Handbook of Social Choice and Voting
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Handbook of Social Choice and Voting

Edited by Jac C. Heckelman and Nicholas R. Miller

This Handbook provides an overview of interdisciplinary research related to social choice and voting that is intended for a broad audience. Expert contributors from various fields present critical summaries of the existing literature, including intuitive explanations of technical terminology and well-known theorems, suggesting new directions for research.
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Chapter 19: The uncovered set and its applications

William T. Bianco, Christopher Kam, Itai Sened and Regina A. Smyth


Virtually all democracies use majority rule in parliamentary decision-making. Throughout business and society, decisions involving voting almost always use some form of majority rule. Many equate majority rule with democracy itself and with decent decision-making rules more broadly. While plurality rule, run-off elections and other methods of voting are discussed in other chapters of this book, variants of pairwise majority rule stand at the heart of most voting procedures aimed at aggregating individual preferences into social decisions about policy. Social choice theorists have paid considerable attention to what we call ‘the majority rule program’ that asks: given a set of alternatives and voters or legislators who have preferences over those alternatives, what outcomes may ensue given majority rule? Of course, outcomes are shaped by procedures that determine the set of alternatives under consideration. However, these constraints are typically endogenous and themselves subject to majority vote. Knowing what decision-makers want, and assuming their control of procedure, what end result we should expect? How does majority rule influence political outcomes of interest, from party influence to electoral reforms and the stability of democracy itself?

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