This paper analyses alternative profiles of opportunity sets for individuals in an exchange economy, without assuming that individuals' choices reveal coherent preferences. It introduces the concept of a 'market-clearing single-price regime', representing a profile of opportunity sets consistent with competitive equilibrium. It also proposes an opportunity-based normative criterion, the Strong Opportunity Criterion, which is analogous with the core in preference-based analysis. It shows that every market-clearing single-price regime satisfies the Strong Opportunity Criterion and that, in the limit as an economy is replicated, only such regimes have this property.