Cycles and Social Choice: The True and Unabridged Story of a Most Protean Paradox

Description

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. C1 03.0_pp_iv_iv_Copyright_page 04.0_pp_v_vi_Dedication 05.0_pp_vii_x_Contents 06.0_pp_xi_xii_Acknowledgements 07.0_pp_1_7_Introduction 08.0_pp_8_23_Condorcets_Two_Discoveries 09.0_pp_24_37_Incidence_of_the_Paradox 10.0_pp_38_49_Social_Rationality 11.0_pp_50_58_Arrovian_Cycle_Theorems 12.0_pp_59_69_Second_Line_of_Cycle_Theorems_Condorcet_Generalizations 13.0_pp_70_75_Top_Cycles_in_a_Fixed_Feasible_Set 14.0_pp_76_85_Strategic_Consequences_of_Cycles 15.0_pp_86_107_Structural_Consequences_of_Cycles 16.0_pp_108_121_Questions_about_Prediction_and_Explanation 17.0_pp_122_139_Questions_about_Prescription_and_Evaluation 18.0_pp_140_142_Concluding_Caveats 19.0_pp_143_150_Underbook_Background_and_Sources_by_Chapter 20.0_pp_151_157_References 21.0_pp_158_162_Index