The centuries-old paradox of voting is that majorities sometimes prefer x to y, y to z, and z to x - a cycle. The discovery of the sources and consequences of such cycles, under majority rule and countless other regimes, constitutes much of the mathematical theory of voting and social choice. This book explores the big questions posed by the paradox of voting: positive questions about how to predict outcomes and explain observed stability, and normative questions about how to hold elections, how to take account of preference intensities, the relevance of social welfare to social choice, and challenges to formal 'rationality', individual and social. The overall lesson is that cycles are facts, ubiquitous, and consequential in non-obvious ways, not puzzles to be solved, much less maladies or misfortunes to be avoided or regretted.

This book illuminates the sources and consequences of cycles and instability in the mathematical theory of voting and social choice.

Originally published in 1951, "Social Choice and Individual Values" introduced "Arrow's Impossibility Theorem" and founded the field of social choice theory in economics and political science. This new edition, including a new foreword by Nobel laureate Eric Maskin, reintroduces Arrow's seminal book to a new generation of students and researchers."Far beyond a classic, this small book unleashed the ongoing explosion of interest in social choice and voting theory. A half-century later, the book remains full of profound insight: its central message, 'Arrow's Theorem, ' has changed the way we think."--Donald G. Saari, author of "Decisions and Elections: Explaining the Unexpected "

The mathematical theory of voting has intellectual roots extending back two centuries to the writings of Borda and Condorcet. Yet it has only been in the last forty years that general theorems have begun to emerge. With the publication of this volume, Norman Schofield brings the results together in a, common framework. SOCIAL CHOICE AND DEMOCRACY, however, is not merely a synthetic exercise, for Schofield's own work over the last decade has constituted a major initiative in deepening and' broadening our general understanding of voting arrangements. At last the results of his research, bits and pieces of which have been reported in a number of journals of international standing and in various collections, are coherently and systematically presented as an entirety. For students of democracy -- chiefly philosophers and political scientists, but increasingly economists as well -- the insights of this volume are profound. From it I infer the following.

Behavioral Social Choice looks at the probabilistic foundations of collective decision-making rules. The authors challenge much of the existing theoretical wisdom about social choice processes, and seek to restore faith in the possibility of democratic decision-making. In particular, they argue that worries about the supposed prevalence of majority rule cycles that would preclude groups from reaching a final decision about what alternative they prefer have been greatly overstated. In practice, majority rule can be expected to work well in most real-world settings. They provide new insights into how alternative model specifications can change our estimates of social orderings.

Using the economic approach of social choice theory, this unique book examines difficulties found in democratic processes involved in the creation and implementation of planning policies. Social choice theory focuses on the hard trade-offs to be made between rationality in decision-making on the one hand, and political values such as democracy, liberalism and freedom from manipulation on the other. As an institution can be seen as a set of rules, the focus on rules and procedures of collective choice makes social choice theory well suited for analysing important political aspects of planning institutions. Special attention is given to communicative planning and the logical reasons why all the desirable properties of dialogue cannot be simultaneously attained. The analysis provides original and significant new insights into the process and the institutions involved. It highlights weak spots of present planning techniques and procedures and suggests further steps towards institutionally enriched planning theory.

The election of populist politicians in recent years seems to challenge the commitment to democracy, if not its ideal. This book argues that majority rule is not the problem; rather, the institutions that stabilize majorities are responsible for the suppression of minority interests. Despite the popular notion that social choice instability (or “cycling”) makes it impossible for majorities to make sound legislation, Yuhui Li argues that the best part of democracy is not the large number of people on the winning side; it is that the winners can be easily divided and realigned with the losers in the cycling process. He shows that minorities’ bargaining power depends on their ability to exploit division within the winning coalition and induce its members to defect, an institutionalized uncertainty that is missing in one-party authoritarian systems. Dividing the Rulers theorizes why such division within the majority is important and what kind of institutional features can help a democratic system maintain such division, which is crucial in preventing the “tyranny of the majority.” These institutional solutions point to a direction of institutional reform that academics, politicians, and voters should collectively pursue.