REQUISITE VARIETY 



11/5 



Table 11/5/1 



one and only one move in response to each possible move 

 of D. His specification, or "strategy" as it might be called, might 

 appear : 



If D selects 1, I shall select y 



2 a 



■^5 5> 5> )» P 





9 



a 



He is, of course, specifying a transformation (which must be single- 

 valued, as R may not make two moves simultaneously): 



\ 



1 2 3 ... 9 



y a ^ . . . a 



This transformation uniquely specifies a set of outcomes — those 

 that will actually occur if D, over a sequence of plays, includes every 

 possible move at least once. For 1 and y give the outcome k, and 

 so on, leading to the transformation : 



(l,y) (2,a) (3,iS) .., (9,a) 



rC /C rC * • • • I 



I 



It can now be stated that the variety in this set of outcomes cannot 

 be less than 



D's variety 



i?'s variety 

 i.e., in this case, 9/3. 



It is easily proved. Suppose R marks one element in each row 

 and concentrates simply on keeping the variety of the marked 



205 



