scholarly journals The Incidence of Some Voting Paradoxes Under Domain Restrictions

2020 ◽  
Vol 29 (6) ◽  
pp. 1107-1120
Author(s):  
Hannu Nurmi
Keyword(s):  
Condorcet Winner ◽  
Additional Restriction ◽  
Voting Rules ◽  
Voting Rule ◽  
Starting Point ◽  
Voting Paradoxes ◽  
Domain Restrictions

Abstract Voting paradoxes have played an important role in the theory of voting. They typically say very little about the circumstances in which they are particularly likely or unlikely to occur. They are basically existence findings. In this article we study some well known voting paradoxes under the assumption that the underlying profiles are drawn from the Condorcet domain, i.e. a set of preference profiles where a Condorcet winner exists. The motivation for this restriction is the often stated assumption that profiles with a Condorcet winner are more likely than those without it. We further restrict the profiles by assuming that the starting point of our analysis is that the Condorcet winner coincides with the choice of the voting rule under scrutiny. The reason for making this additional restriction is that—intuitively—the outcomes that coincide with the Condorcet winner make those outcomes stable and, thus, presumably less vulnerable to various voting paradoxes. It will be seen that this is, indeed, the case for some voting rules and some voting paradoxes, but not for all of them.

scholarly journals Decision Making in Committees: Transparency, Reputation, and Voting Rules

2007 ◽  
Vol 97 (1) ◽  
pp. 150-168 ◽  
Author(s):  
Gilat Levy
Keyword(s):  
Decision Making ◽  
Career Concerns ◽  
Decision Making Process ◽  
Voting Rules ◽  
The Public ◽  
Voting Rule ◽  
The Right

In this paper I analyze the effect of transparency on decision making in committees. I focus on committees whose members are motivated by career concerns. The main result is that when the decision-making process is secretive (when individual votes are not revealed to the public), committee members comply with preexisting biases. For example, if the voting rule demands a supermajority to accept a reform, individuals vote more often against reforms. Transparent committees are therefore more likely to accept reforms. I also find that coupled with the right voting rule, a secretive procedure may induce better decisions than a transparent one. (JEL D71, D72)

Deliberation, Preference Uncertainty, and Voting Rules

2006 ◽  
Vol 100 (2) ◽  
pp. 209-217 ◽  
Author(s):  
DAVID AUSTEN-SMITH ◽  
TIMOTHY J. FEDDERSEN
Keyword(s):  
Information Sharing ◽  
Majority Rule ◽  
Common Knowledge ◽  
General Setting ◽  
Full Information ◽  
Information Revelation ◽  
Voting Rules ◽  
Unanimity Rule ◽  
Preference Uncertainty ◽  
Voting Rule

A deliberative committee is a group of at least two individuals who first debate about what alternative to choose prior to these same individuals voting to determine the choice. We argue, first, that uncertainty about individuals' private preferences is necessary for full information sharing and, second, demonstrate in a very general setting that the condition under which unanimity can support full information revelation in debate amounts to it being common knowledge that all committee members invariably share identical preferences over the alternatives. It follows that if ever there exists an equilibrium with fully revealing debate under unanimity rule, there exists an equilibrium with fully revealing debate under any voting rule. Moreover, the converse is not true of majority rule if there is uncertainty about individuals' preferences.

scholarly journals Strategic Abstention based on Preference Extensions: Positive Results and Computer-Generated Impossibilities

2019 ◽  
Vol 66 ◽  
Author(s):  
Florian Brandl ◽  
Felix Brandt ◽  
Christian Geist ◽  
Johannes Hofbauer
Keyword(s):  
Propositional Logic ◽  
Pareto Optimal ◽  
Large Problem ◽  
Voting Rules ◽  
Natural Conditions ◽  
Voting Rule ◽  
Joint Decisions ◽  
Sat Solver ◽  
Unsatisfiable Core ◽  
Positive Results

Voting rules allow multiple agents to aggregate their preferences in order to reach joint decisions. A common flaw of some voting rules, known as the no-show paradox, is that agents may obtain a more preferred outcome by abstaining from an election. We study strategic abstention for set-valued voting rules based on Kelly's and Fishburn's preference extensions. Our contribution is twofold. First, we show that, whenever there are at least five alternatives and seven agents, every Pareto-optimal majoritarian voting rule suffers from the no-show paradox with respect to Fishburn's extension. This is achieved by reducing the statement to a finite - yet very large - problem, which is encoded as a formula in propositional logic and then shown to be unsatisfiable by a SAT solver. We also provide a human-readable proof which we extracted from a minimal unsatisfiable core of the formula. Secondly, we prove that every voting rule that satisfies two natural conditions cannot be manipulated by strategic abstention with respect to Kelly's extension and give examples of well-known Pareto-optimal majoritarian voting rules that meet these requirements.

The Study of Strategic Voting

2019 ◽  
pp. 291-309 ◽  
Author(s):  
André Blais ◽  
Arianna Degan
Keyword(s):  
Survey Data ◽  
Empirical Research ◽  
Strategic Voting ◽  
Conventional Wisdom ◽  
Strategic Vote ◽  
Plurality Rule ◽  
Voting Rules ◽  
Electoral Outcomes ◽  
Lab Experiments ◽  
Voting Rule

This chapter stresses the necessity of distinguishing between a strategic vote and a strategic voter. The sincere voter always casts a sincere vote, while the strategic voter casts a sincere or strategic vote depending on the context and the voting rule. This leads to two definitions of strategic voting: a broad one, where a strategic vote is one that is partly based on expectations about the outcome of the election, and a narrow one, where a strategic vote also entails not voting sincerely. The chapter then reviews three types of empirical research that differ with respect to the type of data used: the observation of electoral outcomes, survey data, and lab experiments. That literature has confirmed that indeed some voters cast a strategic vote, though many studies have found most votes to be sincere. That research has also shown that there is some degree of strategic voting under all kinds of voting rules; that, contrary to conventional wisdom, there is as much strategic voting under proportional representation as under plurality rule; and that the propensity to vote strategically depends very much on the type of information that is available.

scholarly journals Optimal Voting Rules

1995 ◽  
Vol 9 (1) ◽  
pp. 51-64 ◽  
Author(s):  
Peyton Young
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Likelihood Estimation ◽  
Voting Rules ◽  
Voting Rule ◽  
Marquis De Condorcet ◽  
Kenneth Arrow

Modern social choice theory, following Kenneth Arrow, treats voting as a method for aggregating diverse preferences and values. An earlier view, initiated by Marquis de Condorcet, is that voting is a method for aggregating information. Voters’ opinions differ because they make errors of judgment; absent these errors they would all agree on the best choice. The goal is to design a voting rule that identifies the best choice with highest probability. This paper examines maximum likelihood estimation. Surprisingly, the optimal rule can also be axiomatized by variations of Arrow's axioms.

scholarly journals Voting with random classifiers (VORACE): theoretical and experimental analysis

2021 ◽  
Vol 35 (2) ◽  
Author(s):  
Cristina Cornelio ◽  
Michele Donini ◽  
Andrea Loreggia ◽  
Maria Silvia Pini ◽  
Francesca Rossi
Keyword(s):  
State Of The Art ◽  
Empirical Evaluation ◽  
Parameter Tuning ◽  
Voting Rules ◽  
Specific Domain ◽  
Ensemble Technique ◽  
Voting Rule ◽  
Input Sample ◽  
Learning Scenarios ◽  
A New Technique

AbstractIn many machine learning scenarios, looking for the best classifier that fits a particular dataset can be very costly in terms of time and resources. Moreover, it can require deep knowledge of the specific domain. We propose a new technique which does not require profound expertise in the domain and avoids the commonly used strategy of hyper-parameter tuning and model selection. Our method is an innovative ensemble technique that uses voting rules over a set of randomly-generated classifiers. Given a new input sample, we interpret the output of each classifier as a ranking over the set of possible classes. We then aggregate these output rankings using a voting rule, which treats them as preferences over the classes. We show that our approach obtains good results compared to the state-of-the-art, both providing a theoretical analysis and an empirical evaluation of the approach on several datasets.

scholarly journals Persuading Voters: It's Easy to Whisper, It's Hard to Speak Loud

2020 ◽  
Vol 34 (02) ◽  
pp. 1870-1877
Author(s):  
Matteo Castiglioni ◽  
Andrea Celli ◽  
Nicola Gatti
Keyword(s):  
Utility Function ◽  
Natural Question ◽  
Voting Rules ◽  
Expected Return ◽  
Fixed Parameter Tractable ◽  
The Public ◽  
Voting Rule ◽  
Private Signals ◽  
Fixed Parameter ◽  
Public Signals

We focus on the following natural question: is it possible to influence the outcome of a voting process through the strategic provision of information to voters who update their beliefs rationally? We investigate whether it is computationally tractable to design a signaling scheme maximizing the probability with which the sender's preferred candidate is elected. We resort to the model recently introduced by Arieli and Babichenko (2019) (i.e., without inter-agent externalities), and focus on, as illustrative examples, k-voting rules and plurality voting. There is a sharp contrast between the case in which private signals are allowed and the more restrictive setting in which only public signals are allowed. In the former, we show that an optimal signaling scheme can be computed efficiently both under a k-voting rule and plurality voting. In establishing these results, we provide two contributions applicable to general settings beyond voting. Specifically, we extend a well-known result by Dughmi and Xu (2017) to more general settings and prove that, when the sender's utility function is anonymous, computing an optimal signaling scheme is fixed-parameter tractable in the number of receivers' actions. In the public signaling case, we show that the sender's optimal expected return cannot be approximated to within any factor under a k-voting rule. This negative result easily extends to plurality voting and problems where utility functions are anonymous.

scholarly journals Convergence of Iterative Scoring Rules

2016 ◽  
Vol 57 ◽  
pp. 573-591 ◽  
Author(s):  
Omer Lev ◽  
Jeffrey S. Rosenschein
Keyword(s):  
Linear Order ◽  
Scoring Rules ◽  
Voting Systems ◽  
Choice Functions ◽  
Stable States ◽  
Voting Rules ◽  
Voting Rule ◽  
Social Choice Functions ◽  
Breaking Mechanism ◽  
Iterative Voting

In multiagent systems, social choice functions can help aggregate the distinct preferences that agents have over alternatives, enabling them to settle on a single choice. Despite the basic manipulability of all reasonable voting systems, it would still be desirable to find ways to reach plausible outcomes, which are stable states, i.e., a situation where no agent would wish to change its vote. One possibility is an iterative process in which, after everyone initially votes, participants may change their votes, one voter at a time. This technique, explored in previous work, converges to a Nash equilibrium when Plurality voting is used, along with a tie-breaking rule that chooses a winner according to a linear order of preferences over candidates. In this paper, we both consider limitations of the iterative voting method, as well as expanding upon it. We demonstrate the significance of tie-breaking rules, showing that no iterative scoring rule converges for all tie-breaking. However, using a restricted tie-breaking rule (such as the linear order rule used in previous work) does not by itself ensure convergence. We prove that in addition to plurality, the veto voting rule converges as well using a linear order tie-breaking rule. However, we show that these two voting rules are the only scoring rules that converge, regardless of tie-breaking mechanism.

scholarly journals Voting Rules in Sequential Search by Committees: Theory and Experiments

2019 ◽  
Vol 65 (9) ◽  
pp. 4349-4364
Author(s):  
Vincent Mak ◽  
Darryl A. Seale ◽  
Amnon Rapoport ◽  
Eyran J. Gisches
Keyword(s):  
Decision Makers ◽  
Majority Voting ◽  
Secretary Problem ◽  
Sequential Search ◽  
Voting Rules ◽  
Unanimity Rule ◽  
Game Theoretic Analysis ◽  
Voting Rule ◽  
Game Theoretic ◽  
The Individual

We propose a committee extension of the individual sequential search model called the “secretary problem,” where collective decisions on when to stop the search are reached via a prespecified voting rule. We offer a game-theoretic analysis of our model and then report two experiments on three-person committees with either uncorrelated or perfectly correlated preferences under three different voting rules followed by a third experiment on single decision makers. Relative to equilibrium predictions, committees with uncorrelated preferences oversearched under minority and majority voting rules but, otherwise, undersearched or approximated equilibrium play. Individually, committee members were often less strategic when their preferences were uncorrelated than when they were perfectly correlated. Collectively, committees’ decisions were more strategic than single decision makers’ only under the unanimity rule, although still not significantly better in terms of the decision makers’ welfare. Finally, across our experiments that involved committee search, the unanimity rule always optimized committee welfare. This paper was accepted by Yan Chen, behavioral economics.

scholarly journals Efficiency, Equity, and Timing of Voting Mechanisms

2007 ◽  
Vol 101 (3) ◽  
pp. 409-424 ◽  
Author(s):  
MARCO BATTAGLINI ◽  
REBECCA MORTON ◽  
THOMAS PALFREY
Keyword(s):  
Political Institutions ◽  
Laboratory Experiments ◽  
Information Aggregation ◽  
Voting Rules ◽  
Voting Games ◽  
Voting Rule ◽  
Sequential Voting ◽  
Participation Costs ◽  
Voting Mechanisms ◽  
Better Than

We compare the behavior of voters under simultaneous and sequential voting rules when voting is costly and information is incomplete. In many political institutions, ranging from small committees to mass elections, voting is sequential, which allows some voters to know the choices of earlier voters. For a stylized model, we generate a variety of predictions about the relative efficiency and participation equity of these two systems, which we test using controlled laboratory experiments. Most of the qualitative predictions are supported by the data, but there are significant departures from the predicted equilibrium strategies, in both the sequential and the simultaneous voting games. We find a tradeoff between information aggregation, efficiency, and equity in sequential voting: a sequential voting rule aggregates information better than simultaneous voting and is more efficient in some information environments, but sequential voting is inequitable because early voters bear more participation costs.

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