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A voter only alters the outcome of an election if her/his vote is pivotal. A leading innovation of recent years in game theory applied to politics is Austen-Smith and Banks' analysis of pivotal voting, yielding a special form of strategic voting such that rational voters would vote against the side they favor if the decision were to be made by their vote alone. This note gives a non-mathematical version of the ASB argument, and explains why the result requires conditions which, in fact, are unlikely ever to be observed under actual conditions of social choice.

Can we devise mechanisms that allow voters to express the intensity of their preferences when monetary transfers are forbidden? Can minorities be decisive over those issues they feel very strongly about? As opposed to the usual voting system (one person – one decision – one vote), we propose a voting system where each agent is endowed with a fixed number of votes that can be distributed freely among a set of issues that need to be approved or dismissed. Its novelty relies on allowing voters to express the intensity of their preferences in a simple manner. This voting system is optimal in a well-defined sense: in a strategic setting with two voters, two issues and preference intensities uniformly and independently distributed across possible values, Qualitative Voting Pareto dominates Majority Rule and, moreover, achieves the only exante optimal (incentive-compatible) allocation. The result also holds true with three voters, as long as the voters' preferences towards the issues differ sufficiently.

Can we devise mechanisms that allow voters to express the intensity of their preferences when monetary transfers are forbidden? Would we then be able to take account of how much voters wish the approval or dismissal of any particular issue? In such cases, would some minorities be able to decide over those issues they feel very strongly about? As opposed to the classical voting system (one person - one decision - one vote), we propose a new voting system where each agent is endowed with a fixed number of votes that can be distributed freely between a predetermined number of issues that must be approved or dismissed. Its novelty relies on allowing voters to express the intensity of their preferences in a simple manner. This voting system is optimal in a well-defined sense: in a setting with two voters, two issues and preference intensities uniformly and independently distributed across possible values, Qualitative Voting Pareto dominates Majority Rule and, moreover, achieves the only ex-ante optimal (incentive compatible) allocation. The result also holds true with three voters as long as the voters preferences towards the issue differ sufficiently.

Can we devise mechanisms that allow voters to express the intensity of their preferences when monetary transfers are forbidden? Would be then be able to take into account how much voters wish the approval or dismissal of any particular issue? In such case, would some minorities be able to decide over those issues they feel very strongly about? As opposed to the classical voting system (one person - one decision - one vote), we propose a new voting system where each agent is endowed with a …xed number of votes that can be distributed freely between a predetermined number of issues that must be approved or dismissed. Its novelty relies on allowing voters to express the intensity of their preferences in a simple manner. This voting system is optimal in a well-de…ned sense: in a setting with two voters, two issues and preference intensities uniformly and independently distributed across possible values, Qualitative Voting Pareto dominates Majority Rule and, moreover, achieves the only ex-ante optimal (incentive compatible) allocation. The result also holds true with three voters as long as the voters preferences towards the issues differ sufficiently.

Cover -- Copyright Page -- Title Page -- Dedication -- Contents -- Preface -- Acknowledgments -- Introduction -- Basic Notation -- Social Choice -- Game Theory -- Game Forms are Voting Rules -- The Quest for Truthful Voting -- Strategyproofness and the Gibbard-Satterthwaite Theorem -- Voting Manipulations -- The Gibbard-Satterthwaite Theorem -- Frequency of Manipulation -- Group Manipulations -- Safe Manipulations -- Irresolute Social Choice Correspondences -- Exercises -- Regaining Truthfulness in Voting -- Domain Restriction -- Single-Peaked Preferences on a Line -- Other Single-Peak Domains -- Dichotomous Preferences -- Complexity Barriers -- Few Candidates and Coalitional Manipulations -- Randomized Voting Rules -- Gibbard's Characterization -- Stronger Impossibility Results -- Output Approximation -- Almost-Strategyproof Rules -- Approximation with Almost-Strategyproof Rules -- Differential Privacy -- Exercises -- Voting and Mechanism Design -- Payments -- The VCG Mechanism -- Range Voting -- Approximation by Randomized Voting Rules -- Facility Location -- Location in a General Metric Space -- Location on a Line -- Location on a Circle -- Other Variations -- Judgment Aggregation -- Formal Framework -- Incentives and Manipulation -- Exercises -- Voting Equilibrium Models -- Simultaneous Voting Games -- Desiderata for Voting Models -- Implementation -- Nash Implementation -- Strong Implementation -- Implementation in Undominated Strategies -- Other Notions of Implementation -- Fallback Strategies -- Truth Bias/Partial Honesty -- Laziness and the Paradox of Voting -- The ``Calculus of Voting'' -- The Expected Value of Voting -- Equilibrium Stability -- Social Networks -- Quantal Response Equilibrium -- Other Equilibrium Models -- Minimax Regret -- Robust Equilibrium -- Iterated Removal of Dominated Strategies -- Exercises.

We introduce a democratic procedure with voting-based proposals called "Pendular Voting". It works as follows: An agenda-setter chooses a proposal meant to replace a given status quo. In the first stage, a random sample of the population votes on the proposal. The result is made public, which may reveal information about the distribution of preferences in the electorate. Depending on the outcome, a third option (next to the proposal and the status quo) is added: This option is either closer to or more distant from the status quo than the original proposal. Then, in a second stage the entire electorate expresses pairwise social preferences over the status quo, the initial proposal, and the third option. We investigate the manipulability and exploitation of this voting procedure and its welfare effects. We show that manipulation is limited or absent and that exploitation can be avoided. Regardless of whether the agenda-setter is altruistic or selfish, Pendular Voting leads to welfare gains in expectation.

Approval voting is a method of voting in which voters can vote for ("approve of") as many candidates as they wish in an election. This article analyzes properties of this method and compares it with other single-ballot nonranked voting systems. Among the theorems proved is that approval voting is the most sincere and most strategyproof of all such voting systems; in addition, it is the only system that ensures the choice of a Condorcet majority candidate if the preferences of voters are dichotomous. Its probable empirical effects would be to (1) increase voter turnout, (2) increase the likelihood of a majority winner in plurality contests and thereby both obviate the need for runoff elections and reinforce the legitimacy of first-ballot outcomes, and (3) help centrist candidates, without at the same time denying voters the opportunity to express their support for more extremist candidates. The latter effect's institutional impact may be to weaken the two-party system yet preserve middle-of-the-road public policies of which most voters approve.