Comment on Game for organizational structure testing

Mon, 08 Apr 2013 21:12:47 GMT

Not sure if this is fruitful path (we would need to justify the logarithm and square root empirically). But it is an interesting problem. Assuming each person is equally productive for now. In pseudo code

S = score

P = vector of proportions

sum ( sqrt (log (p*S)) ) = S

This can be simplified (if my rarely used math muscles are correct) to

sum ( sqrt( log pi + log S) /S) = 1

I can't see anything to solve it analytically easily. So let us assume that we have 3 people and they are equally distributed to for now. As I expect this is the maxima?

sqrt(log(1/3) + log(S) ) / S - 1/3 = 0

Newton's method isn't being very helpful at the moment. I'll try some other numerical methods tomorrow.

Hmm. Wolfram Alpha suggests it doesn't have any positive solutions. Have I made an error in the maths?

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