We extend approval voting so as to elect multiple candidates, who may be either individuals or members of a political party, in rough proportion to their approval in the electorate. We analyze two divisor methods of apportionment, first proposed by Jefferson and Webster, that iteratively depreciate the approval votes of voters who have one or more of their approved candidates already elected. We compare the usual sequential version of these methods with a nonsequential version, which is computationally complex but feasible for many elections. Whereas Webster apportionments tend to be more representative of the electorate than those of Jefferson, the latter, whose equally spaced vote thresholds for winning seats duplicate those of cumulative voting in 2-party elections, is even-handed or balanced.

With approval voting, voters can approve of as many candidates as they want, and the one approved by the most voters wins. This book surveys a wide variety of empirical and theoretical knowledge accumulated from years of studying this method of voting.

"Satisfaction Approval Voting" presents an innovative electoral system designed to improve voter satisfaction and representational outcomes. This book explores how Satisfaction Approval Voting (SAV) integrates approval voting principles with enhancements that optimize democratic processes. 1-Satisfaction Approval Voting-An introduction to SAV and its revolutionary approach to electoral satisfaction. 2-Approval Voting-A look at approval voting, allowing voters to support multiple candidates for fairness. 3-Proportional Representation-Explores proportional representation’s role in achieving equitable outcomes. 4-Score Voting-Discusses score voting, a system where voters assign scores to candidates. 5-Two-round System-Analyzes how the two-round system ensures broad candidate support. 6-Single Transferable Vote-Unpacks the single transferable vote system for proportional outcomes. 7-Strategic Voting-Covers strategic voting and its influence on electoral results. 8-Voting-Provides a comprehensive overview of voting principles and systems. 9-Electoral System-Analyzes the impact of different electoral systems on democracy. 10-Cardinal Voting-Explores how cardinal voting rates candidates, highlighting its strengths. 11-Multiple Non-Transferable Vote-Examines this system's role in specific electoral contexts. 12-Ranked Voting-Discusses ranked voting and its preference-based candidate ranking. 13-Proportional Approval Voting-Explores how this method combines approval voting with proportionality. 14-Sequential Proportional Approval Voting-Looks at a sequential approach to improve proportional outcomes. 15-Combined Approval Voting-Analyzes how this method integrates multiple voting systems. 16-STAR Voting-A breakdown of STAR (Score Then Automatic Runoff) voting and its benefits. 17-Social Utility Efficiency-Explores how voting systems can optimize social utility. 18-Justified Representation-Focuses on achieving fair representation in electoral processes. 19-Multiwinner Approval Voting-Covers how multiwinner approval voting represents diverse interests. 20-Multiwinner Voting-Discusses various multiwinner systems for balanced representation. 21-Multi-Issue Voting-Explores multi-issue voting for elections involving multiple topics. "Satisfaction Approval Voting" is more than a book—it's a valuable resource for anyone interested in democratic reform. Whether you're a professional, student, or enthusiast, this book offers powerful insights into how SAV can transform voting and representation. Dive in to explore the future of electoral reform.

Approval Voting-Enhancing Democratic Representation in Political Science What is Approval Voting? This book explores approval voting systems and their impact on democratic representation, voter satisfaction, and efficiency. It offers a deep dive into the benefits and challenges of using this system in elections. Chapters Overview 1-Approval Voting-Introduction to the core concepts and principles of approval voting. 2-Score Voting-Compares score voting and its outcomes with approval voting. 3-Condorcet Method-Discusses the Condorcet method and its differences from approval voting. 4-Strategic Voting-Analyzes strategic voting and how approval voting interacts with it. 5-Borda Count-Reviews the Borda count system and its comparative advantages. 6-Condorcet Winner Criterion-Evaluates approval voting against the Condorcet winner criterion. 7-Condorcet Loser Criterion-Investigates how approval voting handles the Condorcet loser criterion. 8-Participation Criterion-Examines approval voting's impact on voter participation. 9-Comparison of Electoral Systems-A detailed comparison of approval voting with other systems. 10-Multiwinner Voting-Explores approval voting’s application in multiwinner elections. 11-Two-Round System-Compares the two-round system with approval voting. 12-Bucklin Voting-Introduction to Bucklin voting and its mechanisms. 13-Majority Criterion-Evaluates approval voting against the majority criterion. 14-Nanson’s Method-Analyzes Nanson’s method and its relevance to approval voting. 15-Later-No-Harm Criterion-Discusses this criterion and its role in voter behavior. 16-Independence of Clones Criterion-Explores the criterion’s importance in approval voting. 17-Instant-Runoff Voting-Compares instant-runoff voting with approval voting. 18-Cardinal Voting-Analyzes cardinal voting systems and voter satisfaction. 19-Ranked Voting-Compares ranked voting systems with approval voting. 20-Later-No-Help Criterion-Investigates this criterion in the context of approval voting. 21-STAR Voting-Introduction to STAR voting and its comparison to approval voting. Who is this book for? This book is invaluable for students, professionals, and enthusiasts seeking a comprehensive understanding of electoral systems, providing essential insights into the nuances of approval voting.

In using approval voting to elect multiple winners to a committee or council, it is desirable that excess votes -- approvals beyond those that a candidate needs to win a seat -- not be wasted. The excess method does this by sequentially allocating excess votes to a voter's as-yet-unelected approved candidates, based on the Jefferson method of apportionment. It is monotonic -- approving of a candidate never hurts and may help him or her get elected -- computationally easy, and less manipulable than related methods. In parliamentary systems with party lists, the excess method is equivalent to the Jefferson method and thus ensures the approximate proportional representation of political parties. As a method for achieving proportional representation (PR) on a committee or council, we compare it to other PR methods proposed by Hare, Andrae, and Droop for preferential voting systems, and by Phragmén for approval voting. Because voters can vote for multiple candidates or parties, the excess method is likely to abet coalitions that cross ideological and party lines and to foster greater consensus in voting bodies.

Voters do not always choose their preferred candidate on election day. Often they cast their ballots to prevent a particular outcome, as when their own preferred candidate has no hope of winning and they want to prevent another, undesirable candidate’s victory; or, they vote to promote a single-party majority in parliamentary systems, when their own candidate is from a party that has no hope of winning. In their thought-provoking book The Many Faces of Strategic Voting, Laura B. Stephenson, John H. Aldrich, and André Blais first provide a conceptual framework for understanding why people vote strategically, and what the differences are between sincere and strategic voting behaviors. Expert contributors then explore the many facets of strategic voting through case studies in Great Britain, Spain, Canada, Japan, Belgium, Germany, Switzerland, and the European Union.

Computational social choice is concerned with the design and analysis of methods for collective decision making. It is a research area that is located at the interface of computer science and economics. The central question studied in computational social choice is that of how best to aggregate the individual points of view of several agents, so as to arrive at a reasonable compromise. Examples include tallying the votes cast in an election, aggregating the professional opinions of several experts, and finding a fair manner of dividing a set of resources amongst the members of a group -- Back cover.