This chapter presents the book Handbook of Social Choice and Welfare in two volumes, essays on past and on-going work in social choice theory and welfare economics. The first volume consists of four parts. In Part 1 (Arrovian Impossibility Theorems), various aspects of Arrovian general impossibility theorems, illustrated by the simple majority cycle first identified by Condorcet, are expounded and evaluated. In Part 2 (Voting Schemes and Mechanisms), the operation and performance of voting schemes and cost-sharing mechanisms are examined axiomatically, and some aspects of the modem theory of incentives and mechanism design are expounded and surveyed. In Part 3 (Structure of Social Choice Rules), the positional rules of collective decision-making (the origin of which can be traced back to a seminal proposal by Borda), the game-theoretic aspects of voting in committees, and the implications of representative democracy in the theoretical arena of social choice theory are examined. In Part 4 (Welfare, Justice and Poverty), the possibility and implications of making use of interpersonal comparisons of welfare (with or without cardinal measurability) are expounded, and the status of utilitarianism as a theory of justice is critically examined.
