Social aggregation theory is concerned with investigating methods of clustering values that individuals in a society attach to different social or economic states into values for the society as a whole. Loosely speaking, a social state, a state of affairs, represents a sketch of the amount of commodities possessed by different individuals, quantities of productive resources invested in different productive activities and different types of collective activities (Arrow 1950). The values that individuals attach to different social states are reflections of respective preferences. Consequently, the problem of social aggregation is to combine individual preferences into a social preference in an unambiguous way. In this monograph, we will use the terms “social aggregation” and “social choice” interchangeably.

Modern social aggregation theory started with the publication of Kenneth J. Arrow’s pioneering contribution Social Choice and Individual Values, his PhD dissertation, in 1951. It can be regarded as the foundation to laying the groundwork of social aggregation theory in view of its innovative facture and revolutionary influence. The idea of aggregating individual preferences into a collective choice rule predates Arrow (1950) by more than 150 years. In 1785, the French mathematician and philosopher Marie-Jean de Condorcet considered the problem of collective decision-making with regard to majority voting. According to majority voting, in a choice between two alternatives x and y, x is declared as the winner if it gets more votes than y. He established that the method of pair-wise majority voting may give rise to cyclicality in social preference. This paradoxical result, popularly known as the Condorcet voting paradox, appears to draw inspiration, to a certain extent, from an earlier contribution by the French mathematician Jean-Charles de Borda (de Borda 1781). In this alternative voting system, known as the Borda count method, voters rank candidates in order of preference.

One of the major goals of this monograph is the analysis of the Arrovian approach to the theory of collective aggregation and later developments on it. We, therefore, focus now on Arrow’s impossibility theorem, which is generally acknowledged as the formative basis of modern social aggregation rules.Arrow’s seminal work examines the possibility of the aggregation of individual preferences into a social preference in order to obtain a social ranking of alternative states of affairs.