mark c. wilson - aucklandmcw/research/... · mark c. wilson. overview missing the point? i focusing...
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![Page 1: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/1.jpg)
Welfare implications of strategic voting
Mark C. Wilson
Department of Computer ScienceUniversity of Auckland
www.cs.auckland.ac.nz/˜mcw/
CMSS Summer Workshop, 2013-12-11
Mark C. Wilson
![Page 2: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/2.jpg)
Overview
References
I Aki Lehtinen. The welfare consequences of strategic behaviourunder approval and plurality voting. European J. PoliticalEconomy 2008.
I Keith Dowding and Martin van Hees. In Praise ofManipulation. British J. Political Science 2007.
I David Thompson et al. Empirical Aspects of Plurality ElectionEquilibria. Proceedings AAMAS 2013.
I Lirong Xia and Vincent Conitzer. Stackelberg Voting Games.Proceedings AAAI 2010.
I Simina Branzei, Ioannis Caragiannis, Jamie Morgenstern, ArielProcaccia. How Bad is Selfish Voting? Proceedings AAAI2013.
Mark C. Wilson
![Page 3: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/3.jpg)
Overview
References
I Aki Lehtinen. The welfare consequences of strategic behaviourunder approval and plurality voting. European J. PoliticalEconomy 2008.
I Keith Dowding and Martin van Hees. In Praise ofManipulation. British J. Political Science 2007.
I David Thompson et al. Empirical Aspects of Plurality ElectionEquilibria. Proceedings AAMAS 2013.
I Lirong Xia and Vincent Conitzer. Stackelberg Voting Games.Proceedings AAAI 2010.
I Simina Branzei, Ioannis Caragiannis, Jamie Morgenstern, ArielProcaccia. How Bad is Selfish Voting? Proceedings AAAI2013.
Mark C. Wilson
![Page 4: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/4.jpg)
Overview
References
I Aki Lehtinen. The welfare consequences of strategic behaviourunder approval and plurality voting. European J. PoliticalEconomy 2008.
I Keith Dowding and Martin van Hees. In Praise ofManipulation. British J. Political Science 2007.
I David Thompson et al. Empirical Aspects of Plurality ElectionEquilibria. Proceedings AAMAS 2013.
I Lirong Xia and Vincent Conitzer. Stackelberg Voting Games.Proceedings AAAI 2010.
I Simina Branzei, Ioannis Caragiannis, Jamie Morgenstern, ArielProcaccia. How Bad is Selfish Voting? Proceedings AAAI2013.
Mark C. Wilson
![Page 5: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/5.jpg)
Overview
References
I Aki Lehtinen. The welfare consequences of strategic behaviourunder approval and plurality voting. European J. PoliticalEconomy 2008.
I Keith Dowding and Martin van Hees. In Praise ofManipulation. British J. Political Science 2007.
I David Thompson et al. Empirical Aspects of Plurality ElectionEquilibria. Proceedings AAMAS 2013.
I Lirong Xia and Vincent Conitzer. Stackelberg Voting Games.Proceedings AAAI 2010.
I Simina Branzei, Ioannis Caragiannis, Jamie Morgenstern, ArielProcaccia. How Bad is Selfish Voting? Proceedings AAAI2013.
Mark C. Wilson
![Page 6: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/6.jpg)
Overview
References
I Aki Lehtinen. The welfare consequences of strategic behaviourunder approval and plurality voting. European J. PoliticalEconomy 2008.
I Keith Dowding and Martin van Hees. In Praise ofManipulation. British J. Political Science 2007.
I David Thompson et al. Empirical Aspects of Plurality ElectionEquilibria. Proceedings AAMAS 2013.
I Lirong Xia and Vincent Conitzer. Stackelberg Voting Games.Proceedings AAAI 2010.
I Simina Branzei, Ioannis Caragiannis, Jamie Morgenstern, ArielProcaccia. How Bad is Selfish Voting? Proceedings AAAI2013.
Mark C. Wilson
![Page 7: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/7.jpg)
Overview
Overview
I I report on joint work with Miranda Emery (UoA student),with some computations by Avinash Saxena (IIT Kharagpurstudent). It is still in progress.
I We consider the usual setup of social choice: n voters, each ofwhich has a sincere strict total preference ordering of the mcandidates, yielding a preference profile.
I Each voter must submit a total order of the candidates (theseare the possible actions).
I If each voter has a cardinal utility for each candidate, we havea usual game in normal form. Otherwise, we have an ordinalgame. In each case we call it a voting game.
I Voting games typically have enormously many Nash equilibria(for most rules, each unanimous profile is a NE).
Mark C. Wilson
![Page 8: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/8.jpg)
Overview
Overview
I I report on joint work with Miranda Emery (UoA student),with some computations by Avinash Saxena (IIT Kharagpurstudent). It is still in progress.
I We consider the usual setup of social choice: n voters, each ofwhich has a sincere strict total preference ordering of the mcandidates, yielding a preference profile.
I Each voter must submit a total order of the candidates (theseare the possible actions).
I If each voter has a cardinal utility for each candidate, we havea usual game in normal form. Otherwise, we have an ordinalgame. In each case we call it a voting game.
I Voting games typically have enormously many Nash equilibria(for most rules, each unanimous profile is a NE).
Mark C. Wilson
![Page 9: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/9.jpg)
Overview
Overview
I I report on joint work with Miranda Emery (UoA student),with some computations by Avinash Saxena (IIT Kharagpurstudent). It is still in progress.
I We consider the usual setup of social choice: n voters, each ofwhich has a sincere strict total preference ordering of the mcandidates, yielding a preference profile.
I Each voter must submit a total order of the candidates (theseare the possible actions).
I If each voter has a cardinal utility for each candidate, we havea usual game in normal form. Otherwise, we have an ordinalgame. In each case we call it a voting game.
I Voting games typically have enormously many Nash equilibria(for most rules, each unanimous profile is a NE).
Mark C. Wilson
![Page 10: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/10.jpg)
Overview
Overview
I I report on joint work with Miranda Emery (UoA student),with some computations by Avinash Saxena (IIT Kharagpurstudent). It is still in progress.
I We consider the usual setup of social choice: n voters, each ofwhich has a sincere strict total preference ordering of the mcandidates, yielding a preference profile.
I Each voter must submit a total order of the candidates (theseare the possible actions).
I If each voter has a cardinal utility for each candidate, we havea usual game in normal form. Otherwise, we have an ordinalgame. In each case we call it a voting game.
I Voting games typically have enormously many Nash equilibria(for most rules, each unanimous profile is a NE).
Mark C. Wilson
![Page 11: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/11.jpg)
Overview
Overview
I I report on joint work with Miranda Emery (UoA student),with some computations by Avinash Saxena (IIT Kharagpurstudent). It is still in progress.
I We consider the usual setup of social choice: n voters, each ofwhich has a sincere strict total preference ordering of the mcandidates, yielding a preference profile.
I Each voter must submit a total order of the candidates (theseare the possible actions).
I If each voter has a cardinal utility for each candidate, we havea usual game in normal form. Otherwise, we have an ordinalgame. In each case we call it a voting game.
I Voting games typically have enormously many Nash equilibria(for most rules, each unanimous profile is a NE).
Mark C. Wilson
![Page 12: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/12.jpg)
Overview
Manipulation
I A voting game where the sincere profile is not a Nashequilibrium is called manipulable. The associated game formis called manipulable if there is some preference profile forwhich the game is manipulable.
I In other words, the voting mechanism is not “dominantstrategy incentive compatible”.
I Gibbard and Satterthwaite (1973–75) proved that if m ≥ 3and n ≥ 2, R is onto and R is not a dictatorship, then forsome preference profile, R is manipulable.
I Much research has been carried out in order to understandhow prevalent manipulability is, and how to minimize it.
Mark C. Wilson
![Page 13: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/13.jpg)
Overview
Manipulation
I A voting game where the sincere profile is not a Nashequilibrium is called manipulable. The associated game formis called manipulable if there is some preference profile forwhich the game is manipulable.
I In other words, the voting mechanism is not “dominantstrategy incentive compatible”.
I Gibbard and Satterthwaite (1973–75) proved that if m ≥ 3and n ≥ 2, R is onto and R is not a dictatorship, then forsome preference profile, R is manipulable.
I Much research has been carried out in order to understandhow prevalent manipulability is, and how to minimize it.
Mark C. Wilson
![Page 14: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/14.jpg)
Overview
Manipulation
I A voting game where the sincere profile is not a Nashequilibrium is called manipulable. The associated game formis called manipulable if there is some preference profile forwhich the game is manipulable.
I In other words, the voting mechanism is not “dominantstrategy incentive compatible”.
I Gibbard and Satterthwaite (1973–75) proved that if m ≥ 3and n ≥ 2, R is onto and R is not a dictatorship, then forsome preference profile, R is manipulable.
I Much research has been carried out in order to understandhow prevalent manipulability is, and how to minimize it.
Mark C. Wilson
![Page 15: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/15.jpg)
Overview
Manipulation
I A voting game where the sincere profile is not a Nashequilibrium is called manipulable. The associated game formis called manipulable if there is some preference profile forwhich the game is manipulable.
I In other words, the voting mechanism is not “dominantstrategy incentive compatible”.
I Gibbard and Satterthwaite (1973–75) proved that if m ≥ 3and n ≥ 2, R is onto and R is not a dictatorship, then forsome preference profile, R is manipulable.
I Much research has been carried out in order to understandhow prevalent manipulability is, and how to minimize it.
Mark C. Wilson
![Page 16: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/16.jpg)
Overview
Aside: manipulation in the COMSOC literature
I Bartholdi, Tovey and Trick (1989) showed that finding amanipulation is NP-hard for some natural voting rules (if m isnot fixed).
I They tackled the slightly easier problem of sensitivity — howeasy is it to change the winner?
I This work has been followed by a large number of papersinvestigating complexity of manipulation, mostly for specialvoting rules.
I Usually manipulation by coalitions is studied. Most commonrules are easy to manipulate in this sense (tricky tie-breakingrules or weighted voters can make it hard).
Mark C. Wilson
![Page 17: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/17.jpg)
Overview
Aside: manipulation in the COMSOC literature
I Bartholdi, Tovey and Trick (1989) showed that finding amanipulation is NP-hard for some natural voting rules (if m isnot fixed).
I They tackled the slightly easier problem of sensitivity — howeasy is it to change the winner?
I This work has been followed by a large number of papersinvestigating complexity of manipulation, mostly for specialvoting rules.
I Usually manipulation by coalitions is studied. Most commonrules are easy to manipulate in this sense (tricky tie-breakingrules or weighted voters can make it hard).
Mark C. Wilson
![Page 18: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/18.jpg)
Overview
Aside: manipulation in the COMSOC literature
I Bartholdi, Tovey and Trick (1989) showed that finding amanipulation is NP-hard for some natural voting rules (if m isnot fixed).
I They tackled the slightly easier problem of sensitivity — howeasy is it to change the winner?
I This work has been followed by a large number of papersinvestigating complexity of manipulation, mostly for specialvoting rules.
I Usually manipulation by coalitions is studied. Most commonrules are easy to manipulate in this sense (tricky tie-breakingrules or weighted voters can make it hard).
Mark C. Wilson
![Page 19: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/19.jpg)
Overview
Aside: manipulation in the COMSOC literature
I Bartholdi, Tovey and Trick (1989) showed that finding amanipulation is NP-hard for some natural voting rules (if m isnot fixed).
I They tackled the slightly easier problem of sensitivity — howeasy is it to change the winner?
I This work has been followed by a large number of papersinvestigating complexity of manipulation, mostly for specialvoting rules.
I Usually manipulation by coalitions is studied. Most commonrules are easy to manipulate in this sense (tricky tie-breakingrules or weighted voters can make it hard).
Mark C. Wilson
![Page 20: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/20.jpg)
Overview
Missing the point?
I Focusing exclusively on ease of manipulation misses the point.More important is its effect.
I I don’t see any compelling argument why truthfulness is animportant design criterion for a voting mechanism.
I Satterthwaite has given some arguments. Dowding and vanHees give convincing replies, in my view. In particular,manipulation allows voters to express information suppressedby the rule, and gives them incentive to understand theirfellow voters.
I Even if manipulability is something to be minimized, we knowhow to do that — dictatorship! Clearly there must be otherthings to (co)optimize, such as overall social welfare.
I Why not just study welfare?
Mark C. Wilson
![Page 21: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/21.jpg)
Overview
Missing the point?
I Focusing exclusively on ease of manipulation misses the point.More important is its effect.
I I don’t see any compelling argument why truthfulness is animportant design criterion for a voting mechanism.
I Satterthwaite has given some arguments. Dowding and vanHees give convincing replies, in my view. In particular,manipulation allows voters to express information suppressedby the rule, and gives them incentive to understand theirfellow voters.
I Even if manipulability is something to be minimized, we knowhow to do that — dictatorship! Clearly there must be otherthings to (co)optimize, such as overall social welfare.
I Why not just study welfare?
Mark C. Wilson
![Page 22: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/22.jpg)
Overview
Missing the point?
I Focusing exclusively on ease of manipulation misses the point.More important is its effect.
I I don’t see any compelling argument why truthfulness is animportant design criterion for a voting mechanism.
I Satterthwaite has given some arguments. Dowding and vanHees give convincing replies, in my view. In particular,manipulation allows voters to express information suppressedby the rule, and gives them incentive to understand theirfellow voters.
I Even if manipulability is something to be minimized, we knowhow to do that — dictatorship! Clearly there must be otherthings to (co)optimize, such as overall social welfare.
I Why not just study welfare?
Mark C. Wilson
![Page 23: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/23.jpg)
Overview
Missing the point?
I Focusing exclusively on ease of manipulation misses the point.More important is its effect.
I I don’t see any compelling argument why truthfulness is animportant design criterion for a voting mechanism.
I Satterthwaite has given some arguments. Dowding and vanHees give convincing replies, in my view. In particular,manipulation allows voters to express information suppressedby the rule, and gives them incentive to understand theirfellow voters.
I Even if manipulability is something to be minimized, we knowhow to do that — dictatorship! Clearly there must be otherthings to (co)optimize, such as overall social welfare.
I Why not just study welfare?
Mark C. Wilson
![Page 24: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/24.jpg)
Overview
Missing the point?
I Focusing exclusively on ease of manipulation misses the point.More important is its effect.
I I don’t see any compelling argument why truthfulness is animportant design criterion for a voting mechanism.
I Satterthwaite has given some arguments. Dowding and vanHees give convincing replies, in my view. In particular,manipulation allows voters to express information suppressedby the rule, and gives them incentive to understand theirfellow voters.
I Even if manipulability is something to be minimized, we knowhow to do that — dictatorship! Clearly there must be otherthings to (co)optimize, such as overall social welfare.
I Why not just study welfare?
Mark C. Wilson
![Page 25: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/25.jpg)
Overview
Simulation setupI We aim to study comprehensively the overall welfare effects of
strategic voting, assuming all voters are strategic, for variousgame-theoretic solution concepts.
I We focus on a few common voting rules: plurality, 2-approval,antiplurality, Borda. Will do more later, e.g. Copeland,instant runoff.
I We randomly generate a sample of sincere preference profiles(sometimes with explicit utilities), independently anduniformly. We use both random utilities in [0, 1] and utilitiesimplied by the various rules.
I We use two measures of aggregate welfare: egalitarian(minimum) and utilitarian (mean). We also use netsatisfaction: net fraction of voters who prefer the givenstrategic result to the sincere outcome. All measures arenormalized.
Mark C. Wilson
![Page 26: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/26.jpg)
Overview
Simulation setupI We aim to study comprehensively the overall welfare effects of
strategic voting, assuming all voters are strategic, for variousgame-theoretic solution concepts.
I We focus on a few common voting rules: plurality, 2-approval,antiplurality, Borda. Will do more later, e.g. Copeland,instant runoff.
I We randomly generate a sample of sincere preference profiles(sometimes with explicit utilities), independently anduniformly. We use both random utilities in [0, 1] and utilitiesimplied by the various rules.
I We use two measures of aggregate welfare: egalitarian(minimum) and utilitarian (mean). We also use netsatisfaction: net fraction of voters who prefer the givenstrategic result to the sincere outcome. All measures arenormalized.
Mark C. Wilson
![Page 27: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/27.jpg)
Overview
Simulation setupI We aim to study comprehensively the overall welfare effects of
strategic voting, assuming all voters are strategic, for variousgame-theoretic solution concepts.
I We focus on a few common voting rules: plurality, 2-approval,antiplurality, Borda. Will do more later, e.g. Copeland,instant runoff.
I We randomly generate a sample of sincere preference profiles(sometimes with explicit utilities), independently anduniformly. We use both random utilities in [0, 1] and utilitiesimplied by the various rules.
I We use two measures of aggregate welfare: egalitarian(minimum) and utilitarian (mean). We also use netsatisfaction: net fraction of voters who prefer the givenstrategic result to the sincere outcome. All measures arenormalized.
Mark C. Wilson
![Page 28: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/28.jpg)
Overview
Simulation setupI We aim to study comprehensively the overall welfare effects of
strategic voting, assuming all voters are strategic, for variousgame-theoretic solution concepts.
I We focus on a few common voting rules: plurality, 2-approval,antiplurality, Borda. Will do more later, e.g. Copeland,instant runoff.
I We randomly generate a sample of sincere preference profiles(sometimes with explicit utilities), independently anduniformly. We use both random utilities in [0, 1] and utilitiesimplied by the various rules.
I We use two measures of aggregate welfare: egalitarian(minimum) and utilitarian (mean). We also use netsatisfaction: net fraction of voters who prefer the givenstrategic result to the sincere outcome. All measures arenormalized.
Mark C. Wilson
![Page 29: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/29.jpg)
Overview
Behavioural assumptions
I Sincere voting.
I Subgame perfect Nash equilibrium via backward induction.
I Iterated regret minimization: introduced by Halpern and Pass(2009).
I Simultaneous best-reply: naive Gibbard-Satterthwaitebehaviour.
I 2-pragmatist: vote for your favourite among the top two inthe sincere poll.
I Best-reply dynamics: repeatedly vote in fixed order until Nashequilibrium reached.
Mark C. Wilson
![Page 30: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/30.jpg)
Overview
Behavioural assumptions
I Sincere voting.
I Subgame perfect Nash equilibrium via backward induction.
I Iterated regret minimization: introduced by Halpern and Pass(2009).
I Simultaneous best-reply: naive Gibbard-Satterthwaitebehaviour.
I 2-pragmatist: vote for your favourite among the top two inthe sincere poll.
I Best-reply dynamics: repeatedly vote in fixed order until Nashequilibrium reached.
Mark C. Wilson
![Page 31: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/31.jpg)
Overview
Behavioural assumptions
I Sincere voting.
I Subgame perfect Nash equilibrium via backward induction.
I Iterated regret minimization: introduced by Halpern and Pass(2009).
I Simultaneous best-reply: naive Gibbard-Satterthwaitebehaviour.
I 2-pragmatist: vote for your favourite among the top two inthe sincere poll.
I Best-reply dynamics: repeatedly vote in fixed order until Nashequilibrium reached.
Mark C. Wilson
![Page 32: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/32.jpg)
Overview
Behavioural assumptions
I Sincere voting.
I Subgame perfect Nash equilibrium via backward induction.
I Iterated regret minimization: introduced by Halpern and Pass(2009).
I Simultaneous best-reply: naive Gibbard-Satterthwaitebehaviour.
I 2-pragmatist: vote for your favourite among the top two inthe sincere poll.
I Best-reply dynamics: repeatedly vote in fixed order until Nashequilibrium reached.
Mark C. Wilson
![Page 33: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/33.jpg)
Overview
Behavioural assumptions
I Sincere voting.
I Subgame perfect Nash equilibrium via backward induction.
I Iterated regret minimization: introduced by Halpern and Pass(2009).
I Simultaneous best-reply: naive Gibbard-Satterthwaitebehaviour.
I 2-pragmatist: vote for your favourite among the top two inthe sincere poll.
I Best-reply dynamics: repeatedly vote in fixed order until Nashequilibrium reached.
Mark C. Wilson
![Page 34: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/34.jpg)
Overview
Behavioural assumptions
I Sincere voting.
I Subgame perfect Nash equilibrium via backward induction.
I Iterated regret minimization: introduced by Halpern and Pass(2009).
I Simultaneous best-reply: naive Gibbard-Satterthwaitebehaviour.
I 2-pragmatist: vote for your favourite among the top two inthe sincere poll.
I Best-reply dynamics: repeatedly vote in fixed order until Nashequilibrium reached.
Mark C. Wilson
![Page 35: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/35.jpg)
Overview
Overview of results
I Really bad outcomes can happen (rarely) with almost anysetup.
I Most profiles lead to sincere voting, since one player can’tchange the outcome.
I Many metrics are close to zero (the value for sincere voting).
I Overall welfare performance is best for SPNE, then IRM, then2-pragmatism and naive best reply.
I Net satisfaction is usually positive for SPNE and IRM, butnegative for the other solution concepts. However utilitarianwelfare is (at least slightly) negative for all.
Mark C. Wilson
![Page 36: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/36.jpg)
Overview
Overview of results
I Really bad outcomes can happen (rarely) with almost anysetup.
I Most profiles lead to sincere voting, since one player can’tchange the outcome.
I Many metrics are close to zero (the value for sincere voting).
I Overall welfare performance is best for SPNE, then IRM, then2-pragmatism and naive best reply.
I Net satisfaction is usually positive for SPNE and IRM, butnegative for the other solution concepts. However utilitarianwelfare is (at least slightly) negative for all.
Mark C. Wilson
![Page 37: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/37.jpg)
Overview
Overview of results
I Really bad outcomes can happen (rarely) with almost anysetup.
I Most profiles lead to sincere voting, since one player can’tchange the outcome.
I Many metrics are close to zero (the value for sincere voting).
I Overall welfare performance is best for SPNE, then IRM, then2-pragmatism and naive best reply.
I Net satisfaction is usually positive for SPNE and IRM, butnegative for the other solution concepts. However utilitarianwelfare is (at least slightly) negative for all.
Mark C. Wilson
![Page 38: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/38.jpg)
Overview
Overview of results
I Really bad outcomes can happen (rarely) with almost anysetup.
I Most profiles lead to sincere voting, since one player can’tchange the outcome.
I Many metrics are close to zero (the value for sincere voting).
I Overall welfare performance is best for SPNE, then IRM, then2-pragmatism and naive best reply.
I Net satisfaction is usually positive for SPNE and IRM, butnegative for the other solution concepts. However utilitarianwelfare is (at least slightly) negative for all.
Mark C. Wilson
![Page 39: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/39.jpg)
Overview
Overview of results
I Really bad outcomes can happen (rarely) with almost anysetup.
I Most profiles lead to sincere voting, since one player can’tchange the outcome.
I Many metrics are close to zero (the value for sincere voting).
I Overall welfare performance is best for SPNE, then IRM, then2-pragmatism and naive best reply.
I Net satisfaction is usually positive for SPNE and IRM, butnegative for the other solution concepts. However utilitarianwelfare is (at least slightly) negative for all.
Mark C. Wilson
![Page 40: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/40.jpg)
Overview
Rank of the strategic winner
Figure : 2-pragmatist, plurality m = 4, n = 5
Mark C. Wilson
![Page 41: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/41.jpg)
Overview
Rank of the strategic winner
Figure : Naive best reply, plurality m = 4, n = 5
Mark C. Wilson
![Page 42: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/42.jpg)
Overview
Net satisfaction
Figure : Borda, m = 4, 2 ≤ n ≤ 20
Mark C. Wilson
![Page 43: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/43.jpg)
Overview
Previous work
I Lehtinen (2008) found that utilitarian welfare increased withexpected-utility maximization model and plurality, Borda,approval voting.
I Xia and Conitzer (2010) found positive mean net satisfactionfor plurality when using backward induction (“Stackelbergvoting”).
I Thompson, Leyton-Brown, Lev, Rosenschein (2013) foundpromising welfare results for plurality using a Nash equilibriumrefinement involving a small penalty for insincerity.
I Branzei, Caragiannis, Morgenstern, Procaccia (2013) derived“price of anarchy” results for some rules under best-replydynamics.
Mark C. Wilson
![Page 44: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/44.jpg)
Overview
Previous work
I Lehtinen (2008) found that utilitarian welfare increased withexpected-utility maximization model and plurality, Borda,approval voting.
I Xia and Conitzer (2010) found positive mean net satisfactionfor plurality when using backward induction (“Stackelbergvoting”).
I Thompson, Leyton-Brown, Lev, Rosenschein (2013) foundpromising welfare results for plurality using a Nash equilibriumrefinement involving a small penalty for insincerity.
I Branzei, Caragiannis, Morgenstern, Procaccia (2013) derived“price of anarchy” results for some rules under best-replydynamics.
Mark C. Wilson
![Page 45: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/45.jpg)
Overview
Previous work
I Lehtinen (2008) found that utilitarian welfare increased withexpected-utility maximization model and plurality, Borda,approval voting.
I Xia and Conitzer (2010) found positive mean net satisfactionfor plurality when using backward induction (“Stackelbergvoting”).
I Thompson, Leyton-Brown, Lev, Rosenschein (2013) foundpromising welfare results for plurality using a Nash equilibriumrefinement involving a small penalty for insincerity.
I Branzei, Caragiannis, Morgenstern, Procaccia (2013) derived“price of anarchy” results for some rules under best-replydynamics.
Mark C. Wilson
![Page 46: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/46.jpg)
Overview
Previous work
I Lehtinen (2008) found that utilitarian welfare increased withexpected-utility maximization model and plurality, Borda,approval voting.
I Xia and Conitzer (2010) found positive mean net satisfactionfor plurality when using backward induction (“Stackelbergvoting”).
I Thompson, Leyton-Brown, Lev, Rosenschein (2013) foundpromising welfare results for plurality using a Nash equilibriumrefinement involving a small penalty for insincerity.
I Branzei, Caragiannis, Morgenstern, Procaccia (2013) derived“price of anarchy” results for some rules under best-replydynamics.
Mark C. Wilson
![Page 47: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/47.jpg)
Overview
SummaryI Solution concepts that involve serious reflection by voters
about other voters’ behaviour appear to lead to better overallwelfare than simple heuristics.
I Most solution concepts do about as well as sincere voting byall our measures.
I Strategic behaviour (by individual voters) is probably not animportant issue, practically or theoretically. For largeelectorates, it seems less likely to occur. Even in small ones, itdoesn’t seriously reduce (and can even increase) overallwelfare, unless voters are very naive in their beliefs aboutothers.
I The choice of a voting rule should perhaps be made on moreclassical criteria for an aggregation rule, related to the sinceremodel. And clever manipulation should perhaps beencouraged!
Mark C. Wilson
![Page 48: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/48.jpg)
Overview
SummaryI Solution concepts that involve serious reflection by voters
about other voters’ behaviour appear to lead to better overallwelfare than simple heuristics.
I Most solution concepts do about as well as sincere voting byall our measures.
I Strategic behaviour (by individual voters) is probably not animportant issue, practically or theoretically. For largeelectorates, it seems less likely to occur. Even in small ones, itdoesn’t seriously reduce (and can even increase) overallwelfare, unless voters are very naive in their beliefs aboutothers.
I The choice of a voting rule should perhaps be made on moreclassical criteria for an aggregation rule, related to the sinceremodel. And clever manipulation should perhaps beencouraged!
Mark C. Wilson
![Page 49: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/49.jpg)
Overview
SummaryI Solution concepts that involve serious reflection by voters
about other voters’ behaviour appear to lead to better overallwelfare than simple heuristics.
I Most solution concepts do about as well as sincere voting byall our measures.
I Strategic behaviour (by individual voters) is probably not animportant issue, practically or theoretically. For largeelectorates, it seems less likely to occur. Even in small ones, itdoesn’t seriously reduce (and can even increase) overallwelfare, unless voters are very naive in their beliefs aboutothers.
I The choice of a voting rule should perhaps be made on moreclassical criteria for an aggregation rule, related to the sinceremodel. And clever manipulation should perhaps beencouraged!
Mark C. Wilson
![Page 50: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/50.jpg)
Overview
SummaryI Solution concepts that involve serious reflection by voters
about other voters’ behaviour appear to lead to better overallwelfare than simple heuristics.
I Most solution concepts do about as well as sincere voting byall our measures.
I Strategic behaviour (by individual voters) is probably not animportant issue, practically or theoretically. For largeelectorates, it seems less likely to occur. Even in small ones, itdoesn’t seriously reduce (and can even increase) overallwelfare, unless voters are very naive in their beliefs aboutothers.
I The choice of a voting rule should perhaps be made on moreclassical criteria for an aggregation rule, related to the sinceremodel. And clever manipulation should perhaps beencouraged!
Mark C. Wilson
![Page 51: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/51.jpg)
Overview
Future work
I Investigate what happens when different strategic typesinteract with each other.
I Is it fruitful to consider evolutionarily stable strategies?
I What about strategic manipulation by coalitions (perhapscompeting)?
I Do non-monotonic rules (such as instant runoff/alternativevote) give substantially different results?
Mark C. Wilson
![Page 52: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/52.jpg)
Overview
Future work
I Investigate what happens when different strategic typesinteract with each other.
I Is it fruitful to consider evolutionarily stable strategies?
I What about strategic manipulation by coalitions (perhapscompeting)?
I Do non-monotonic rules (such as instant runoff/alternativevote) give substantially different results?
Mark C. Wilson
![Page 53: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/53.jpg)
Overview
Future work
I Investigate what happens when different strategic typesinteract with each other.
I Is it fruitful to consider evolutionarily stable strategies?
I What about strategic manipulation by coalitions (perhapscompeting)?
I Do non-monotonic rules (such as instant runoff/alternativevote) give substantially different results?
Mark C. Wilson
![Page 54: Mark C. Wilson - Aucklandmcw/Research/... · Mark C. Wilson. Overview Missing the point? I Focusing exclusively on ease of manipulation misses the point. More important is its e ect](https://reader034.vdocuments.mx/reader034/viewer/2022050304/5f6cdd51997e595ef737db7e/html5/thumbnails/54.jpg)
Overview
Future work
I Investigate what happens when different strategic typesinteract with each other.
I Is it fruitful to consider evolutionarily stable strategies?
I What about strategic manipulation by coalitions (perhapscompeting)?
I Do non-monotonic rules (such as instant runoff/alternativevote) give substantially different results?
Mark C. Wilson