Advances in Group Decision and Negotiation 9 Adiel Teixeira de Almeida Danielle Costa Morais Hannu Nurmi Systems, Procedures and Voting Rules in Context A Primer for Voting Rule Selection Advances in Group Decision and Negotiation Volume 9 Series Editor Melvin F. Shakun, New York University, New York, USA The book series, Advances in Group Decision and Negotiation - as an extension of the journal, Group Decision and Negotiation - is motivated by unifying approaches to group decision and negotiation processes. These processes are purposeful, adaptive and complex cybernetic and self-organizing and involve relation and coordination in multiplayer, multicriteria, ill-structured, evolving dynamic problems in which players (agents) both cooperate and conflict. Group decision and negotiation involves the whole process or flow of activities relevanttogroupdecisionandnegotiationsuchas,communicationandinformation sharing, problem definition (representation) and evolution, alternative generation, social-emotional interaction, coordination, leadership, and the resulting action choice. Areas of application include intraorganizational coordination (as in local/global strategy, operations management and integrated design, production, finance, marketing and distribution e.g., as for new products), computer supported collaborative work, labor-management negotiation, interorganizational negotiation (business, government and nonprofits), electronic negotiation and commerce, mobiletechnology,cultureandnegotiation,interculturalandinternationalrelations and negotiation, globalization, terrorism, environmental negotiation, etc. More information about this series at http://www.springer.com/series/5587 Adiel Teixeira de Almeida (cid:129) Danielle Costa Morais (cid:129) Hannu Nurmi Systems, Procedures and Voting Rules in Context A Primer for Voting Rule Selection 123 AdielTeixeira deAlmeida Danielle Costa Morais Universidade FederaldePernambuco Universidade FederaldePernambuco (UFPE) (UFPE) Recife, Brazil Recife, Brazil Hannu Nurmi University of Turku Turku,Finland ISSN 1871-935X Advances in GroupDecision andNegotiation ISBN978-3-030-30954-1 ISBN978-3-030-30955-8 (eBook) https://doi.org/10.1007/978-3-030-30955-8 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Thisbookhasbeeninthemakingforalongtime.Lookingback,afirstwhiffofthe idea for it arose at the Group Decision and Negotiation (GDN) 2012 Conference held in Recife, Brazil, which was organized by Adiel de Almeida and Danielle Morais.Atthisevent,HannuNurmigaveaplenarypresentationonvotingtheoryin whichheoutlinedhowithaddevelopedinhistoricaltermsandhealsosetoutsome oftheprincipalresultsfromsocialchoicetheory.Theensuingdiscussionsrevealed, somewhat to our surprise, that voting theory is not a topic that is typically mulled overingroupdecisionandnegotiationsituations.Yet,itwasrecognizedthatvoting plays an important role in a wide variety of circumstances whether these be for formalreasons(e.g.,elections)orforinformalpurposes(e.g.,impromptugatherings of people at which a decision is taken on an issue of common interest). Business organizations were also known to resort to voting when making important decisions. The background of our deliberations was punctuated by three puzzling obser- vations. First, it was clear that a large number of different voting procedures are used to reach a seemingly common goal: to find the “will of the group,” a shared viewonpolicies,candidatesorsimilarmatters.So,whydowehavesuchavariety of procedures if they all are supposed to deliver the same thing? Second, the properties of the procedures used differ and can lead to strongly contrasting out- comes even when the distribution of opinions is fixed. So, shouldn’t it be asked if some procedures are particularly well suited for some circumstances and work poorlyinothers,andifthisisso,cancontextsbesketchedoutwhichindicatewhere each type of procedure works best? Third, since the business decision-making differs in many respects from political decision-making, is it possible to single out procedures that are particularly appropriate for business contexts? Throughout these discussions, other ideas were put forward about how to go about selecting voting rules, and so, some papers were published by Adiel de AlmeidaandHannuNurmiatGDN2014inToulouse,France,andatGDN2015in Warsaw, Poland. Both papers set out preliminary ideas for a framework for choosingavotingprocedure,whichwasappliedindifferentcontexts:theformerin abusinessorganizationandthelatterinaleisurecontext.Thesepaperswerebased v vi Preface on multi-criteria decision-making/aiding (MCDM/A) models that aim to support decision-makers to select an appropriate voting procedure to reach a decision. Underthatperspective,weresolvedtokeepworkingonthatissueuntilwewere ready to present every idea coherently. It is now four years later, and this book is the result. Our primary motivation in writing it is to offer basic tools that aid decision-makers to make intelligent choices with regard to selecting voting rules thatwillbeusedinbusinesscontexts.Thetoolsconsistofbasicdescriptivedevices, central results, comparisons of existing procedures and explaining some funda- mentalparadoxes.Mostchaptershaveappendiceswhichdiscuss specificproblems inordertoillustratethematerialpresented.Thisisintendedtosupporttheeventual classroom use of the book in advanced courses on business administration and management science. Basically, all the chapters are self-contained. The book is structured into three parts and has a total of 19 chapters. The first part (Chaps. 1–3) deals with the background of voting procedures. Selecting voting rules is seen as a special case of a more general problem of why and how the rules of cooperation emerge in communities. Since the majority principleiscommonlythoughttobethecornerstoneofgroupdecision-making,itis therefore given particular attention in this part of the book. The second part (Chaps. 4–11) presents how voting procedures should be evaluatedandthejustificationforthis.Themainproprietiesandstrategicaspectsof voting procedures are discussed. The discussion in these chapters starts from the classic assumptionabout theindividualswhoengage ingroup decision-making.In particular,theseindividualsareassumedtobeendowedwithconsistentviewsabout thedecisionalternatives.Moretechnically,theyareassumedtohavecompleteand transitive preference relations over the decision alternatives (policies and candi- dates). In addition, the criteria of performance of various voting rules are defined and set out in some detail. We deal with Condorcet criteria, monotonicity criteria, thestrategicpropertiesofrulesandotherissuespertainingtostandardtheory.This partthusbuildsuponthefoundationsofstandardsocialchoicetheory.Theaimisto provide tools for rule selection in contexts where the assumptions of standard theory hold. Thencomes thethirdpart (Chaps. 12–19)oftheframeworkandtheprocessfor choosing rules. Chapter 12 discusses the decision process in the business context andhowtodealwithaggregatingdecision-makingpreferences.Chapter13givesan overview of the MCDM/A methods. Chapter 14 presents the framework for choosing the voting procedure and how it is integrated into the overall decision process in a business organization. Chapters 15–18 present applications of this framework in different contexts, as follows: assessing the readiness of technology for generating energy; tackling a water resource management problem; identifying technology for generating renewable electric power; and evaluating a voting pro- cedure for a Group Decision Support System (GRUS). Finally, Chap. 19 summarizes important issues that should be analyzed when choosing a voting procedure. Preface vii Overthelongprocessofwritingupthisbook,theauthorshaveincurredalarge number of intellectual debts, in fact too many to be exhaustively enumerated here. We are extremely grateful to everyone whom we have consulted for their advice and opinions and/or who have taken part in trialling our material. We attempt to acknowledge all this below. Adiel deAlmeida andDanielleMoraiswouldliketothanktheircolleagues and students, who jointly worked with them on modeling MCDM/A problems in diversecontextsandwhohavetaughtorstudiedattheCenterforDecisionSystems and Information Development (CDSID) of Universidade Federal de Pernambuco (UFPE). From CDSID, they acknowledge, in particular, the valuable contributions madebyAnaPaulaCosta,LucianaHazin,JonatasdeAlmeida,EduardaAsforaFrej andLuciaRoselli.TheyalsothankPascaleZaratéforadditionalinformationgiven inordertoorganizetheapplicationinrelationtoGRUS(inChap.18).Theyarealso grateful to their sponsors (especially CNPq—the Brazilian Research Council) for their partial financial support and also to CGEE (Centro de Gestão e Estudos Estratégicos,inEnglish,theCenterforManagementandStrategicStudies)forthe valuable information for the application in Chap. 15. HannuNurmi isgrateful to Dan S. Felsenthal oftheUniversity ofHaifa, Israel, for cooperating with him over a long period. Some results of this cooperation are referred to in this book. Our thanks are also due to Professors Maija Setälä and Matti Wiberg of the University of Turku, Finland, for hosting meetings where preliminary versions of this work were discussed and developed. AdieldeAlmeidaandHannuNurmialsogreatlyvaluedtheinteractionwithLihi Dery of Ariel University, Israel, arising from some discussions on applying the proposed framework in the context of leisure activities. Wewouldliketoacknowledgethatsomepassagesinthisbookhavebeentaken fromearlierstudiesofHannuNurmiandAdieldeAlmeida,previouslypublishedin Springerbooksorjournals.Moreparticularly,theyacknowledgethatChap.5draws on Nurmi’s contribution to Transactions of Computational Collective Intelligence XXXIII, pp. 149–168; Chap. 7 draws on Nurmi’s contribution to the GDN 2015 volume (ed. by T. Tzapiro et al.); Chap. 9 (Sects. 9.1–9.3) draws on Nurmi’s monograph Voting Procedures under Uncertainty (pp. 49–59); Chap. 13 draws on de Almeida, A. T., et al. (2015) Multicriteria and Multiobjective Models for Risk, Reliability and Maintenance Decision Analysis (see Chaps. 1–2). Full references are given in each chapter. We would also like to thank the editors of Springer for their professional help and cooperation all during the development of this book, and finally, but most of all, we thank our families, who continuously supported and encouraged us in our research work, despite the stresses and strains that we all went through, and the anonymous referees of this book who gave many important feedbacks. Recife, Brazil Adiel Teixeira de Almeida Recife, Brazil Danielle Costa Morais Turku, Finland Hannu Nurmi Contents 1 Voting Rules in Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Topics for Further Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Suggestions for Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Calculus of Consent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Individualism and Unanimity. . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The Cost Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Topics for Further Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Suggestions for Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 The Majority Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Rae on Binary Decisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 Necessary and Sufficient Conditions . . . . . . . . . . . . . . . . . . . . 16 3.4 Topics for Further Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.5 Suggestions for Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4 More Than Two Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 Voting Procedures Under Study. . . . . . . . . . . . . . . . . . . . . . . . 24 4.3 Some Descriptive Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.4 Topics for Further Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.5 Suggestions for Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 ix x Contents 5 Strategic Aspects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.2 The Concept of Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.3 Is the Condorcet Winner Criterion Plausible?. . . . . . . . . . . . . . 33 5.4 Principal Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.5 The Practical Significance of the Results . . . . . . . . . . . . . . . . . 40 5.6 Difficulty of Manipulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.7 Safe and Unsafe Manipulation. . . . . . . . . . . . . . . . . . . . . . . . . 45 5.8 Topics for Further Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.9 Suggestions for Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 6 Sequential Voting by Veto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.2 The Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.3 Topics for Further Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.4 Suggestions for Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 7 Criterion Based Choice of Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . 57 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 7.2 The Emergence of Some Voting Procedures. . . . . . . . . . . . . . . 59 7.3 From Criterion Preferences to Voting Systems . . . . . . . . . . . . . 61 7.4 Topics for Further Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.5 Suggestions for Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 8 Two Procedures Based on Ratings . . . . . . . . . . . . . . . . . . . . . . . . . 67 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 8.2 Majority Judgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 8.3 Range Voting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8.4 Topics for Further Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . 70 8.5 Suggestions for Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 9 Qualified Majorities and Expert Choice . . . . . . . . . . . . . . . . . . . . . 73 9.1 Condorcet’s Jury Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 9.2 Relaxing the Independence Assumption. . . . . . . . . . . . . . . . . . 77 9.3 Optimal Jury Decision Making . . . . . . . . . . . . . . . . . . . . . . . . 79 9.4 Epistemic Paradoxes and Their Relevance . . . . . . . . . . . . . . . . 81 9.5 Topics for Further Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . 84 9.6 Suggestions for Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85