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Comment author: 110phil 08 January 2015 02:21:57AM 0 points [-]

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.

Comment author: 110phil 02 August 2014 12:02:24AM 0 points [-]

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.

Comment author: 110phil 05 May 2014 04:10:26AM 26 points [-]

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.

Comment author: 110phil 19 March 2012 02:31:08AM 5 points [-]

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?

Comment author: 110phil 19 March 2012 02:17:06AM 3 points [-]

"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.

In response to Practical debiasing
Comment author: 110phil 20 November 2011 02:52:23PM 2 points [-]

"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.

Comment author: lessdazed 31 October 2011 07:59:43AM 0 points [-]

In the example, someone assumes that readers will not realize that a third party (The Bruins) having been wrong is good for them, even though there is no ego involved for most readers.

Comment author: 110phil 31 October 2011 02:01:55PM 1 point [-]

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.

Comment author: lessdazed 30 October 2011 07:08:25AM *  5 points [-]

The mistaken attitude comes from both status considerations and a map-territory confusion. I think the author could do better by being explicit about what the cause or causes of the problem are, and also by putting more emphasis on the second issue.

It seems that in his post, Birnbaum implicates status as most if not all of the cause of our misperception,

And I should add that I'm not saying that I, personally, know how to suppress my own ego, or even that I succeed in doing it when I try. I'm just saying that I know I should.

However, the map-territory error is a significant cause of confusion. The mechanism is that people might feel that by believing something about the world, they can make it true in the world.

While I don't follow baseball or baseball sabermetrics at all, and have never taken a course on statistics, I learned about statistics through GVT, VUKOTA, Corsi, qualcomp, and the other hockey sabermetrics. Here is something from just a few days ago:

We've already concluded that it doesn't seem to stem from any lingering injury effects. Nor does it make sense to be a case of suddenly diminished skills…after all, we're talking about a talented player in his mid-20s. So what option does that leave?

The most obvious remaining choice is a change in usage under current head coach Claude Julien. So let's examine some of Bergeron's statistics to find out if the talented pivot isn't being non-optimally utilized on the man advantage. If the answer is yes, it's actually good news for Boston, believe it or not. There could be a significant untapped resource for providing more goal-scoring production (Bergeron is signed through 2013-14) sitting on the Bruins roster, waiting to be taken advantage of.

Emphasis added. I agree with what the author of the above quote implies, that even when ego is not at stake, when evaluating third parties' situations, it is counter-intuitive to think that someone's having been wrong or foolish until now indicates they are in a good situation. This indicates that however important ego and status are, the map-territory confusion is sufficient to cause the mistake the blog post warns of.

Comment author: 110phil 30 October 2011 01:13:10PM 2 points [-]

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.

Comment author: ahartell 29 October 2011 10:45:41PM *  15 points [-]

I like the idea in the quotation, but it seems a little off. Being wrong isn't like winning the lottery; being wrong is bad. It's like "winning the lottery" to find out you're wrong, because then you stop being in that bad state (hopefully). Phil Birnbaum knows this (he says so in the post), but that doesn't make the line "Being wrong is like winning the lottery" much less annoying.

Comment author: 110phil 29 October 2011 10:58:07PM *  16 points [-]

Thanks! Now changed in original.

Comment author: 110phil 09 October 2011 01:53:05PM 2 points [-]

I like the castling analogy, might be able to use it someday.

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