238 A. Rapoport 



by the fact that all eight groups increased the number of moves from Problem 2 

 to Problem 3. When the groups were rank-ordered on their performance on 

 Problem 2, the rank order was preserved (with just one reversal of two con- 

 secutive groups) on Problem 3. Another set of eight groups was given Problem 

 2 and then Problem 3 with a money incentive to minimize the number of 

 moves on the latter. Under these conditions again all eight groups decreased 

 the number of moves (averaging only eight on Problem 3). In spite of the 

 radically changed situation, the rank order of these eight groups was again 

 preserved from Problem 2 to Problem 3 (again with a reversal of only one 

 pair of consecutive groups). 



When groups are rank-ordered according to time of solution, no discernible 

 correlation appears from one problem to another. These results point to a 

 possible stable relation between the complexity of the problem and the effec- 

 tiveness of solution strategy adopted by each of our trios of subjects. The 

 lack of correlation in rates of perfonnance points to possible extraneous effects 

 such as the nature of the discussion process itself. At any rate the fact that 

 the most prominent regularities are found in the performances as measured 

 by the number of moves raises the hope that these regularities are the reflections 

 of the uncertainty content of the problems as perceived by the subjects. It is 

 noteworthy that, while on the level of observable crude facts and on the level 

 of inferences about the meanings of the arrows, the two problems have the 

 same uncertainty contents (about sixteen and ten bits each), on the level of 

 major inference involving the circled buttons. Problem 2 has four bits of uncer- 

 tainty while Problem 3 has six. The approximately 50 per cent increase in the 

 average number of moves from Problem 2 to Problem 3 may well be a reflection 

 of the increase in uncertainty on that level. Whatever the case may be, the 

 results warrant further experimentation with a view of establishing the expected 

 level of performance of a given subject on a given problem, once the set of 

 uncertainties on various levels of observation and inference characteristic of 

 the problem and certain factors of strategy efficiency characteristic of the 

 subject are known. It is evident that the number of various problems which 

 can be programmed into the PSl apparatus is astronomical. 



REFERENCES 



1. B. DeFinetti: La Prevision : ses lois logiques, ses sources subjectives. Ann. Inst. Henri 

 Poincare 7, 1-68 (1937). 



2. L. J. Savage: The Foundations of Statistics, J. Wiley and Sons, New York (1954). 



3. E. R. John: Contributions to t/ie study of the problem-solving process. Preprint No. 1, 

 Mental Health Research Institute, University of Michigan, Ann Arbor (1956). 



4. C. E. Shannon: A symbolic analysis of relay and switching circuits. Trans. Amer. Inst. 

 Elect. Eng. 57, 713-723 (1938). 



5. W. S. McCuLLOCH and W. Pitts: A logical calculus of the ideas immanent in nervous 

 activity. Bull. Math. Biophys. 5, 115-133 (1943). 



