This article re-examines the prevalent view that classical/neoclassical economics contains only bases or ingredients of rational choice theory, i.e., the economic model of human action and society. Instead, it proposes that elements or implications of alternative ‘irrational choice theory’ also coexist with those of ‘rational choice’ and are relatively important in much of classical and neoclassical economics. The article identifies and considers certain elements and implications of irrational choice theory in classical and neoclassical economics. These consist of the reality, possibility, and realm –i.e., conception and observation – of irrational choices in the economy. The article contributes to understanding better how traditional economics relates to contemporary economic-sociological rational choice theory and its alternative.