Table Of ContentAdvances 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
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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)
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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
