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David Simmons's avatar

As a mathematician, the obvious solution to this problem seems to me to be to take the geometric mean of the max and min, rather than either the arithmetic mean or the Malatesta estimate. That solves the problem of the minimum being bounded below without the arbitrariness of subtracting a third or the awkwardness of not working when the maximum and minimum are "too close". It also gives more intuitive estimates if the maximum and minimum differ greatly on a logarithmic scale, e.g. if the maximum is a million and the minimum is 10,000, then the estimate according to the geometric mean is 100,000, which seems like a reasonable estimate given those two bounds, unlike the Malatesta estimate of 337k, which seems too high. Finally, I should point out that in the example you give, the geometric mean estimate does approximately as well as Malatesta estimate (the geometric mean estimate would be 894k).

No reason to defer to an estimate just because it has a fancy name attached.

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Overcoming Bias Commenter's avatar

Anders, you are probably right if we can limit our Max and Min estimates to people who are acting rationally. There are complications though. One is pronouncements by persons who seek to be dramatic and have no concern with being believed. A second issue is the problem of "many" or "gazillions". In the Bible and the Middle East one finds frequent use of the number 40, e.g., Ali Baba and the Forty thieves, Moses wandering in the desert for 40 years, 40 paras equals one piastre, etc. Possibly or apparently in some ur-Semitic language the word for 40 and the word for myriad sounded alike, perhaps modulo vowels. Some size estimates may be nothing more than a loose way of saying many, many, many supporters. I suspect that in these cases something like a Benford's Law will be at work, so that we get disproportionately many estamiates that begin with the number 1, i.e., one hundred, one thousand, etc.

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