What I Learned Today - Which will you elect Miss Rheingold? This was an...

31st January 2008

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Which will you elect Miss Rheingold?

This was an ad campaign throughout the 40s and 50s for Rheingold Beer, a New York brewery established in Bushwick in 1855. Viewers were to mail in their choice of which girl should be the new “Miss Rheingold.” This was once the second largest election in the country, with millions of people casting ballots. The girl with the most votes received money and fame. The viewers who chose the winner were rewarded or moved into the next round of the contest.

Now, notice that the viewers who chose the winner were rewarded. That means to vote strategically, you’d vote not for the girl whom you think is the prettiest, but for the girl whom you think the other voters think is the prettiest. Going a step beyond that, you’d vote for the girl whom you think the other voters think everyone else thinks is the prettiest.

Keynes (of Keynesian economics) commented “It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligence to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees.”

Consider the Financial Times Mastering Finance Competition from 1997 of the Guess the Number Game. Contestants were to choose a whole number between 0 and 100. Whomever chooses the number closest to 2/3 of the AVERAGE of all of the entries won 2 business class tickets between London and New York. There were 1382 entries.

Can you guess what the number was? What would you choose?

0^th degree: You have no idea. You’ll choose 50.
1^st degree: You think the other guys have no idea so they’ll choose 50. You’ll choose 2/3 of 50: 33.
2^nd degree: You think that most people will be thinking in the 1^st degree and pick 33, so you’d pick 2/3 of that: 22.
3^rd degree: You think most people understand the game. You think that THEY think most people will guess 33, making their guess 22. So, you’ll choose 2/3 of 22: 15.

The answer: The average guess was 18.9. 2/3 of that is 12.7. There were 31 entries with the winning guess, 13.

We played this game in a class of mine today. The answer (2/3 of the average of total guesses): 14.74. The same game was played in my prof’s previous class. That answer was exactly the same. To the decimal.

Now relate this to the stock market, poker, or what have you. Basically, you should be making bets based on what you think other people will bet on. Or what you think other people think the other people will bet on. Or what you think other people think the other people will think the other people will bet on. See what I’m getting at here?

Tagged: economics