Better safe than sorry?

posted at 2:05 pm on August 30, 2011 by Ed Morrissey

Allahpundit gave his thoughts on the backlash to Hurricane Irene coverage last night, from the perspective of someone who was in the path of the storm.  I spent the hurricane over a thousand miles away from any of the damage, but I agree entirely with AP’s conclusion that while Irene may not have done the damage predicted before it hit the East Coast, the damage it did do justified the attention and the warnings issued.  In my column for The Week, written before I read AP’s take, I argue that overprepared beats underprepared:

There is a legitimate concern about the danger of hyperbole in crisis-management situations. If every storm that approaches an American shore gets billed as another Katrina — a comparison often heard over the past week — the people who warnings are intended to help will start disregarding them. We saw the reluctance of residents in Irene’s path to follow evacuation requests; if they hear dire warnings of disasters that fail to materialize, then compliance with safety measures and evacuation orders will decrease, and put people at more risk. Hyperbolic estimates of damage and lack of essential services can also prompt unnecessary hoarding and artificial shortages of water and food that will end up making those goods both more expensive and less available even after an event-free storm.

Fortunately, the damage done by Irene came is far less than predicted — but the damage is not insignificant. Initial estimates of economic value lost have come to $7 billion, and that may go up as flooding continues in some areas. More significantly, at least 38 people died in the storm — as far south as Florida and as far west as Pennsylvania. The victims include an 89-year-old Connecticut woman who died when downed power lines set her home on fire, a New Jersey EMT who died in a Princeton flood, and a middle-aged New York man who had tried to rescue a child in a flood and got electrocuted by power lines.

Clearly, this was not a “manufactured” event. Irene may not have packed the punch that many predicted, but for those families and communities across 11 states who have to bury their dead and repair their homes, it wasn’t merely a photo opportunity. It was a real disaster, even if its scope was much more limited than initially feared.

Furthermore, we have a “dog that didn’t bark” dimension to this story. The storm was bad enough to kill dozens of people across 11 states. Without the warnings and the hyperbole, would the death toll have gone higher? None of the deaths appear to have resulted from excess zeal to seek safety or shelter. In fact, a number of them came from people who continued their recreational activities despite the storm. How many more were convinced to stay home instead?

Frankly, I’m a bit mystified about the complaints over saturation coverage.  It’s not as if there weren’t other options, even for news junkies.  As the storm approached, the coverage I saw reflected the loss of strength in the hurricane.  It didn’t require as many breathless updates as the cable news networks provided, perhaps, but that’s a criticism that applies to cablers in general.

Much of the criticism went to the public demonstrations of leadership by executives like NYC Mayor Mike Bloomberg, New Jersey Governor Chris Christie, and Barack Obama.  After Katrina, does anyone expect politicians to play it casual when hurricanes approach American shores?  Besides, as I write in my column, even if one believes that these three were grandstanding at times — for which a fair argument can be made — it’s not going to make much difference for any of them politically, even in the short run.  Americans expect executives to publicly demonstrate leadership, which means that all they get is a pass from the voters, not a bump, when things go right.  Only in extreme circumstances, like Rudy Giuliani in New York City on 9/11, do politicians get long-term benefit from public demonstration of crisis management.  Otherwise, these situations are mostly about not doing damage, both in real terms and to political reputations.

This storm did do real damage, and killed dozens of people.  We should just be happy that it didn’t turn out as bad as we’d feared.

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Hurricanes form off the Horn of Africa

Hog Wild on August 31, 2011 at 3:06 AM

Hurricanes form off Africa’s east coast? Uh, no.

Ronnie on August 31, 2011 at 4:57 AM

You jumped a logical step, Skippy. The NHC was never claiming to be expecting a disastrous outcome. Just because you believe that the possibility was reasonable doesn’t mean that it was.

Wrong, right, wrong. Wrong,I did not skip a logical step. Right, NHC did not claim to be EXPECTING disaster. Wrong regarding REASONABLE possibility: NHC provided maps with zones of surge probabilities – separate maps showing probability zones for storm surges of 1,2,3,4,5,6 feet. I saw them. There were areas from the Hudson, around the battery, up the East River, thru Hell Gate, past City Island, and beyond where 5 foot storm surges had a probability of 10% or more. “Reasonable” is a subjective and contextual term, and I consider 10% to be a reasonable possibility in this case.

Check back in the thread. I stated that doomsday damage isn’t being reported in response to someone saying that the doomsday predications WERE ACCURATE.

I’ll take your word for it.

The expression “better safe than sorry” is used by sane and otherwise reasonable persons to justify any level of over-predaredness even if such level was irrational and based on poor risk management. That’s EXACTLY what’s it’s used for.

I think we would agree that anyone who used the expression “better safe than sorry” to justify any level of over-preparedness, even if such level was irrational, would be thinking irrationally. Most people are usually rational, in my experience.

Um, this isn’t a demand for data.

No, but you have demanded data in various other comments on this thread.

I’m merely asking you to quantify something. Quantifying something doesn’t require any data at all. Do you understand the difference?

Yes I understand the difference. That’s why I used both terms; I was not trying to be redundant; that’s why I wrote “demands that everything be quantified and proven with data”. Sorry if I did not make the distinction clear.

“Expected” implies a 50% cumulative probability.

No, a confidence interval is something else entirely. Google it.

In a normal distribution, the expected value is the point at which the integral represents 50% of the total area under the curve. Google it… I did, just to be sure I wasn’t talking off the side of my head like a complete idiot.

What you’re describing is a confidence interval of 50%.

No, a confidence interval is something else entirely. Google it.

What’s sad is that you could have merely Googled the term and provided a better answer.

What’s sad is you telling me to Google it when you did not do so yourself, or were not knowledgeable enough to understand what you read.

If I asked you how many 6′s you’d “expect” to get from rolling a die 30 times the answer would be five. That doesn’t mean that there’s a 50% probability of getting five 6′s. The probability of getting exactly five 6′s is much, much less than 50%.

What it means is that the area underneath the probablity curve of getting five or fewer 6′s is approximately 50%. I say approximately because you have chosen a discrete, non-continuous function.

I know statistics. I know calculus-based statistics.

Well, then it’s time for you to take a refresher course.

Quit pretending that you know what you are talking about.

Likely does not mean expected

Yes, it does.

Look up the definition of “mode.” It is defined as the value that occurs (or is expected to occur) most frequently in a data set or a probability distribution and is considered the “likely” outcome – even if the probability of such outcome is significantly less than 50%.
The mode is the most frequent value, but not the expected value. Mode is a measure of actual data, not probability. If we have a data set of 1,1,1,1,6. The mode is 1, the mean, which estimates the expected value, is 2. If we are rolling dice, the expected value is 3.5, which is neither likely nor the mode, since it is impossible to roll a 3.5. But it is the expected value. Google it.

Likely does not mean expected; it means having a high probability, and “high” is not defined statistically.

No, it doesn’t –

Yes it does. Likely means having a high probability. BY DEFINITION. GOOGLE IT!!!!!!!

Image a die that is weighted so that 4 comes up more often than any other number. It’s perfectly acceptable to say that 4 is the LIKELY outcome of one roll even if the probability of rolling a 4 is only 25%. This is because it’s the outcome which would occur more often than any other outcome – NOT because the probability of this outcome is greater than 50%.

It is the most likely because it has the highest probability. BY DEFINITION. GOOGLE IT!!!!!!!

In a model of a stochastic system there are thousands of possible outcomes

“Stochastic” does not refer to the number of possible outcomes. Flipping a coin is a stochastic process, even though there are only two possible outcomes. BY DEFINITION. GOOGLE IT!!!!!!!

Prudent risk management implies weighing the expected loss against the cost to insure against that loss.

On this, we agree 100%. But one must also factor in averseness to risk. Otherwise, there would be no reason to purchase insurance, for reasons you describe.

Let me ask you a question. Would you pay $10 to insure against a 1% chance of losing $100? If not, then why not? Better safe than sorry. Right? Better to err on the side of caution. Right?

Answer: No, I would not. I can afford to absorb a $100 lost. I would pay $1,000 to insure against a 1% chance of losing $90,000. In this case, better safe than sorry.

Are you starting to see why you are looking at this concept incorrectly?
blink on August 31, 2011 at 12:04 AM

You clearly have zero understanding of how I am looking at this concept.

topdog on August 31, 2011 at 12:05 PM

Sorry, error in block quote formatting.
Here is a correction of middle section:

Likely does not mean expected

Yes, it does.

No. It doesn’t.

Look up the definition of “mode.” It is defined as the value that occurs (or is expected to occur) most frequently in a data set or a probability distribution and is considered the “likely” outcome – even if the probability of such outcome is significantly less than 50%.

The mode is the most frequent value, but not the expected value. Mode is a measure of actual data, not probability. If we have a data set of 1,1,1,1,6. The mode is 1, the mean, which estimates the expected value, is 2. If we are rolling dice, the expected value is 3.5, which is neither likely nor the mode, since it is impossible to roll a 3.5. But it is the expected value. Google it.

Likely does not mean expected; it means having a high probability, and “high” is not defined statistically.

No, it doesn’t –

Yes it does. Likely means having a high probability. BY DEFINITION. GOOGLE IT!!!!!!!

Image a die that is weighted so that 4 comes up more often than any other number. It’s perfectly acceptable to say that 4 is the LIKELY outcome of one roll even if the probability of rolling a 4 is only 25%. This is because it’s the outcome which would occur more often than any other outcome – NOT because the probability of this outcome is greater than 50%.

It is the most likely because it has the highest probability. BY DEFINITION. GOOGLE IT!!!!!!!

topdog on August 31, 2011 at 12:22 PM

Right, NHC did not claim to be EXPECTING disaster.

I’m not sure what else needs to be said. After admitting this, then how can you claim that the disaster level reporting was justified?

storm surges had a probability of 10% or more.

Media coverage went completely beyond this.

If they went beyond reporting POSSIBILITY of disaster, then I agree with you. If that is what you experienced, I suggest changing networks. My experience was that they were forecasting a danger, not a certainty.

In a normal distribution, the expected value is the point at which the integral represents 50% of the total area under the curve.

Are you claiming that damage level predictions from the hurricane were a normal distribution?

No, I agree the distribution is not “normal”. However, a normal distribution is frequently used as an approximation, just as economic theory assumes perfect markets: for simplification. I will be happy to split hairs for you. My point remains: in statistical language, the expected value is not necessarily the most likely value. Expected has a very specific meaning.

In probability theory, the expected value (or expectation, or mathematical expectation, or mean, or the first moment) of a random variable is the weighted average of all possible values that this random variable can take on. The weights used in computing this average correspond to the probabilities in case of a discrete random variable, or densities in case of a continuous random variable. From a rigorous theoretical standpoint, the expected value is the integral of the random variable with respect to its probability measure.(Wikipedia)

Perhaps you would like to go on Wikipedia and dispute with them the actual meaning of “expected” in statistics.
Note that this value is not necessarily the most likely value, and in the example of rolling dice, it is not even a possible value. Rolling a 3.5 would certainly be unexpected, but statistically speaking it is the expected value.

No, a confidence interval is something else entirely.

No, a 50% confidence interval is exactly what you described.

A 50% confidence interval ALSO relates to the integral of the probability curve, but with DIFFERENT limits. A coinfidence interval has limits that are the lower and upper boundaries of the confidence interval. The expected value integral has a lower limit of negative infinity (or zero, as the case may be) and an upper limit of the expected value.

Ha ha ha ha ha!

Is that insane laughter?

[F]ive or fewer” is NOT five!

Clear grasp of the obvious, at least sometimes.

Just admit that your definition was pathetically inaccurate.

My definition coincides with Wikipedia. Can you do better?

Your statement regarding “five or fewer” being 50% is inaccurate as well.

As I said, it is an approximation, and it is not precise because this is not a continuous function. I don’t care to do the math, but I would guess that the probability of five or fewer would be closer to 51%.

The mode is the most frequent value, but not the expected value.

Only an idiot wouldn’t “expect” the most frequent outcome.

Or a statistician. Do you want to talk mathematical language or common parlance? The meanings are different. I assumed since you were discussing standard deviations, etc., that we were using the mathematical definitions.

Mode is a measure of actual data, not probability.

When building a model, such as a hurricane model, actual data is used. Probabilities built into these models are based on the actual data. The mode is relevant. Expectation is relevant.

The mode has no role in calculating expected value. Expectation is relevant, but certainly not the only important information.

Likely means having a high probability.

Again, no it doesn’t. The “likely” outcome is the outcome which would be most expected.

It is the most likely because it has the highest probability.

EXACTLY!!!

So, is you response “No” or “Exactly”?

This should tell you that likely doesn’t need to exceed 50%.

Obviously.

In a model of a stochastic system there are thousands of possible outcomes
That should have read, “…a stochastic system when there are…”

Gotcha. No problem. I don’t remember your original point, though.

1. Aversion to risk doesn’t need to be considered in prudent risk management. Aversion to risk is a reason to modify what prudent risk management suggests.

Perhaps you have a definition with which I am not familiar. I googled the expression and found nothing to support you.

2. There are plenty of reasons for purchasing insurance even for risk tolerant decision makers.

True, but I don’t see your point.

So quantifying the downside risk must be a factor in determining the level of resources expended to mitigate the risk.

That is what we have both been saying. Where do we differ on this?

I would pay $1,000 to insure against a 1% chance of losing $90,000.

Really?

Yes really. $900 would be probabilistic breakeven; the other $100 would buy me peace of mind.

Would you pay $25,000 to insure against a 1% chance of losing $90,000?

No. That peace of mind would be too expensive.

Remember, better safe than sorry!
blink on August 31, 2011 at 2:08 PM

Thanks, I’ll remember that.

topdog on August 31, 2011 at 3:44 PM

Game over.
Thanks for playing

topdog on August 31, 2011 at 9:57 PM

heh

topdog on September 1, 2011 at 8:51 AM

1/6+2/6+3/6+4/6+5/6+6/6=3.5
Pure Mathematics.
You won’t accept any authority higher than yourself, even the entire field of mathematics, because there is no authority higher than yourself. This is why you are no fun to play with.
Game over.

topdog on September 1, 2011 at 9:04 AM

That wasn’t very nice of me.

I don’t care to debate with you any longer, but I would be happy to explain why the expected value is 3.5. I know it is weird and counter-intuitive, but there is a simple explanation.

If I were to make you a gamble that if you pay me $3 I would pay you the amount that came up on one roll of a die, would that be a good bet? How about $4? The amount of a bet that would be fair to both of us turns out to be $3.50. That is the expected value.

If I roll a die 600 times, I would expect, on average, to get 100×1, 100×2, 100×3, …, 100×6. So the expected value of 600 rolls would be $2,100. That being the case, the expected value of each roll would be $2,100/600 = $3.50.

The word “expected” in statistics means something quite different than in everyday usage. While a roll of 3.5 is not only “unexpected” but virtually impossible, it is the “expected” value when speaking statistically.

The word “likely” does not mean the same thing as “expected” does in statistics. In fact, to the best of my knowledge, the word “likely” is not even defined as a statistical term. Sometimes “likely” is used incorrectly to describe the mode, but there is an important distinction that is often missed: the “mode” refers to actual data, whereas “likely” implies “probability”, which refers to as-yet undetermined outcomes.

I used to teach this stuff, but if you don’t want to take my word for it you can consult almost any textbook on algebra or probability or basic statistics. I will be happy to provide you internet-based references, but I suggest you do your own research. Try googling “expected value of one die roll”.

I hope this has been helpful.

topdog on September 1, 2011 at 10:10 AM

What I am about to write is entirely sincere, without irony or sarcasm.

You are obviously smarter than me because you fooled me for so long into thinking you were serious. You are smart enough to understand the concepts of normal distribution, sigma and skew, but not weighted averages? But not expected value? I don’t think so!

I lied earlier: it has been fun! I didn’t learn anything, but you certainly helped me to hone my thinking skills.

I am very intrigued by you and this game you are playing. Would you be willing to step out of character and chat? Or, is this sort of an Andy Kaufman thing that requires you to always stay in character?

Again, this is entirely sincere, without irony or sarcasm.

topdog on September 1, 2011 at 12:47 PM

I get your point, and I think you get mine. You were using “outcome” and I was using “value”. If at any point I used the phrase “expected outcome” when I meant “expect value” I apologize.

As I said before, I thought we were talking statistics, and there “expected value” has a specific meaning. “Expected outcome” does not have a defined meaning in statistics. When an outcome is a value, then “expected outcome” is sometimes used synonymously with “expected value”, although I admit that that usage would be less than rigorous. When an outcome is NOT a value, then “expected outcome” is undefined statistically.

Statistically speaking, if the outcomes are heads and tails, there is no answer to your last question, since the phrase “expected outcome” is undefined. There are two possible outcomes, each equally probable. The outcomes have no value. There is no expected outcome.

In plain (non-statistical) language There are two possible outcomes, each equally likely. Neither outcome would be unexpected, neither would be expected. Note that as I have used the words here, “likely” and “expected” have different meanings.
If I recall correctly, that was the point you were disputing.

If instead the coins are labelled “1″ and “2″ the same answer applies. If one side is assigned the value of 1 and the other side the value of 2, then the expected value of the outcome would be 1.5. If your point is that it is imprecise to use the phrase “expected value of the outcome” in place of “expected outcome” then I accept your point.

Where are you going with this?

topdog on September 1, 2011 at 4:01 PM

On the other hand, I think you use “expected outcome” to mean “outcome with the highest probability”. I am not familiar with this usage in statistics.

topdog on September 1, 2011 at 4:14 PM

This is silly.

I am sorry you did not get my point. To much water under the bridge to try to recreate it.

You tried to claim that the term “most likely outcome” had to be an outcome with a greater than 50% probability

That would have been ignorant if that had been me. I would have fervently argued the opposite. Maybe somebody else?
What I did say was ““Expected” implies a 50% cumulative probability” For example, if the expected wind speed at a certain point and time is 50 knots, then there is a 50% chance that the wind speed will be less than or equal to 50%. I also differentiated between “expected” and “likely”. Entire quote:

“Expected” implies a 50% cumulative probability. Likely does not mean expected; it means having a high probability, and “high” is not defined statistically. If I have heart surgery with a 10% fatality rate, that is a “high” risk to me even though it is a low probability. Prudent risk management does not imply only preparing for “likely” outcomes, especially if there are unlikely outcomes which are very negative.
topdog on August 30, 2011 at 9:18 PM

You have not dissuaded me of that position.

My point is that if the highest probability outcome is skewed towards less damage, then the media does everyone a disservice by frightening people with disproportionate coverage.

Can’t disagree. Disproportionate coverage would be, well, disproportionate.

Additionally, I’ve done more research about these hurricane models

Interesting observations. Thank you for passing them on.

topdog on September 6, 2011 at 5:25 PM

Correction:
What I did say was ““Expected” implies a 50% cumulative probability” For example, if the expected wind speed at a certain point and time is 50 knots, then there is a 50% chance that the wind speed will be less than or equal to 50% 50 knots.

topdog on September 6, 2011 at 5:40 PM

No, it was you. You freaked out at the word “likely.” You insisted that anything with the word likely had to mean greater than 50%.

Pay attention. I have never thought this to be true and never stated this to be true.
You could easily prove your point if it were true. It is not.
CITE ME!!!!!!!! (unintentional play on words!)

A skewed probability distribution means that there’s not an equal probability that the wind velocity will 40 knots and an equal probability that the wind will be 60 knots.

True. That follows from the definition of “skewed”.

It’s quite possible that there’s a much higher probability for the winds to be 40 knots.

Theoretically possible, of course. “quite” and “much” are subjective terms. If you are asserting that the probability distribution is skewed, I agree!

This means that it’s quite possible that there is NOT an equal probability that the winds will be more damaging and an equal probability that the winds will be less damaging.

True, to the extent that the probability distribution is skewed. Just as the median can differ from the mean. I think I made it clear I was using a normal approximation (if not, my apologies…) Do you have any info suggesting that the skew is sufficient enough to make the normal distribution unusable as an approximation? Do you know whether the NHC models use a normal approximation? I do not know.

I’m learning that the hurricane models (…) predictions are skewed to [due?] to energy loss in more northern latitudes.

I think you mean “biased”? Interesting. I am surprised that water temperature is not adequately accounted for. That seems pretty basic… or is there some other factor in northern latitudes that they are not accounting for? (i am not challenging you…just curious for more on this).

Overall, your point didn’t address the issue which was being discussed.

We have both been OT for a while. My original point was that one cannot conclude that the media coverage was over-hyped solely on the basis that the actual damage was less than what was reported as reasonably possible. Also, a threat does not have to have a high probability (likelihood) to be worth preparing for. We don’t prepare for the possibility of being struck by a meteorite, but we do get out of the pool when we hear thunder even though actually being struck is not very likely.

Of course, I haven’t attempted to prove the opposite, that the media coverage was not over-hyped. In some cases it may have been, but that was not my experience. The NHC analyses I saw indicated a non-trivial possibility of disaster. I never heard any media source refer to disaster as anything more than a “possibility”. In my opinion, preparations were justified.

topdog on September 7, 2011 at 2:15 PM

It’s much less likely that any distribution that occurs within nature to be normal rather than skewed.

True, but for statistical purposes it is extremely common to use normal as an approximation.

Btw, I think it’s time for you to correct this statement. I’m quite sure you know that expected doesn’t mean a 50% probability for neither the expected value nor the expected outcome.

For a non-skewed (symmetrical) continuous function this is true, if you insert the word CUMULATIVE before “probability”. “Expected” implies a 50% cumulative probability for a normal distribution, and I think for any symmetrical (non-skewed) continuous distribution as well.

Think about it. There is not a 50% probability that a die roll will result in a 3.5.
Even if there’s a 50% probability of a value between 0 and 3.5 doesn’t mean that there’s a 50% probability of a 3.5.

You are right: it means that there is a 50% cumulative probability of 3.5. Please stop arguing against my statements with the word “cumulative” removed.
“Definition for cumulative probability:
In probability theory and statistics, the cumulative distribution function (CDF), or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x.” – Wikipedia. Not good enough? Find a better definition.

My original point was that one cannot conclude that the media coverage was over-hyped solely on the basis that the actual damage was less than what was reported as reasonably possible.

And I repeatedly stated that my conclusion wasn’t based on this. Nothing I wrote indicated that it was.

I understood you to argue that the reported damage was far less than the hype. What was your point in mentioning this if not to bolster your claim that it was hype? (not a rhetorical question)

but you need to stop pretending that I’m arguing against the sophomoric statement that you just made.

All right, I will take you at your word that the statement does not represent your intended argument. I am glad we agree that the statement is true. Now will you PLEASE quit arguing against my”cumulative probability” statements while mis-characterizing what I said by dropping the word “cumulative”.

The rest of what you wrote is simply our opinions and our experiences differing, and there is no further point in rehashing our positions.

topdog on September 7, 2011 at 5:00 PM

And I repeatedly stated that my conclusion wasn’t based on this. Nothing I wrote indicated that it was.

For the record, what you wrote was the following:

As far as I know, there has been no doomsday damage reported. Doomsday is what the media was hyping.

blink on August 30, 2011 at 5:16 PM

I interpreted this to mean: “The media was hyping disaster. Disaster did not happen. Therefore, the media hype was, in fact, hype.”

A reasonable interpretation, but I do understand that this is not what you meant to say. I am still in the dark regarding what you did mean by what you wrote.

topdog on September 7, 2011 at 10:08 PM

Thank you for your thoughts.
I’ll leave you with the last word.
See you on the next thread.

Over and out.

topdog on September 9, 2011 at 2:26 PM

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