Quantification of Performance in a Logical Task With Uncertainty 231 



'subjectivist' notions are also, I think, at the root of many philosophical objec- 

 tions to quantum theories. 



The question of where to draw the line between subjective and objective 

 frames of reference also arises in connection with attempts to link information 

 theory with thermodynamics so as to make it useful in theoretical molecular 

 biology. Whatever the merits of the attempts may be, this area of investigation 

 does bring out rather pointedly the necessity of examining the possibly 'subjec- 

 tive' postulates underlying the description of the situations studied, indeed, the 

 philosophical question 'What is a subjective postulate?' comes to the forefront 

 in the region where thermodynamics, quantum theory and information theory, 

 meet — a triple point. 



There is an area of possible application of information theory, however, 

 where clearly subjective postulates are not only unavoidable but central. This 

 is the area of psychology. Psychology is a study of behavior. Since psychology 

 has gradually outgrown the austere positivistic restrictions of strict behaviorism, 

 it has become respectable again to include into psychological theory considera- 

 tions based on how the situation looks from inside the subject. To be sure, 

 these matters must somehow be inferred from overt behavior, but once they are 

 inferred there is no reason why these 'subjective variables', for example, sub- 

 jective probabilities, utility functions, and so on, cannot enter as parameters in 

 a theory. Indeed, if these parameters are determinable and stable, they serve to 

 'objectify' the subjective and thus contribute to the success of psychology as a 

 science. 



Information theory was applied from its very inception to psychological 

 investigations. These applications have often been criticized. The grounds for 

 criticism have been many, but a recurrent theme has been the failure of many 

 psychologists to realize that information theory is worthless without an under- 

 lying set of postulates for each situation. Just as the application of probability 

 theory to any situation necessitates the determination of a 'sample space', that 

 is, a set of elementary events with a priori assignment of probabilities or a 

 probability distribution function, so is the case with information theory. 



Yet it was shown by de Finetti (1), Savage (2), and others that a rigorous 

 theory of probability could be constructed backwards. That is to say, beginning 

 with certain preferences of individuals for certain outcomes as reflected in their 

 choices of actions under uncertainty, a set of subjective probabilities of events 

 could be inferred, provided certain 'rationality criteria' of behavior were satisfied 

 by the individuals. The question to what degree such rationality criteria are 

 in actuahty satisfied is another question which has led to many interesting 

 investigations in their own right; so it is not entirely an unfortunate one. It 

 must in any case be admitted that the 'subjective probability' of an event can 

 in principle be defined, and thus statements such as, 'The Democrats will with 

 probability 0.6 win in I960,' are not wholly devoid of operational sense, pro- 

 vided the expressed 'subjective' probability is inferrable by explicit rules from 

 observed behavior and enjoys a certain stability. Such assertions have no 

 sense in the conceptual framework of the objectivist school, since the election 

 of 1960 is a unique event whose 'probability' cannot be deduced from a fre- 

 quency of occurrence. 



The operational definition of subjective probability introduces probability 



