Houston is in the midst of the largest power outage repair project in history. After Hurricane Ike passed through, about 2.5 million customers were without electricity. Now I hear that they’re down to half a million customers without power.

Let’s suppose the 80-20 rule applies to the repair effort. This seems reasonable since CenterPoint Energy understandably started with the easiest repairs. So with power restored to 2 million customers, they’ve completed 80% of their task. The 80-20 rule would predict that they have expended 20% of their effort. So if it took 10 days to restore the first 80% of customers, it will take another 40 days before they get to the last customer.

This not meant to be a precise estimate of the work that remains, only back-of-the-napkin speculation. But I do imagine a lot of work remains even though the repairs are in some sense 80% complete. This is not meant as a criticism of the heroic efforts of thousands of repairmen from around the US and Canada. I hope it increases appreciation for their efforts when progress, measured by percentage of customers restored, inevitably slows down.

As one of the “20″, I think that:

1) The application of the 80/20 rule is spot on.

2) I hope I’m wrong.

I like the 80/20 rule, but mostly beacuse it reminds me that many populations are highly inhomogenous. It seems like it kinda-sorta fits many situations, but I suspect the values are not even good to one significant figure. Also, the fact that it does not fit many situations makes me think that there is a continuum of such proportions, such as the 80/30 rule, the 80/10 rule, etc. if it applies generally at all.

As an example, think of the 80/20 rule in terms of relative means. 20% of “things” producing 80% of “output” simply means that the top 20% are on average 4 times as productive as the overall average. So far so plausible, but not all populations are this variable. Take commute times for example. My commute to or from work (one way) takes about an hour. The 80/20 rule implies that 20% of my commutes, or about one per five day work week, take 4 times as long as the overall mean. But I honestly can never recall in years a single time it took 4 hours to go either to or from work. It is possible that it got close to that once or twice, but I have made this commute many hundreds of times.

In fact, the more I think about it, the more I think it does not apply that often. Do we consume 80% of our calories in 20% of our meals? Do we win 80% of our money in 20% of our lottery tickets? I mean, I guess I could buy that 80% of the music I listen to comes from 20% of my CDs but … I really have no idea except that I know there are discs I listen to a lot more than others.

Even if we changed the name to the “most/few” rule or “majority/minority” rule, which I suspect would be more accurate with respect to the truth for some populations and to what is signified, it still only applies to certain populations and it hinges completely on the variance.

Or am I totally missing the point? Or does the 80/20 rule apply most of the time in the same way that most data have a Gaussian distribution?

I just remembered another “rule of thumb” I ran across some years ago while reading the New Yorker. A friend of the author had read an article on the Mediocrity Principle and decided to start making confidence intervals for time periods based on it. Here was their thesis IIRC:

1. Assume the Mediocrity Principle applies to the current time as a point in some span of time, such as the exitence of the human race, the run of Cats on Broadway, what have you.

2. Conclude from this that there is a 10% chance that we are in the first 10% of the overall time span, and a 10% chance that we are in the last 10% of the time span.

3. Assume the limiting cases, and letting

tbe the time elapsed since the span began, calculate that there is an 80% probability that the overall lengthTof the time span will be in the interval (1.1*t, 10*t).[If I recall correctly, the article was referring to 90% confidence intervals. I think they made an arithmetic error, because (1.05*

t, 20*t) seems bigger than I recall, but it doesn't matter too much.]OK, you say. Let’s try a few thought experiments:

To borrow your example first, right now it is about 12 days (I’d argue 13) since Ike turned out the lights. How long until power is restored? Using the above method, there is an 80% chance that the power will be restored 12.1 to 120 days after Ike hit. Plausible, you might think, but perhaps a bit wide.

Back to the article. I can’t remember how long Cats had been on Broadway then, but at the time it was the longest running show in Broadway’s history. Take a wild guess of 8 years (I really have no idea). Then there is an 80% chance that Cats will run for 8.8 to 80 years. Plausible again. At this point the author got really excited.

How long will the United States exist? There is an 80% chance that the US will exist 250 to 2,300 years.

How about the Earth? Taking the age of the Earth to be 4 billion years, there is an 80% chance the Earth will exit for 4.4 billion to 40 billion years.

I think at this point the author was convinced that their friend was Isaac Newton reincarnated. All these estimates seem so plausible!

IIRC the author was curious to see if the “predictions” panned out, and thought this method might gain a lot of notice.

I was really surprised that it got that far. Sure, the confidence intervals are plausible, but

so what?Even setting aside theoretical or philosophical objections, they are almost totally worthless. All they say is that whatever is going on now will probably keep going on a little while at least, but not forever. And that’s only with 80% confidence! Give me a break!Take my age. I’m 41, so according to this formulation there is a good chance that I will make it to 45 and a half, but I probably won’t see 410.

Of course, the fact that these intervals are ridiculously wide and uninformative is precisely because they are predicated on the Mediocrity Principle. The only possible virtue they have is that they require no information about the expected life span distribution of any of these phenomena, beyond one single censored observation.

As the old saying goes, “Garbage in, garbage out.”

Did you ever find out if this speculation was correct?