More On Clarity In Discussing Probability

Lynne Kiesling

I am posting this comment for Robert Schwartz, who for some reason was unable to get through the spam filter.

Lynne:

You were not alone in your reading of the Judge’s statement. I, also, was flummoxed and commented at the esteemed Becker Posner Blog:

http://www.becker-posner-blog.com/archives/2005/01/the_tsunami_and.html#comments

Dear Judge Posner:

Above you wrote:

“First, although a once-in-a-century event is as likely to occur at the beginning of the century as at any other time, it is much less likely to occur in the first decade of the century than later.”

In a series of independent trials (e.g. the proverbial flip of a fair coin) that statement is clearly not true, as any given result (e.g.
heads) may occur in any given trial regardless of the results of other trials. That much I remember from Statistics and Probability 101 taken many long years ago.

Whether or not an earthquake/tsunami is like a coin flip is a subject I will leave to the scientists in the audience. However, even if they are not independent of each other, I do not see why they should arrange themselves according to human calendric conventions.

It may be the first decade of the 21st century of the Christian era, but that is hardly a fact of universal significance. It is the third decade of the 15th century of the Muslim era a fact that may be as important in Indonesia. And in the Chinese system, also very important culturally in that part of the world, it is the year of the (jia or wood) Monkey in the 78th cycle. See the Calendar FAQ:

http://www.tondering.dk/claus/calendar.html

and

http://emr.cs.iit.edu/home/reingold/calendar-book/Calendrica.html

I think that what may be of more importance is that modern bureaucratic government is relatively young in South Asia. The cultures in that area maybe ancient, but the states formed as a result of de-colonization and anti-imperialism in the middle of the twentieth century. As those governments mature they may well develop the institutional mechanisms to deal with these types of problems.

Posted by Robert Schwartz at January 5, 2005 10:42 AM

Robert, you misunderstood Judge Posner. The reason a once-in-a-century event is less likely to occur in the first decade of a century than later is that the first decade is only ten years long, while “later” is ninety years long. He is not saying that events “arrange themselves according to human calendric conventions.” On the contrary, he wrote that “a once-in-a-century event is as likely to occur at the beginning of the century as at any other time.”

Posted by AF at January 5, 2005 11:12 AM | direct link

Robert Schwartz,

He was perfectly accurate.

“First, although a once-in-a-century event is as likely to occur at the beginning of the century as at any other time, it is much less likely to occur in the first decade of the century than later.”

I think he meant the probability of the event happening within 10 years is less than it happening in the following 90. Which is correct. He is pointing out that politicians have a limited tenure, and will thus plan accordingly–not long term. We see the same myopia with respect so Social Security.

Posted by Palooka at January 5, 2005 11:35 AM | direct link

AF and Palooka: I see your point.

Judge Posner wrote:

“First, although a once-in-a-century event is as likely to occur at the beginning of the century as at any other time, it is much less likely to occur in the first decade of the century than later.”

The sentence is elliptical. Your reading, which fills in the ellipsis as “the later 90 years of the century” renders the clause true, but trivial.

I had filled it in as “the later decades of the century” which made it less trivial but more incorrect.

Your reading, which gives the learned Judge more credit should be preferred. But I think my point that the real issue being the maturity of the governmental institutions in these countries is of some importance.

Posted by Robert Schwartz at January 5, 2005 01:06 PM | direct link

Robert,

It is an ambiguous sentence, but in context it’s meaning is not trivial. He is pointing out that because of the limited time for which a politician has responsibility over a country they will not properly plan for the long term. The probability of an event happening within one year is smaller than ten, and smaller in ten than in 100. The point, I think, is that the public needs to understand the danger over the long term and insist their leaders plan accordingly.