Quantification of Performance in a Logical Task With Uncertainty 237 



w hich do or do not light the node of the juncture. Some trials yield more 

 than one fact, but some yield no new facts. The fact yield is also recorded, 

 counting the facts which the subject had the opportunity to observe, but not 

 counting the inferences which he could have made. 



Combinations of these facts make possible inferences about the meanings 

 of the arrows at each juncture. For example, in Fig. 4, the facts '1 does not 

 light 8' and '6 does not light 8' allow the inference that the arrows at this 

 juncture should be labeled as shown in Fig. 5. 



1 



Fig. 5. 



These possible juncture inferences are also recorded, and thus their rate 

 of accumulation. Finally, the juncture inferences collate into the bits of 

 infonnation directly related to the solution of the problem — whether or not 

 to push the circled buttons involved in the successive time periods. 



When all this information is available (by inference, of course), there is 

 no formal uncertainty left in the problem. However, in most cases the problem 

 is not yet solved. The extra trials made by the subject, who has the solution 

 available by inference, constitute the 'inferential lag'. We thus have various 

 possible measures of subjective uncertainty over and above the 'objective' 

 measures. The most obvious difference is revealed in the repetitions of trials 

 (ordinary failure to record information obtained). Next we have the explicitly 

 redundant trials, that is, those which while being new trials yield no new facts. 

 Next the inferential lag already mentioned. All these can be measured both 

 in time units and in numbers of trials. 



The apparatus and the analysis of the problem solving process offer many 

 opportunities for elaborate experimental designs, but they all hang on the 

 question of how 'standard' these tasks are. In other words one needs to answer 

 the question of whether there is a level of performance on each problem 

 characteristic of a given subject, so that the variance in performance in a 

 population of subjects can be adequately accounted for by a variance of some 

 inherent abihty. 



Although this question has not yet been answered definitively, there are 

 indications of a certain stability of performance. A set of experiments was 

 performed at the Mental Health Research Institute, University of Michigan, 

 in which the 'subject' in each case was a group of three students who solved 

 the problems cooperatively by discussing each move and by coming to unanimous 

 decisions on which move to make next. Eight such groups solved Problem 2 

 and then went on to solve Problem 3. The average number of moves for Problem 

 2 was about thirteen and for Problem 3 about nineteen. This is a first indication 

 of the relative difficulty of the problems. That this difference is real is indicated 



