Many decisions of public concern cannot be left to the market because cooperative opportunities will not be efficiently utilized by decentralized actions of the agents. The most prominent examples include the provision of public goods, pricing of a natural monopoly, as well as all decisions taken by vote. To remedy these market failures, welfare economists have come up with a variety of normative solutions and tried to convince the decision makers of their relevance.

The theoretical foundation of these normative arguments is axiomatic. This point was clearly made in Amartya Sen’s landmark book (Collective Choice and Social Welfare, first published in 1970). Since then the axiomatic literature has considerably expanded its scope and refined its methods: The whole theory of cooperative games has played a central role in the analysis of cost sharing when there are increasing returns to scales; our understanding of voting rules now encompasses the impact of strategic manipulations; several refined measurements of inequality have been constructed and abundantly tested; and so on.

This book describes the recent successes of the axiomatic method in four areas: welfarism (the construction of collective utility functions and inequality measures as well as the axiomatic bargaining approach); cooperative games (the core and the two most popular value operators - Shapley value and nucleolus); public decision making (cost sharing of a public good and pricing of a regulated monopoly, in both the first-best and strategic-second-best perspectives); and voting and social choice (majority voting a la Condorcet and scoring methods a la Borda; the impossibility of aggregating individual preferences into a social preference).