This unique book develops an operational approach to preference and rationality as the author
employs operators over binary relations to capture the concept of rationality. A preference is
a basis of individual behavior and social judgment and is mathematically regarded as a binary
relation on the set of alternatives. Traditionally an individual social preference is assumed
to satisfy completeness and transitivity. However each of the two conditions is often
considered to be too demanding and then weaker rationality conditions are introduced by
researchers. This book argues that the preference rationality conditions can be captured
mathematically by operators which are mappings from the set of operators to itself. This
operational approach nests traditional concepts in individual social decision theory and
clarifies the underlying formal structure of preference rationality. The author also applies
his approach to welfare economics. The core problem of 'new welfare economics ' developed by
Kaldor Hicks and Samuelson is the rationality of social preference. In this book the author
translates the social criteria proposed by those three economists into operational forms which
provide new insights into welfare economics extending beyond 'new welfare economics.'
