On the Value of Information

Based on the definition of information acquisition as the reduction in uncertainty, the concept of ignorance is defined as the state of uncertainty. Two basic types of ignorance are then defined as substitutes for information: guessing and belief. Two types of frequency distribution are presented as the most general dichotomy that can be applied to all possible types of frequency distribution and from them two limits are deduced between which all types of frequency distribution can be placed. Using games of chance—roulette and horse racing—as representatives of two basic types of frequency distribution, the comparison is presented of different results that can be theoretically obtained by the informed, the guessing, and the belief approaches. The value of information is a function of the type of frequency distribution of data that form its contents. The limits established for the types of frequency distribution are also boundary conditions for information value from nil to some finite number that depends also on the number of alternatives involved in case of a discrete set, and on range size, accuracy of measurement, and its precision in case of continuous parameters.