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Assuming optimization took place

The explanation of WRR's results by optimization was suggested by various people and there is a comprehensive ongoing study by Bar Hillel, Bar-Natan and McKay concerning this possibility. It was previously believed that in both experiments there was some optimization (either intentionally or unintentionally) in order to improve the significance as much as possible. The above experiment suggests that, in fact, in the second test the results were improved until reaching the level of significance of the first test.

Indeed, without assuming this stopping procedure, there is no reason to believe that the P2 ratio of the original partition will not be smaller than that of a random partition and in fact, there are reasons to believe the contrary: in the two tests we have two distinct populations of Rabbis, the possible optimizations are different in the two tests (some parameters were determined by the first test) and the optimization skills are perhaps improved between them.



Gil Kalai
9/2/1997