Hruska was a US senator in office when I was a kid growing up in rural Nebraska. Here is some more context that suggests other names to associate with outcomes in this game, perhaps.... Brandeis, Frankfurter, and Cardozo ***** Responding to criticism that Carswell had been a *mediocre* judge, *Hruska* argued: Even if he were *mediocre*, there are a lot of *mediocre* judges and *people* and lawyers. They are entitled to a little representation, aren't they, and a little chance? We can't have all Brandeises, Frankfurters and Cardozos. On Sat, Apr 25, 2020 at 10:15 AM Gareth McCaughan < gareth.mccaughan@pobox.com> wrote:
On 25/04/2020 13:06, James Propp wrote:
About 30 years ago my friends Bruce Smith and Dan Ullman and I shared a bank of seats on a plane, and played a game in which the questions are Fermi problems and the goal of each guesser on a given turn is to guess the MEDIAN of the three guesses. (Any odd number of odd people can play.)
Did we invent this?
Something similar (though not quite the same -- it lacks the Fermi-problem element) is in one of Douglas Hofstadter's "Metamagical Themas" columns from Scientific American (and in his book of that name that collects them).
The column is called "Undercut, Flaunt, Pounce and Mediocrity: Psychological games with numbers", and it's from August 1982. (So, somewhat more than 30 years ago.) Here's the relevant bit:
One day [...] somehow it came to us to play a number game involving _three_ persons. We decided that on each turn, each of us would choose a number in a certain range, and, since it seemed too boring to let the biggest number win, and equally boring if the littlest number won, it became obvious that the _middlemost_ number should be rewarded. So we decided that on each turn, only the "most mediocre" player's score would be allowed to increase. It would increase, of course, by the mediocre number; the other players' scores would stay fixed.
And, since it's Hofstadter, of course there has to be a bit of meta-ness.
Thus at the end of, say, five turns, we would all compare our scores, and the highest one ... No, wait a minute. Why should we let the _highest_ score win? To do that would be, after all, contrary to the spirit of each turn. We saw quite clearly that, if the spirit of the _whole_ was to be consistent with the spirit of its _parts_, then the player in the _middle_ should win! We called our game "Mediocrity", but occasionally I like to refer to it as "Hruska".
He explains that this is because of a remark praising mediocre people, made by Roman Hruska when he was senator for Nebraska. Anyway, of course he goes on to suggest that if you play multiple games of Mediocrity, then again whoever won the _middlemost_ number of games should win, and proposes an ever-increasing hierarchy of levels, and describes some attempts to refine the ruleset and deal nicely with ties. He says:
I can testify that the strategy for playing even Level Two Mediocrity gets mighty confusing very quickly. I have played Level Three Mediocrity on a couple of occasions, and found it completely beyond my reach.
-- g
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