"Of the major areas into which experimental psychology has been traditionally partitioned, motivation is the least well understood and systematized. This is true whether we consider theory, experimental paradigms or experimental results. Moreover, of the various notions usually considered to be primarily motivational, preference is the only one that mathematical psychologists have attempted to analyze with any care: there are almost no satisfactory formal theories concerning, for example, drive and incentive, and those that exist are best discussed as aspects of learning. So this chapter on mathematical theories of motivation is limited to a study of preference and the closely related constructs of utility and subjective probability." (Luce and Suppes., 1965, p. 252). In this thesis we develop certain aspects of the theories of preference discussed in the above mentioned chapter.