding.
I have occasionally done 20 km/h over the limit (80 in a 60 zone), and so my risk was 16 times. But, still, the overall incidence is only twice as high. So there can be only 6% of drivers like me -- maybe 4%, if you include innocent other drivers in the death count -- and that's if you assume that there are ZERO drivers doing 5, 10, 15, 25, 30, or any other number of km/h over the limit.
Is there something wrong with my calculations?
"The Road and Traffic Authority of New South Wales claims that “speeding… is a factor in about 40 percent of road deaths.” Data from the NHTSA puts the number at 30%."
What does this mean, "is a factor"? If it means "at least one car was speeding," then it sounds like speeding might reduce the chance of a fatality. Suppose 40% of all drivers speed. Then, if speeding has no effect, the chance that neither driver is speeding is only 36%, which means speeding would be a factor in 64% of fatalities, not 40% or 30%.
Of course, I've made some assumptions here. The linked site doesn't tell us what percentage of drivers speed, and it doesn't say what "is a factor" means. So, the factoid, as presented, is meaningless.
"Provide reasons" helps for me. Many times I think something is obviously true, and when I start writing a blog post about it, where I have to explain and justify, I realize, mid-paragraph, that what I'm writing is not quite correct, and I have to rethink it.
Despite the fact that this has happened to me several times, my gut still doesn't quite say "it may not be that obvious, and you may be somewhat wrong." Rather, my gut now says, "the argument, written down, may not be as simple as you think."
So I feel like I still have a ways to go.
Ah, OK.
That's a slightly different case, though, isn't it? The author is not saying "it's good news for Boston [fans]" because they now are right when they were wrong before, and now their map is more accurate. Rather, he's saying that it's good news for Boston [fans] because the state of the world in the "right" case means more future Boston success than the state of the world in the "wrong" case.
Suppose Bergeron was doing well instead of poorly, and the author argued that it's because the coach is playing him too much and he's going to get tired or injured. In that case, the author might argue "Is Bergeron being played on every power play when he used to be played only rarely? If the answer is yes, it's actually bad news for Boston, believe it or not."
In other words, the "good news" and "bad news" don't seem to refer to the desirability of the map matching the territory. In this particular context, they refer to the desirability of the territory itself.
The point is well-taken that there are causes other than ego, and I could have mentioned that in the post.
I'm not sure what you're getting at with the hockey example, though.
Thanks! Now changed in original.
I like the castling analogy, might be able to use it someday.
Nitpick: When you mentioned the 2-4-6 experiment, I didn't know what it was, so I clicked on the link and read about it. That was unnecessary, because you immediately explained it ... but, somehow, the wording of the narrative didn't signal that the explanation was coming.
Could be just me.
OK, fair enough.
It sounds to me, though, like it should be possible to somehow quantify the benefit of donating a kidney, on some scale, at least. Or do you think the benefit is so small, relative to one suicide, that my original argument doesn't hold?
I guess it's an empirical question. A death creates two kidneys. Are there usually two people on a waiting list who need the kidneys and would otherwise die? If not, then perhaps I am indeed being too optimistic.
Yes, I assumed that the breakup value of the organs was higher. That seems reasonable to me: two kidneys save two lives, one liver saves a third life, and so on. And only one life is lost, and that one voluntarily.
Also, my argument was not contingent on anyone being paid ... donating organs on the black market works too.
Right, that's true if you're connecting them randomly -- you have a 50% probability of getting it right either way.
But if your intent is to connect red to positive, and black to negative, and you do that fairly reliably but with some chance of a mistake, then there are twice as many chances to make an error, and your chance of getting it wrong by making an odd number of errors is higher (although not exactly twice as high, which I incorrectly implied).
In recent years, portable battery boosters have become cheaper, which means you won't need jumper cables at all.
For $50ish, you get a battery in a sealed plastic case, with two "jumper-cable"-type alligator clamps, one red and one black. You flip the on switch, then clip the red onto your battery's positive terminal, and the black onto your battery's negative terminal. Then you start the car. Once the car is running, you remove the black connector, then the red connector, and you're done.
There are at least two advantages over jumper cables. First, you don't need anyone else's car or help. Second, there's 50% less chance of error, since you're connecting only two clamps and not four.
If I am not mistaken, some of the deluxe models have built in protection against putting the clamps on backwards. But I'm not 100% sure about that.
Voted up, because, this post I understand.
Nitpick: shouldn't the answer to the disease question be 1/50.95 (instead of 1/50)? One person has the disease, and 49.95 (5% of 999) are false positives. So there are 50.95 total positives.
"An alternative approach would be to allow such evidence at trial, and severely punish investigators who breach rights. ... However, a reluctance to punish high-status investigators means this approach could just result in more breaches of rights."
What if you allowed the convicted person to sue the investigators? That mitigates the reluctance to punish investigators -- or at least, the reluctance to begin proceedings against the investigators.
The convict could sue to get X years deducted from his sentence, and the investigator would have to serve a percentage of X depending on the egregiousness of the breach.
Sorry, what is "NT"? I read this blog often enough that I feel like I should know, but I don't.
I wish there were some examples (other than the Soviet nails) ... if I had some better idea of what G and G* might actually represent, I'd be able to more easily get my head around the rest of the post.
Ah, but now you're changing the argument! In the post, you argued that it's OK to interfere because people are being tricked (an argument for which I have some sympathy). Now, you're arguing that it's OK to interfere because the only purpose of the cards is to match borrowers with lenders. That, I dont agree with at all.
People choose a card for many different reasons. I can imagine people choosing to (perhaps falsely) signal their high wealth by choosing a high-rate card (their friends will assume they pay it off every month). They might choose the "trick" card to give themselves an incentive to pay on time. They may enjoy trying to "outwit" others by paying the card off on time and letting others cover the issuer's expenses.
In a competitive market, the money the company makes by "tricks" is competed down: other cards will find it profitable to enter the market and charge less (even if they use the same "tricks"). So a larger cost is borne by those who fall for the "tricks". Still, those people might not be happier with the tricks removed.
For instance, suppose I forget to pay on time every five years (which is probably about right). And suppose my forgetting costs $60. Now, the government comes along and decrees that, instead of charging me $60 when I forget, they'll charge me $1 a month regardless.
I wouldn't like that. It might be irrational, but that's still my preference. Haven't you, the government, done me wrong by eliminating the "trick" that I understood but chose anyway? Does my being less happy than before rank at zero on your scale of costs and benefits?
Suppose the terms "if you are even one day late with a payment, your interest rate jumps to 29.99% forever" are in very large print on the contract, and the cardholder has to read it and initial it (or, perhaps, copy it out in full!) before the card is approved.
And suppose that consumers accept those terms even after understanding them.
Would that weaken your argument?
(The reason I ask: I am fully capable of paying off my balance every month. Sometimes I forget. When I forget, it costs me $80 in interest. I am capable of borrowing money at a rate that would cost me only $10 in interest for that kind of debt.
Therefore, I see the interest I paid as a bit of a "gotcha". But I am willing to accept it. I figure it's part of the cost of the card, that it's going to cost me $80 or so every few years on the rare occasions I forget.
I entered the agreement knowing that was there, and I would do so again. I figure there are indeed people out there who would voluntarily accept the "one late payment and your interest rate is 29.99%" condition too.
Maybe they think they would just apply for a low-interest card and transfer the balance, but, when push comes to shove, they're just too lazy to do that. Or maybe they might figure that other people might forget to pay, but not them. Or maybe a host of other reasons. )
I've done the same thing!
Perhaps you were assuming that your net wealth was a certain fixed amount, and that if the bill had been a $5 instead of a $1, it would have meant that there was $4 less at home or in the bank.
In that case, you're rooting only for having the right change on you, rather than having less money overall.
I'd like to see an adult child hold a grudge and use the "my house, my rules" tactic against visiting parents.
"Dad, I appreciate you and Mom coming to visit all the way from Houston. But you weren't home by 10:30 as per the rules of this house, which I paid for. You're grounded for two days. I've taken your car keys. Also, Mom, if you want to live under this roof, even for a week, you'll stop using that Lady Grecian formula. No mother of mine is going out looking like a blonde harlot. And I don't care if your other 64-year-old friends are doing it."
In the community of sports statistical analysis, the most-accepted hypothesis is that coaches are reluctant to try new strategies for rational reasons. If the new strategy succeeds, they get a bit of utility, but if the new strategy fails, they get fired -- and so lose a lot more utility.
Being a maverick has a negative expectation for the coach, even though it might have a positive expectation for the team.
This hypothesis makes a lot more sense to me than assuming that coaches are unaware of the result.
The "Players whose names start with K tend to strikeout more" study, is, I believe, flawed. It's true that K names struck out more historically, but that's because K names (Kyle, Kevin, etc.) are much more common now, when strikeout rates are high, than they were in previous generations, when strikeout rates were low.
See:
http://sabermetricresearch.blogspot.com/2007/11/k-study-for-real_26.html
This may be related ... a friend once said that when she half-wakes from a dream, if she rolls over and goes back to sleep, the dream ends. But if she doesn't roll over, the dream continues.
I believe this works for me, too. Perhaps it's not just a change in sight, but in touch too. Or perhaps in any of the senses.
The man has done nothing shameful: (a) his life is his own; and (b) the insurance company bet, with its eyes open, that sufficient suicide-intenders would back down from their plans within two years that the policies would still be profitable. It lost its bet, but it was a reasonable bet.
The man has done nothing admirable, either; he has taken money from the shareholders of the insurance company, and given it to charity. Presumably this is something the shareholders could have done themselves, if they chose to. So from a libertarian standpoint, this is not an admirable act -- he forced the shareholders to do something they didn't want to do. Even though he did this through "voluntary" means.
However, I can see that if you're of the opinion that it's a good thing to take money from shareholders (who presumably are wealthier than average) and use it to save lives, then I can see how you would think this to be an admirable act.
You could also argue that the insurance company isn't stupid: it may have sold a thousand policies to intended-suiciders, and this was the only one who went through with it. In that case, the insurance company made a profit, and this man actually had a 99.9% probability of being one of the mind-changers. Unless he had strong reason to believe that he'd be the exception, he should have realized that there was a large probability, that, like the others, he was irrationally believing that his probability was higher than 0.1%.
What he should have done was contingently committed to selling his organs on the black market before committing suicide. Then, there would have been a net benefit to his death, instead of it being zero-sum, and his actions would have been admirable.