Describing Sen's Transitivity Condition in Inequalities and Equations

In social choice theory, Sen's value restriction condition is a sufficiency condition restricted to individuals' ordinal preferences so as to obtain a transitive social preference under the majority decision rule. In this article, Sen's transitivity condition is described by use of inequality and equation. First, for a triple of alternatives, an individual's preference is represented by a preference map, whose entries are sets containing the ranking position or positions derived from the individual's preference over that triple of those alternatives. Second, by using the union operation of sets and the cardinality concept, Sen's transitivity condition is described by inequalities. Finally, by using the membership function of sets, Sen's transitivity condition is further described by equations.