Handbook of Social Choice and Welfare 2

952 Pages·2011·9.04 MB·English

by  Kenneth J. Arrow

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VOLUMETWO
H
ANDBOOK OF
SOCIAL CHOICE AND WELFARE
Editedby
KENNETHJ.ARROW
AMARTYASEN
KOTAROSUZUMURA
AMSTERDAM•BOSTON•HEIDELBERG•LONDON
NEWYORK•OXFORD•PARIS•SANDIEGO
SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO
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Copyright(cid:13)c 2011ElsevierBV.Allrightsreserved.PartIIofChapter13usedwithkindpermissionfrom
SpringerScience+BusinessMedia:Kelley,J.S.(1987).AnInterviewwithKennethJ.Arrow,SocialChoice
andWelfare,Vol.4,pp.43-62.
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PREFACE
The Handbook of Social Choice and Welfare presents, in two volumes, essays on past and
ongoing work in social choice theory and welfare economics. The first volume, which
consists of twelve chapters in four parts—Part I (Arrovian Impossibility Theorems), Part II
(Voting Schemes and Mechanisms), Part III (Structure of Social Choice Rules), and Part IV
(Welfare, Justice, and Poverty)—, was published in 2002. This is the long overdue second
volume of the Handbook, which also consists of four parts.
InPartV(Foundations),someverybasicissuesinwelfareeconomicsandsocialchoice
theoryarediscussed.Thetopicscoveredincludetheinitialinsightsbehindandthebasic
functionsofsocialchoicetheory,theinformationalbasisofnormativeandpositivesocial
choicetheory,thestatusofcompetitivemarketmechanismsassocialchoiceprocedures,
and the main ingredients of nonwelfaristic approaches in welfare economics and social
choice theory along the line of the theory of functionings and capabilities.
Part VI (Developments of the Basic Arrovian Schemes) consists of four chapters that
are lineal descendants of Part I in the first volume. Recollect that three chapters in
Part I discussed the basic Arrovian schemes in an abstract space of social alternatives.
Here, Part VI addresses itself to the important variations of the basic schemes, such
as impossibility theorems on economic domains, topological theories of social choice,
nonbinary social choice theory, and social choice theory with fuzzy preferences.
In Part VII (Fairness and Rights), several new dimensions in welfare economics and
social choice theory are introduced through the well-known conflicts of values such
as equity-efficiency tradeoffs, compensation and responsibility, the tension between the
requirement of social efficiency and the claim of individual liberties and rights, and the
social choice theoretical analysis of freedom, opportunity, and well-being.
Finally,PartVIII(VotingandManipulation)goesbacktotheissuesdiscussedinPartII
ofthefirstvolume.Herethebasicissuesofstrategy-proofsocialchoicerulesarecovered
as well as probabilistic and spatial models of voting, and the geometry of voting.
Theliteratureonsocialchoicetheoryisnowquitevast,andwehopethiscollection
of critical surveys in two volumes will be of interest to readers who would like to be
introduced to the writings on human well-being and collective decision-making that
have been pursued within this literature.
The initial plan of this Handbook was conceived soon after the publication of the
Proceedings of the International Economic Association Roundtable Meeting on Social
Choice Theory by us in 1996/1997. We are most grateful to the authors of the two
volumes of the Handbook for their contributions. The editors apologize for the fact that
xvii
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xviii Preface
some of the authors had to wait long for publication and had to update their chap-
ters as the other essays were coming in. We should also express our sincere gratitude
to those readers of the first volume who provided important suggestions for the sec-
ond volume, aside from encouraging us to complete what proved to be a remarkably
ambitious project. We very much hope that the completed Handbook will live up to the
expectations of our colleagues and readers.
We conclude this “extra” preface by reiterating the last paragraph of the Preface
to the Handbook as a whole, which was printed in the first volume: “The primary
purpose of this Handbook is to provide an accessible introduction to the current state
of the art in social choice theory and welfare economics. But we also believe that the
expoundedtheoryhasastrongandconstructivemessageforpursuinghumanwell-being
and facilitating collective decision-making.”
Kenneth Arrow
Amartya Sen
Kotaro Suzumura
AStatementfromKennethArrowandAmartyaSen
We would like to acknowledge our debt to Kotaro Suzumura for doing the lion’s share
of the editorial work, and for doing this ungrudgingly in a way that can be done
onlybyapersonoftheremarkablegenerositythatKotarohas.Weareimmenselygrateful
to him.
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LIST OF CONTRIBUTORS
Chapter13
Kenneth Arrow
StanfordUniversity,Stanford,CA
Amartya Sen
HarvardUniversity,Cambridge,MA
Kotaro Suzumura
WasedaUniversity,Tokyo,Japan
Chapter14
Amartya Sen
HarvardUniversity,Cambridge,MA
Chapter15
Peter J. Hammond
UniversityofWarwick,Coventry,UK
Chapter16
Kaushik Basu
CornellUniversity,Ithaca,NY
Luis F. Lo´pez-Calva
UnitedNationsDevelopmentProgramme,NewYork,NY
Chapter17
Michel Le Breton
Universite´ deToulouse,Toulouse,France
John A. Weymark
VanderbiltUniversity,Nashville,TN
Chapter18
Nicholas Baigent
LondonSchoolofEconomicsandPoliticalScience,London,UK
Chapter19
Rajat Deb
SouthernMethodistUniversity,Dallas,TX
Chapter20
Richard Barrett
UniversityofBirmingham,Birmingham,UK
xix
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xx ListofContributors
Maurice Salles
l’Universite´ deCaen,Caen,France
Chapter21
William Thomson
UniversityofRochester,Rochester,NY
Chapter22
Marc Fleurbaey
CNRS,UniversityParis-Descartes,Paris,France
Franc¸ois Maniquet
Universite´ CatholiquedeLouvain,Louvain-La-Neuve,Belgium
Chapter23
Kotaro Suzumura
WasedaUniversity,Tokyo,Japan
Chapter24
James E. Foster
OxfordPovertyandHumanDevelopmentInitiative,Oxford,UK
Chapter25
Salvador Barbera`
UniversitatAuto`nomadeBarcelona,Bellaterra,Spain
Chapter26
Peter Coughlin
UniversityofMaryland,CollegePark,MD
Chapter27
Donald G. Saari
UniversityofCalifornia,Irvine,CA
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CHAPTERTHIRTEEN
Kenneth Arrow on Social Choice Theory
KennethArrow*,AmartyaSen**,andKotaroSuzumura***
*ProfessorEmeritus,StanfordUniversity,Stanford,CA
**ThomasW.LamontUniversityProfessor,andProfessorofEconomicsandPhilosophy,HarvardUniversity,Cambridge,MA
***ProfessorofEconomics,WasedaUniversity,Shinjuku-ku,Tokyo,Japan
Contents
PartI: AnEditorialNote 3
PartII: AnInterviewwithKennethJ.Arrow 4
References 23
PartIII: TheClassificationofSocialChoicePropositions 24
PartI: AnEditorialNote
AmartyaSenandKotaroSuzumura
Kenneth Arrow founded the modern form of social choice theory in a path-breaking
contributionatthemiddleofthetwentiethcentury.We—theeditorsoftheHandbookof
Social Choice and Welfare other than Arrow—want to begin this final volume by noting
the continuing need to read Arrow’s decisive contribution in his epoch-making book,
SocialChoiceandIndividualValues,whichstartedoffthecontemporaryroundofresearch
on social choice theory. (Kenneth J. Arrow, Social Choice and Individual Values, New
York: John Wiley & Sons, 1st edition, 1951, 2nd edition, 1963.)
We are also including in this chapter an interview that Kenneth Arrow gave to
Professor Jerry Kelly some years ago, which was published in Social Choice and Welfare
in 1987. This presents Arrow’s thinking on the subject as it developed since his own
pioneering contribution.
Finally, this chapter also includes some new observations by Arrow, “The Classifi-
cation of Social Choice Propositions,” dealing particularly with the distinction between
normativeanddescriptivestatementsinsocialchoicetheory.Thesenotes,whichArrow
haswrittenforthisvolumeataverydifficulttimeforhim,reflect,inevitablyinahighly
compressedform,somerecentthoughtsofthefounderofthedisciplineonanimportant
methodological issue in social choice theory.
HandbookofSocialChoiceandWelfare,VolumeII Copyright(cid:13)c 2011,ElsevierBV.
ISSN:1574-0110,DOI:10.1016/S0169-7218(10)00013-4 Allrightsreserved. 3
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4 KennethArrowandJ.S.Kelly
This is also an occasion for us—the editors other than Arrow—to acknowledge the
huge benefit that the subject of social choice theory has received through the active
contributions of the founder of this modern discipline over the last sixty years. We also
would like to say how privileged we have been to work with Arrow in editing this
two-volume Handbook of Social Choice and Welfare.
April 2010
PartII: AnInterviewwithKennethJ.Arrow
KennethArrowandJ.S.Kelly
The following is an edited transcript of an interview conducted on March 4, 1986,
with Professor Arrow while he was visiting Syracuse University to deliver the Frank
W. Abrams Lecture Series to be published as The Uncertain Future and Present Action by
SyracuseUniversityPress.1 Thisinterviewwastoelaborateonhisdescription,presented
inVolume1ofhisCollectedPapers(HarvardUniversityPress,1983)oftheoriginsofhis
work in collective choice theory.
JK. You started off the story in the collected papers with remarks about studying relational logic
while you were in Townsend-Harris High School in New York City.
KA. Not in high school in the sense of [being] in my high school courses, but during
this period I was an omnivorous reader and got into all sorts of things. One of them
was Bertrand Russell’s Introduction to Mathematical Philosophy, and it made a tremendous
impression on me. It was the idea of logic that was in there. I don’t really recall, for
example, if there was a formal definition of a relation as a set of ordered pairs, but I
learned the ideas of mathematical logic and its applications to mathematics in Russell’s
book. It seems to me that I also read one or two other logic books around that time.
JK.Later,whenyouwenttoCityCollegeofNewYorkasamathematicsmajor,youencountered
more mathematical logic.
KA. Yes, but again the logic study was on my own, there were no courses in it. I
don’t really remember exactly what I read. I remember once taking out the Principia
Mathematica, but of course it’s not the sort of thing one really reads from. I was looking
up some theorems in it and things like that. I really am not prepared to tell you what I
read,butatsomepointthingsliketheideaofdefiningrationalnumbersbyorderedpairs
and equivalence classes by ordered pairs was something I got to know. I was fascinated
1AccordingtoJerryKelly,thislecturewasneverwrittenupforpublication.
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KennethArrowonSocialChoiceTheory 5
by this and used to aggravate my professors by writing out proofs in very strictly logical
form, avoiding words as much as possible and things of that kind.
JK.YoudidtakeaformalcoursewithTarskiinthePhilosophyDepartment;howdidyouhappen
to take that course?
KA. Yes. Well, I knew that Alfred Tarski was a great and famous logician, and there he
was in my last term in school, and obviously I was going to take a course with Alfred
Tarski. It turned out he had two courses. One was a kind of introductory course and I
felt I knew more than that. The other course he gave was in the calculus of relations.
To say it was in the calculus of relations meant that he gave an axiomatic treatment of
relations, although he motivated it of course by motivating the axioms. You never had
xRy; you only had R and S and T. You see, he never mentioned individuals in the
formal theory. He had an axiomatic theory like an axiomatic treatment of set theory.
Relationshavesomespecialaspects,inparticulartheideaofrelativeproduct,RS.Ifthere
is a z such that xRz and zSy, then xRSy. The relative square, R2=RR, is especially
interesting; if the relative square is included in R you have transitivity.
So it was a fascinating thing, although it was really very elementary, really very easy.
The concepts were not very subtle compared with the deep things he was working on
like the truth principle.
JK. At this point you were involved in translating some of Tarski’s work.
KA. He wrote a textbook called Introduction to Logic (Tarski 1941), which is one of the
modern treatments, modern as of 1940. It had been published in German, may even
havebeenorginallypublishedinPolish.Ididn’ttranslateit.Whathappenedwashehad
a translator and I read the proofs. I was just finishing college and he asked me to read
theproofsforhim.Hedidn’tknowanyEnglish,yousee.Thiswastheinterestingthing.
He came to this country in September 1939, for some kind of congress or conference
and was trapped here by the outbreak of the war. He knew Polish, he knew German,
but he didn’t know any English, so he spent the Fall term learning some English so
he could teach us in the Spring. At first we couldn’t understand a word he was saying,
but after about a week or so we began to catch on and we realized it wasn’t his rate of
progressitwasour rateofprogressthatwasrelevant.Hisstresseswereallwrong.Hewas
awareofthisandthereforefelthecouldn’tproofreadinEnglish.It’sratherinterestingas
a coincidence that the translator was a German philosopher named Olaf Helmer, and
Helmer comes back into my story eight years later.
It’s interesting...Tarski, although his English was weak, had a very good sense of
language, and he kept on asking me, “Is that really good English?” Not in the sense
of being grammatically correct, but, well for example, Helmer was very fond of using
the word “tantamount,” and Tarski got the feeling that somehow it’s not a word used
very often. Actually his instincts for language were extremely good. I suppose that was
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6 KennethArrowandJ.S.Kelly
connected with his general work on formalizations and metalanguages. Anyway, I was
just a proofreader.
JK. You write that as a graduate student at Columbia you spent time, as an exercise, translating
consumertheoryinthelogicofrelationsandorderings.Whatgotyoustartedonthatandwhatdid
you get out of it?
KA. I went to Columbia because...well there were several problems. One was that
we were extremely poor and the question of going anywhere depended on resources.
Columbia had the great advantage, of course, that I could live at home, which wasn’t
true anywhere else. I didn’t get any financial support for my first year, none at all.
But another of the things I had learned on my own at college was mathematical
statistics, and I really had become fascinated with it. There was a course in statistics [at
City College New York]; the teacher, a man by the name of Robinson, had no real
knowledgeofitIwouldsay,basically—Iwon’tevensayhehadagoodreadinglist—but
he did list one book, J. F. Kenney (1939), if I remember correctly, which happened
to have an excellent bibliography. It was not one of those cookbooks in statistics but
actually did have some attempts at mathematics. Kenney had references to R. A. Fisher
and gave you enough to get you interested. So I started reading Fisher, and one of the
first things was trying to work out his derivation of the distribution of the correlation
coefficient under the null hypothesis, which was an integration in n-dimensional space.
InFisheritwasdonebyintuition.Imeanit’srigorousifyou’resufficientlysophisticated;
to me it was gibberish. But I knew enough multivariate calculus to be able to translate
it into rigorous form, at least a form that I understood, and then I could see that he
reallywasright.ButIcouldn’tseeitthewayhewroteit.ThenIsupposebecauseofmy
logicalbackgroundwhatwasreallyimportantwasreadingtheNeyman–Pearsonpapers,
which were then new and written in rather obscure places, but they were available in
the [CCNY] library. From Fisher alone, I think I would have been hopelessly confused
about the logic of statistical tests, although Fisher was great on deriving distributions.
So, I knew I wanted to study mathematical statistics, which however was not
a field, not a Department at Columbia. It was spread out in other Departments.
I knew that Hotelling was one of the major figures, but he was in the Economics
Department. I rather naively thought I would study mathematics and then would take
the statistics from Hotelling. I had no interest in Economics.
I was in the Mathematics Department, taking courses like Functions of a Real Vari-
able, but I was going to take courses from Hotelling. In the first term he happened
to give a course in Mathematical Economics. So out of curiosity I took this and got
completely transformed.
ThecoursetoanextentrevolvedaroundHotelling’sownpapers.But,asithappens,
they were kind of central. He gave a rigorous derivation of supply and demand. There
wasonepaperonthetheoryofthefirm,oneonthetheoryoftheconsumer(Hotelling