Re:Are You Trading or Gambling?
by kqr on Saturday February 27, 2021 @09:17AM
(#26284979)
Exemplified in a competition in -- I think -- The New York Times: readers were instructed to guess a number between 1 and 100, and were told the winning guess would be the one closest to 2/3 of the average guess.
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No mention of a NYT version of the game ever happening on the wikipedia article - https://en.wikipedia.org/wiki/Guess_2/3_of_the_average - but that wiki page is a good write up of the basic idea and its relationship to the Keynesian Beauty Contest
What was the result?
If I remember correctly, somewhere in the range 17--23.
The way one should have thought of it, with hindsight, is that there are going to be several groups of people:
- those who don't understand the problem and just guess a number between 1 and 100,
- those who only reason to one degree, and guess 33,
- those who only reason to two degrees (ah but if everyone else guesses 33 I should aim for two thirds of that!)
- those who reason to initiate degree and guess 0
The real competition is guessing the proportions of these groups.
The way you originally stated the problem was to pick a number between 1 and 100, so 0 wouldn't even be an option, and 1 is probably the pareto optimal strategy (proof left as an exercise for the reader, etc.).
But then you probably still have to account in your strategy for estimating the proportion of people who will reason to infinite degree and estimate 1, as well as the proportion who will reason to an infinite degree and misread the rules, and guess 0...