Arkadii Slinko | The University of Auckland (original) (raw)

Papers by Arkadii Slinko

Research paper thumbnail of Right representations of algebras

Algebra and Logic, Sep 1, 1974

UDC 519.48 A/I into End¢ (IV) induced by the representation j9 is not a right representahon of th... more UDC 519.48 A/I into End¢ (IV) induced by the representation j9 is not a right representahon of the algebra A. Here the algebra A can be even associative and finite-dimensional. *Dedicated to the memory of our teacher, Konstantin Aleksandrovich Zhevlakov.

Research paper thumbnail of Achieving Fully Proportional Representation: Approximability Results

arXiv (Cornell University), Dec 14, 2013

Research paper thumbnail of Fully Proportional Representation as Resource Allocation: Approximability Results

arXiv (Cornell University), Aug 8, 2012

We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource a... more We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexity-theoretic assumptions, there are no constantfactor approximation algorithms. Yet, we also show cases where good approximation algorithms exist (briefly put, these variants correspond to optimizing total voter satisfaction under Borda scores, within Monroe's and Chamberlin and Courant's voting systems).

Research paper thumbnail of Modeling Representation of Minorities Under Multiwinner Voting Rules

arXiv (Cornell University), Apr 8, 2016

The goal of this paper is twofold. First and foremost, we aim to experimentally and quantitativel... more The goal of this paper is twofold. First and foremost, we aim to experimentally and quantitatively show that the choice of a multiwinner voting rule can play a crucial role on the way minorities are represented. We also test the possibility for some of these rules to achieve proportional representation.

Research paper thumbnail of Committee Scoring Rules: Axiomatic Characterization and Hierarchy

arXiv (Cornell University), Feb 19, 2018

Committee scoring voting rules are multiwinner analogues of positional scoring rules which consti... more Committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-kcounting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and k-Approval Chamberlin-Courant as the only nontrivial rules in pairwise intersections of these classes. We provide some axiomatic characterizations for these classes, where monotonicity properties appear to be especially useful. The class of decomposable rules is new to the literature. We show that it strictly contains the class of OWA-based rules and describe some of the applications of decomposable rules.

Research paper thumbnail of Voting-based group formation

International Joint Conference on Artificial Intelligence, Jul 9, 2016

We study a combinatorial problem formulated in terms of the following group-formation scenario. G... more We study a combinatorial problem formulated in terms of the following group-formation scenario. Given some agents, where each agent has preferences over the set of potential group leaders, the task is to partition the agents into groups and assign a group leader to each of them, so that the group leaders have as high support as possible from the groups they are assigned to lead. We model this scenario as a voting problem, where the goal is to partition a set of voters into a prescribed number of groups so that each group elects its leader, i.e., their leader is a unique winner in the corresponding election. We study the computational complexity of this problem (and several of its variants) for Approval elections.

Research paper thumbnail of Homogeneity and monotonicity of distance-rationalizable voting rules

Adaptive Agents and Multi-Agents Systems, May 2, 2011

Distance rationalizability is a framework for classifying voting rules by interpreting them in te... more Distance rationalizability is a framework for classifying voting rules by interpreting them in terms of distances and consensus classes. It also allows to design new voting rules with desired properties. A particularly natural and versatile class of distances that can be used for this purpose is that of votewise distances [12], which "lift" distances over individual votes to distances over entire elections using a suitable norm. In this paper, we continue the investigation of the properties of votewise distance-rationalizable rules initiated in [12]. We describe a number of general conditions on distances and consensus classes that ensure that the resulting voting rule is homogeneous or monotone. This complements the results of [12], where the authors focus on anonymity, neutrality and consistency. We also introduce a new class of voting rules, that can be viewed as "majority variants" of classic scoring rules, and have a natural interpretation in the context of distance rationalizability.

Research paper thumbnail of Achieving Fully Proportional Representation by Clustering Voters

Adaptive Agents and Multi-Agents Systems, May 9, 2016

We provide experimental evaluation of a number of known and new algorithms for approximate comput... more We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe's and Chamberlin-Courant's rules. Our experiments, conducted both on real-life preference-aggregation data and on synthetic data, show that even very simple and fast algorithms can in many cases find near-perfect solutions. Our results confirm and complement very recent theoretical analysis of Skowron et al., who have shown good lower bounds on the quality of (some of) the algorithms that we study.

Research paper thumbnail of Multiwinner Rules with Variable Number of Winners

European Conference on Artificial Intelligence, 2020

We consider voting rules for approval-based elections that select committees whose size is not pr... more We consider voting rules for approval-based elections that select committees whose size is not predetermined. Unlike the study of rules that output committees with a predetermined number of winning candidates, the study of rules that select a variable number of winners has only recently been initiated. We first mention some scenarios for which such rules are applicable. Then, aiming at better understanding these rules, we study their computational properties and report on simulations regarding the sizes of their committees.

Research paper thumbnail of Multiwinner Analogues of the Plurality Rule: Axiomatic and Algorithmic Perspectives

Proceedings of the ... AAAI Conference on Artificial Intelligence, Feb 21, 2016

Research paper thumbnail of What Do Multiwinner Voting Rules Do? An Experiment Over the Two-Dimensional Euclidean Domain

Proceedings of the ... AAAI Conference on Artificial Intelligence, Feb 10, 2017

We visualize aggregate outputs of popular multiwinner voting rules-SNTV, STV, Bloc, k-Borda, Monr... more We visualize aggregate outputs of popular multiwinner voting rules-SNTV, STV, Bloc, k-Borda, Monroe, Chamberlin-Courant, and PAV-for elections generated according to the two-dimensional Euclidean model. We consider three applications of multiwinner voting, namely, parliamentary elections, portfolio/movie selection, and shortlisting, and use our results to understand which of our rules seem to be best suited for each application. In particular, we show that STV (one of the few nontrivial rules used in real high-stake elections) exhibits excellent performance, whereas the Bloc rule (also often used in practice) performs poorly.

Research paper thumbnail of Achieving fully proportional representation is easy in practice

arXiv (Cornell University), May 6, 2013

We provide experimental evaluation of a number of known and new algorithms for approximate comput... more We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe's and Chamberlin-Courant's rules. Our experiments, conducted both on real-life preference-aggregation data and on synthetic data, show that even very simple and fast algorithms can in many cases find near-perfect solutions. Our results confirm and complement very recent theoretical analysis of Skowron et al., who have shown good lower bounds on the quality of (some of) the algorithms that we study.

Research paper thumbnail of Committee scoring rules: axiomatic classification and hierarchy

International Joint Conference on Artificial Intelligence, Jul 9, 2016

We consider several natural classes of committee scoring rules, namely, weakly separable, represe... more We consider several natural classes of committee scoring rules, namely, weakly separable, representation-focused, top-k-counting, OWAbased, and decomposable rules. We study some of their axiomatic properties, especially properties of monotonicity, and concentrate on containment relations between them. We characterize SNTV, Bloc, and k-approval Chamberlin-Courant, as the only rules in certain intersections of these classes. We introduce decomposable rules, describe some of their applications, and show that the class of decomposable rules strictly contains the class of OWA-based rules.

Research paper thumbnail of Committee Scoring Rules

ACM transactions on economics and computation, Feb 23, 2019

Committee scoring voting rules are multiwinner analogues of positional scoring rules which consti... more Committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-kcounting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and k-Approval Chamberlin-Courant as the only nontrivial rules in pairwise intersections of these classes. We provide some axiomatic characterizations for these classes, where monotonicity properties appear to be especially useful. The class of decomposable rules is new to the literature. We show that it strictly contains the class of OWA-based rules and describe some of the applications of decomposable rules.

Research paper thumbnail of Cloning in elections: finding the possible winners

arXiv (Cornell University), Sep 1, 2011

We consider the problem of manipulating elections by cloning candidates. In our model, a manipula... more We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote with a block of these new candidates, ranked consecutively. The outcome of the resulting election may then depend on the number of clones as well as on how each voter orders the clones within the block. We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of common voting rules, characterize the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each clone, and study the complexity of finding a minimum-cost cloning manipulation. Finally, we compare cloning with two related problems: the problem of control by adding candidates and the problem of possible (co)winners when new alternatives can join.

Research paper thumbnail of Distance rationalization of voting rules

Social Choice and Welfare, Apr 17, 2015

The concept of distance rationalizability allows one to define new voting rules or rationalize ex... more The concept of distance rationalizability allows one to define new voting rules or rationalize existing ones via a consensus, i.e., a class of elections that have a unique, indisputable winner, and a distance over elections: A candidate is declared an election winner if she is the consensus candidate in one of the nearest consensus elections. Many classic voting rules are defined or can be represented in this way. In this paper, we focus on the power and the limitations of the distance rationalizability approach. Lerer and Nitzan (1985) and Campbell and Nitzan (1986) show that if we do not place any restrictions on the notions of distance and consensus then essentially all voting rules can be distance-rationalized. We identify a natural class of distances on electionsvotewise distances-which depend on the submitted votes in a simple and transparent manner, and investigate which voting rules can be rationalized via distances of this type. We also study axiomatic properties of rules that can be defined via votewise distances.

Research paper thumbnail of On distance rationalizability of some voting rules

The concept of distance rationalizability has several applications within social choice. In the c... more The concept of distance rationalizability has several applications within social choice. In the context of voting, it allows one to define ("rationalize") voting rules via a consensus class (roughly, a set of elections in which it is obvious who should win) and a distance function: namely, a candidate is said to be an election winner if it is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be represented in this manner. In this paper, we provide new results on distance rationalizability of several well-known voting rules such as all scoring rules, Approval, Young's rule and Maximin. We also show that a previously published proof of distance rationalizability of Young's rule is incorrect: the consensus notion and the distance function used in that proof give rise to a voting rule that is similar to-but distinct from-the Young's rule. Finally, we demonstrate that some voting rules cannot be rationalized via certain notions of consensus. To the best of our knowledge, these are the first non-distance-rationalizability results for voting rules.

Research paper thumbnail of Multiwinner Voting: A New Challenge for Social Choice Theory

Research paper thumbnail of Swap Bribery

Springer eBooks, 2009

In voting theory, bribery is a form of manipulative behavior in which an external actor (the brib... more In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that the voter is asked to implement. Specifically, in our model the briber can change a voter's preference list by paying for a sequence of swaps of consecutive candidates. Each swap may have a different price; the price of a bribery is the sum of the prices of all swaps that it involves. We prove complexity results for this model, which we call swap bribery, for a broad class of election systems, including variants of approval and k-approval, Borda, Copeland, and maximin.

Research paper thumbnail of Good Rationalizations of Voting Rules

Proceedings of the ... AAAI Conference on Artificial Intelligence, Jul 4, 2010

We explore the relationship between two approaches to rationalizing voting rules: the maximum lik... more We explore the relationship between two approaches to rationalizing voting rules: the maximum likelihood estimation (MLE) framework originally suggested by Condorcet and recently studied in (Conitzer and Sandholm 2005; Conitzer, Rognlie, and Xia 2009) and the distance rationalizability (DR) framework (Meskanen and Nurmi 2008; Elkind, Faliszewski, and Slinko 2009). The former views voting as an attempt to reconstruct the correct ordering of the candidates given noisy estimates (i.e., votes), while the latter explains voting as search for the nearest consensus outcome. We provide conditions under which an MLE interpretation of a voting rule coincides with its DR interpretation, and classify a number of classic voting rules, such as Kemeny, Plurality, Borda and Single Transferable Vote (STV), according to how well they fit each of these frameworks. The classification we obtain is more precise than the ones that result from using MLE or DR alone: indeed, we show that the MLE approach can be used to guide our search for a more refined notion of distance rationalizability and vice versa.

Research paper thumbnail of Right representations of algebras

Algebra and Logic, Sep 1, 1974

UDC 519.48 A/I into End¢ (IV) induced by the representation j9 is not a right representahon of th... more UDC 519.48 A/I into End¢ (IV) induced by the representation j9 is not a right representahon of the algebra A. Here the algebra A can be even associative and finite-dimensional. *Dedicated to the memory of our teacher, Konstantin Aleksandrovich Zhevlakov.

Research paper thumbnail of Achieving Fully Proportional Representation: Approximability Results

arXiv (Cornell University), Dec 14, 2013

Research paper thumbnail of Fully Proportional Representation as Resource Allocation: Approximability Results

arXiv (Cornell University), Aug 8, 2012

We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource a... more We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexity-theoretic assumptions, there are no constantfactor approximation algorithms. Yet, we also show cases where good approximation algorithms exist (briefly put, these variants correspond to optimizing total voter satisfaction under Borda scores, within Monroe's and Chamberlin and Courant's voting systems).

Research paper thumbnail of Modeling Representation of Minorities Under Multiwinner Voting Rules

arXiv (Cornell University), Apr 8, 2016

The goal of this paper is twofold. First and foremost, we aim to experimentally and quantitativel... more The goal of this paper is twofold. First and foremost, we aim to experimentally and quantitatively show that the choice of a multiwinner voting rule can play a crucial role on the way minorities are represented. We also test the possibility for some of these rules to achieve proportional representation.

Research paper thumbnail of Committee Scoring Rules: Axiomatic Characterization and Hierarchy

arXiv (Cornell University), Feb 19, 2018

Committee scoring voting rules are multiwinner analogues of positional scoring rules which consti... more Committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-kcounting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and k-Approval Chamberlin-Courant as the only nontrivial rules in pairwise intersections of these classes. We provide some axiomatic characterizations for these classes, where monotonicity properties appear to be especially useful. The class of decomposable rules is new to the literature. We show that it strictly contains the class of OWA-based rules and describe some of the applications of decomposable rules.

Research paper thumbnail of Voting-based group formation

International Joint Conference on Artificial Intelligence, Jul 9, 2016

We study a combinatorial problem formulated in terms of the following group-formation scenario. G... more We study a combinatorial problem formulated in terms of the following group-formation scenario. Given some agents, where each agent has preferences over the set of potential group leaders, the task is to partition the agents into groups and assign a group leader to each of them, so that the group leaders have as high support as possible from the groups they are assigned to lead. We model this scenario as a voting problem, where the goal is to partition a set of voters into a prescribed number of groups so that each group elects its leader, i.e., their leader is a unique winner in the corresponding election. We study the computational complexity of this problem (and several of its variants) for Approval elections.

Research paper thumbnail of Homogeneity and monotonicity of distance-rationalizable voting rules

Adaptive Agents and Multi-Agents Systems, May 2, 2011

Distance rationalizability is a framework for classifying voting rules by interpreting them in te... more Distance rationalizability is a framework for classifying voting rules by interpreting them in terms of distances and consensus classes. It also allows to design new voting rules with desired properties. A particularly natural and versatile class of distances that can be used for this purpose is that of votewise distances [12], which "lift" distances over individual votes to distances over entire elections using a suitable norm. In this paper, we continue the investigation of the properties of votewise distance-rationalizable rules initiated in [12]. We describe a number of general conditions on distances and consensus classes that ensure that the resulting voting rule is homogeneous or monotone. This complements the results of [12], where the authors focus on anonymity, neutrality and consistency. We also introduce a new class of voting rules, that can be viewed as "majority variants" of classic scoring rules, and have a natural interpretation in the context of distance rationalizability.

Research paper thumbnail of Achieving Fully Proportional Representation by Clustering Voters

Adaptive Agents and Multi-Agents Systems, May 9, 2016

We provide experimental evaluation of a number of known and new algorithms for approximate comput... more We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe's and Chamberlin-Courant's rules. Our experiments, conducted both on real-life preference-aggregation data and on synthetic data, show that even very simple and fast algorithms can in many cases find near-perfect solutions. Our results confirm and complement very recent theoretical analysis of Skowron et al., who have shown good lower bounds on the quality of (some of) the algorithms that we study.

Research paper thumbnail of Multiwinner Rules with Variable Number of Winners

European Conference on Artificial Intelligence, 2020

We consider voting rules for approval-based elections that select committees whose size is not pr... more We consider voting rules for approval-based elections that select committees whose size is not predetermined. Unlike the study of rules that output committees with a predetermined number of winning candidates, the study of rules that select a variable number of winners has only recently been initiated. We first mention some scenarios for which such rules are applicable. Then, aiming at better understanding these rules, we study their computational properties and report on simulations regarding the sizes of their committees.

Research paper thumbnail of Multiwinner Analogues of the Plurality Rule: Axiomatic and Algorithmic Perspectives

Proceedings of the ... AAAI Conference on Artificial Intelligence, Feb 21, 2016

Research paper thumbnail of What Do Multiwinner Voting Rules Do? An Experiment Over the Two-Dimensional Euclidean Domain

Proceedings of the ... AAAI Conference on Artificial Intelligence, Feb 10, 2017

We visualize aggregate outputs of popular multiwinner voting rules-SNTV, STV, Bloc, k-Borda, Monr... more We visualize aggregate outputs of popular multiwinner voting rules-SNTV, STV, Bloc, k-Borda, Monroe, Chamberlin-Courant, and PAV-for elections generated according to the two-dimensional Euclidean model. We consider three applications of multiwinner voting, namely, parliamentary elections, portfolio/movie selection, and shortlisting, and use our results to understand which of our rules seem to be best suited for each application. In particular, we show that STV (one of the few nontrivial rules used in real high-stake elections) exhibits excellent performance, whereas the Bloc rule (also often used in practice) performs poorly.

Research paper thumbnail of Achieving fully proportional representation is easy in practice

arXiv (Cornell University), May 6, 2013

We provide experimental evaluation of a number of known and new algorithms for approximate comput... more We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe's and Chamberlin-Courant's rules. Our experiments, conducted both on real-life preference-aggregation data and on synthetic data, show that even very simple and fast algorithms can in many cases find near-perfect solutions. Our results confirm and complement very recent theoretical analysis of Skowron et al., who have shown good lower bounds on the quality of (some of) the algorithms that we study.

Research paper thumbnail of Committee scoring rules: axiomatic classification and hierarchy

International Joint Conference on Artificial Intelligence, Jul 9, 2016

We consider several natural classes of committee scoring rules, namely, weakly separable, represe... more We consider several natural classes of committee scoring rules, namely, weakly separable, representation-focused, top-k-counting, OWAbased, and decomposable rules. We study some of their axiomatic properties, especially properties of monotonicity, and concentrate on containment relations between them. We characterize SNTV, Bloc, and k-approval Chamberlin-Courant, as the only rules in certain intersections of these classes. We introduce decomposable rules, describe some of their applications, and show that the class of decomposable rules strictly contains the class of OWA-based rules.

Research paper thumbnail of Committee Scoring Rules

ACM transactions on economics and computation, Feb 23, 2019

Committee scoring voting rules are multiwinner analogues of positional scoring rules which consti... more Committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-kcounting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and k-Approval Chamberlin-Courant as the only nontrivial rules in pairwise intersections of these classes. We provide some axiomatic characterizations for these classes, where monotonicity properties appear to be especially useful. The class of decomposable rules is new to the literature. We show that it strictly contains the class of OWA-based rules and describe some of the applications of decomposable rules.

Research paper thumbnail of Cloning in elections: finding the possible winners

arXiv (Cornell University), Sep 1, 2011

We consider the problem of manipulating elections by cloning candidates. In our model, a manipula... more We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote with a block of these new candidates, ranked consecutively. The outcome of the resulting election may then depend on the number of clones as well as on how each voter orders the clones within the block. We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of common voting rules, characterize the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each clone, and study the complexity of finding a minimum-cost cloning manipulation. Finally, we compare cloning with two related problems: the problem of control by adding candidates and the problem of possible (co)winners when new alternatives can join.

Research paper thumbnail of Distance rationalization of voting rules

Social Choice and Welfare, Apr 17, 2015

The concept of distance rationalizability allows one to define new voting rules or rationalize ex... more The concept of distance rationalizability allows one to define new voting rules or rationalize existing ones via a consensus, i.e., a class of elections that have a unique, indisputable winner, and a distance over elections: A candidate is declared an election winner if she is the consensus candidate in one of the nearest consensus elections. Many classic voting rules are defined or can be represented in this way. In this paper, we focus on the power and the limitations of the distance rationalizability approach. Lerer and Nitzan (1985) and Campbell and Nitzan (1986) show that if we do not place any restrictions on the notions of distance and consensus then essentially all voting rules can be distance-rationalized. We identify a natural class of distances on electionsvotewise distances-which depend on the submitted votes in a simple and transparent manner, and investigate which voting rules can be rationalized via distances of this type. We also study axiomatic properties of rules that can be defined via votewise distances.

Research paper thumbnail of On distance rationalizability of some voting rules

The concept of distance rationalizability has several applications within social choice. In the c... more The concept of distance rationalizability has several applications within social choice. In the context of voting, it allows one to define ("rationalize") voting rules via a consensus class (roughly, a set of elections in which it is obvious who should win) and a distance function: namely, a candidate is said to be an election winner if it is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be represented in this manner. In this paper, we provide new results on distance rationalizability of several well-known voting rules such as all scoring rules, Approval, Young's rule and Maximin. We also show that a previously published proof of distance rationalizability of Young's rule is incorrect: the consensus notion and the distance function used in that proof give rise to a voting rule that is similar to-but distinct from-the Young's rule. Finally, we demonstrate that some voting rules cannot be rationalized via certain notions of consensus. To the best of our knowledge, these are the first non-distance-rationalizability results for voting rules.

Research paper thumbnail of Multiwinner Voting: A New Challenge for Social Choice Theory

Research paper thumbnail of Swap Bribery

Springer eBooks, 2009

In voting theory, bribery is a form of manipulative behavior in which an external actor (the brib... more In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that the voter is asked to implement. Specifically, in our model the briber can change a voter's preference list by paying for a sequence of swaps of consecutive candidates. Each swap may have a different price; the price of a bribery is the sum of the prices of all swaps that it involves. We prove complexity results for this model, which we call swap bribery, for a broad class of election systems, including variants of approval and k-approval, Borda, Copeland, and maximin.

Research paper thumbnail of Good Rationalizations of Voting Rules

Proceedings of the ... AAAI Conference on Artificial Intelligence, Jul 4, 2010

We explore the relationship between two approaches to rationalizing voting rules: the maximum lik... more We explore the relationship between two approaches to rationalizing voting rules: the maximum likelihood estimation (MLE) framework originally suggested by Condorcet and recently studied in (Conitzer and Sandholm 2005; Conitzer, Rognlie, and Xia 2009) and the distance rationalizability (DR) framework (Meskanen and Nurmi 2008; Elkind, Faliszewski, and Slinko 2009). The former views voting as an attempt to reconstruct the correct ordering of the candidates given noisy estimates (i.e., votes), while the latter explains voting as search for the nearest consensus outcome. We provide conditions under which an MLE interpretation of a voting rule coincides with its DR interpretation, and classify a number of classic voting rules, such as Kemeny, Plurality, Borda and Single Transferable Vote (STV), according to how well they fit each of these frameworks. The classification we obtain is more precise than the ones that result from using MLE or DR alone: indeed, we show that the MLE approach can be used to guide our search for a more refined notion of distance rationalizability and vice versa.