Paretian quasi-orders: the regular two-agent case
Let \(X\) be a compact and connected set of alternatives. Let \(\succeq_i\) be the preference order of agent \(i\) \((i=1,2)\). \(\succeq_1\) and \(\succeq_2\) define a Pareto relation \(R^*\) on \(X\). \((\succeq_1, \succeq_2)\) are regular if certain continuity conditions are fulfilled (Definition 1). The paper answers the following question: ``If \(R\) is a quasi-order on \(X\), under what conditions does there exist a regular preference profile \((\succeq_1, \succeq_2)\) whose Pareto relation \(R^*\) coincides with \(R\)?'' A theorem is proved which gives a necessary and sufficient condition for \(R\) to coincide with a Pareto relation \(R^*\). The theorem is based on properties of intermediateness.
scientific article; zbMATH DE number 1736552