Results to Numbers Contest NUM5
These are the results to Numbers Contest NUM5.
First place goes to Jonathan Dushoff, with a score of 439.
Andrew Krywaniuk and Gerrit de Blaauw come in a close second and third,
with scores of 463 and 515. Congratulations!
There were only 13 entrants to this contest. Personally, I was
pretty interested in finding out the results for this contest, but I can
also see why it's not one of the more popular contests.
One interesting aspect of this contest was that all but one of
the questions had "correct" answers (from a game theory perspective),
and all these answers could be trivially calculated. However, it was not
clear that it was good to give these game theory answers. Nis Jorgensen
gave the game theory answer to all the questions, and came in
5th out of 13.
One side comment on Michael Mendelsohn's contest, for any of you
who were wondering. He checked with me before running his parallel contest.
His contest is obviously "discussion" of my contest, but I since all the
information is going in one direction, I didn't see how it could produce
any serious distortion of my contest. Also, his entry to my contest was
sent before he had received any entries to his contest, so that's OK too.
However, I had already received some entries to my contest by the time
that he posted his, so I didn't feel like I could enter his contest.
Here are all the entries and their scores. All answers are rounded
to the nearest integer for nice formatting in the table below. The more
detailed decimal answers (which are, of course, the ones actually used
in computing the scores) are listed further down.
Name A B C D E F G H I Score
------------------ - - - - - - - - - -----
1.Jonathan Dushoff 50 25 15 6 2 88 85 97 0 4.392e+02
2.Andrew Krywaniuk 42 30 21 15 6 100 97 100 0 4.627e+02
3.Gerrit de Blaauw 48 7 5 3 1 100 100 100 0 5.150e+02
4.Michael Mendelsohn 50 28 18 8 3 87 75 95 0 7.506e+02
5.Nis Jorgensen 50 0 0 0 0 100 100 100 0 8.989e+02
6.Jarmo Monttinen 50 30 21 11 7 95 69 82 0 1.368e+03
7.Henrik Eriksson 50 25 20 7 2 80 90 100 47 2.954e+03
8.Larry Tapper 50 28 18 7 6 91 77 94 49 3.074e+03
9.Andy Jakcsy 50 32 22 12 5 78 70 90 50 4.132e+03
10.FatPhil 50 32 22 12 5 78 70 90 50 4.132e+03
11.Ted Schuerzinger 50 32 28 14 10 67 67 67 10 4.172e+03
12.David McElfresh 50 40 33 25 17 63 60 70 40 6.969e+03
13.Seattle Max 48 38 32 24 16 60 58 68 46 7.923e+03
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> A. target = arithmetic mean of all responses to this question
A: target=49.0769
42, 48, 48, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50
Question A was the one question with no game theoretic answer.
Nevertheless, it's pretty obvious, and I expected everyone to answer 50,
or something near it. Basically, I just wanted to make sure that we were
all on the same page, and we were. Good.
> B. target = (4/5)*(arithmetic mean of all responses to this question)
B: target=21.4154
0, 7, 25, 25, 28, 28.6, 30, 30, 32, 32, 32, 38.4, 40
> C. target = (2/3)*(arithmetic mean of all responses to this question)
C: target=13.0841
0, 5, 15, 18, 18.14, 20, 21, 21, 22, 22, 28, 32, 33
> D. target = (1/2)*(arithmetic mean of all responses to this question)
D: target=5.57077
0, 3, 6, 7, 7, 8.84, 11, 12, 12, 14, 15, 24, 25
> E. target = (1/3)*(arithmetic mean of all responses to this question)
E: target=2.05667
0, 1, 2, 2, 3.21, 5, 5, 6, 6, 7, 10, 16, 17
These questions are obviously all pretty similar. Clearly, from
a game theory perspective, questions B-E should all be answered with 0. I
assume that everyone in this newsgroup sees this, but just to spell it
out. . . Assume everyone is rational, and everyone knows that everyone
is rational, and everyone knows that everyone knows that everyone is
rational, and so on. Initially, without any thought, the mean should be
50. But since everyone knows this, they should aim for k*50 (where k<1,
and is different for each of these questions). But since everyone knows
that everyone is answering k*50, they should really aim for (k^2)*50.
But since everyone . . . [Infinite logical chain deleted].
However, we're not in the game theory world, and the assumption
of infinitely nested knowledge of rationality is clearly untrue. Suppose
that almost everyone gives the game theory answer of 0. However, it's
reasonable to suppose that there's one "nutcase" out there, who for some
"nutty" reason, just doesn't understand game theory, and gives a
non-zero answer -- say 15, or 21. Well, given that there's this nutcase
out there, the mean will be at least a little higher than zero, and we
can beat all the game theorists by raising our answer a little, to 1 or
2, or whatever we think the new target is. Of course, now we're a
"nutcase" too, so the "nutty" reason is actually quite reasonable. And
if everyone realizes this, everyone should use nutty logic, and give
non-zero answers.
I conclude from the results here that everyone in these
newsgroups is rational, and that the average reader in this newsgroups
knows that everyone is rational, and knows that almost everyone knows
that everyone is rational. But the fact stated in my previous sentence
is not common knowledge.
> F. target = (1.25)*(arithmetic mean of all responses to this question)
F: target=104.553
60, 63, 67, 78, 78, 80, 87.35, 88, 91, 95, 100, 100, 100
> G. target = 10+(arithmetic mean of all responses to this question)
G: target=88.3077
58, 60, 67, 69, 70, 70, 75, 77, 85, 90, 97, 100, 100
> H. target = 20+(arithmetic mean of all responses to this question)
H: target=108.692
67, 68, 70, 82, 90, 90, 94, 95, 97, 100, 100, 100, 100
For questions F-H, the game theorist should answer 100. However,
these questions are different from B-E. Here, 100 is a reasonable
answer even without the assumption of infinitely nested rationality. In
questions B-E, only one nutty answer was necessary to make the target
greater than zero. However, for questions F-H, multiple nutty answers
are necessary to make the target drop below 100, and they need to be
very nutty (i.e. quite a bit below 100). And, in fact, for F and H,
while the majority of answers were nutty, they were not nutty enough,
and the target stayed above 100.
> I. target = geometric mean of all responses to this question
I: target=0
0, 0, 0, 0, 0, 0, 10, 40, 46.71, 47, 49.6, 50, 50
This was the only question that I've asked with an indisputably
correct answer. I feel a little bad (just a little) about having a trick
question. But removal of this question would not have affected the rakings
of the top three entries anyway.
Momo