So­cial choice and so­cial wel­fare

Financial Mirror (Cyprus) - - FRONT PAGE -

Hu­man be­ings have al­ways lived in groups, and their in­di­vid­ual lives have in­vari­ably de­pended on group de­ci­sions. But the chal­lenges of group choice can be daunt­ing, par­tic­u­larly given the di­ver­gent in­ter­ests and con­cerns of the group’s mem­bers. So, how should col­lec­tive decision-mak­ing be car­ried out?

A dic­ta­tor who wants to con­trol ev­ery as­pect of peo­ple’s lives will seek to ig­nore the pref­er­ences of ev­ery­one else. But that level of power is hard to achieve. More im­por­tant, dic­ta­tor­ship of any kind can read­ily be seen to be a ter­ri­ble way to gov­ern a so­ci­ety.

So, for both eth­i­cal and prac­ti­cal rea­sons, so­cial sci­en­tists have long in­ves­ti­gated how the con­cerns of a so­ci­ety’s mem­bers can be re­flected in one way or another in its col­lec­tive de­ci­sions, even if the so­ci­ety is not fully demo­cratic. For ex­am­ple, in the fourth cen­tury BC, Aris­to­tle in Greece and Kau­tilya in In­dia ex­plored var­i­ous pos­si­bil­i­ties of so­cial choice in their clas­sic books, Pol­i­tics and Eco­nomics, re­spec­tively (the San­skrit ti­tle of Kau­tilya’s book, Arthashastra, trans­lates lit­er­ally as “the dis­ci­pline of ma­te­rial well­be­ing”).

The study of so­cial choice as a for­mal dis­ci­pline first came into its own in the late eigh­teenth cen­tury, when the sub­ject was pi­o­neered by French math­e­ma­ti­cians, par­tic­u­larly J. C. Borda and Mar­quis de Con­dorcet. The in­tel­lec­tual cli­mate of the time was greatly in­flu­enced by the Euro­pean En­light­en­ment, with its in­ter­est in rea­soned con­struc­tion of a so­cial or­der, and its com­mit­ment to the cre­ation of a so­ci­ety re­spon­sive to peo­ple’s pref­er­ences.

But the the­o­ret­i­cal in­ves­ti­ga­tions of Borda, Con­dorcet, and oth­ers of­ten yielded rather pes­simistic re­sults. For ex­am­ple, the so-called “vot­ing para­dox” pre­sented by Con­dorcet showed that majority rule can reach an im­passe when ev­ery al­ter­na­tive is de­feated in vot­ing by some other al­ter­na­tive, so that no al­ter­na­tive is ca­pa­ble of stand­ing up to the chal­lenge of ev­ery other al­ter­na­tive.

So­cial choice the­ory in its mod­ern and sys­tem­atic form owes its rig­or­ous foun­da­tion to the work of Ken­neth J. Ar­row in his 1950 Columbia Univer­sity PhD dis­ser­ta­tion. Ar­row’s the­sis con­tained his fa­mous “im­pos­si­bil­ity the­o­rem,” an an­a­lyt­i­cal re­sult of breathtaking el­e­gance and reach.

Ar­row’s the­o­rem shows that even very mild con­di­tions of rea­son­able­ness in ar­riv­ing at so­cial de­ci­sions on the ba­sis of sim­ple pref­er­ence rank­ings of a so­ci­ety’s in­di­vid­u­als could not be simultaneously sat­is­fied by any pro­ce­dure. When the book based on his dis­ser­ta­tion, So­cial Choice and In­di­vid­ual Val­ues, was pub­lished in 1951, it be­came an in­stant clas­sic.

Econ­o­mists, po­lit­i­cal the­o­rists, moral and po­lit­i­cal philoso­phers, so­ci­ol­o­gists, and even the gen­eral pub­lic rapidly took no­tice of what seemed like – and in­deed was – a dev­as­tat­ing re­sult. Two cen­turies after vi­sions of so­cial ra­tio­nal­ity flow­ered in En­light­en­ment think­ing, the project sud­denly seemed, at least su­per­fi­cially, to be in­escapably doomed.

It is im­por­tant to un­der­stand why and how Ar­row’s im­pos­si­bil­ity re­sult comes about. Scru­tiny of the for­mal rea­son­ing that es­tab­lishes the the­o­rem shows that re­ly­ing only on the pref­er­ence rank­ings of in­di­vid­u­als makes it dif­fi­cult to dis­tin­guish be­tween very dis­sim­i­lar so­cial choice prob­lems. The us­abil­ity of avail­able in­for­ma­tion is fur­ther re­duced by the com­bined ef­fects of in­nocu­ous-seem­ing prin­ci­ples that are popular in in­for­mal dis­cus­sions.

It is es­sen­tial, par­tic­u­larly for mak­ing judg­ments about so­cial wel­fare, to com­pare dif­fer­ent in­di­vid­u­als’ gains and losses and to take note of their rel­a­tive af­flu­ence, which can­not be im­me­di­ately de­duced only from peo­ple’s rank­ings of so­cial al­ter­na­tives. It is also im­por­tant to ex­am­ine which types of clus­ters of pref­er­ence rank­ings are prob­lem­atic for dif­fer­ent types of vot­ing pro­ce­dures.

Nonethe­less, Ar­row’s im­pos­si­bil­ity the­o­rem ul­ti­mately played a hugely con­struc­tive role in in­ves­ti­gat­ing what democ­racy de­mands, which goes well beyond count­ing votes (im­por­tant as that is). En­rich­ing the in­for­ma­tional base of democ­racy and mak­ing greater use of in­ter­ac­tive pub­lic rea­son­ing can con­trib­ute sig­nif­i­cantly to mak­ing democ­racy more work­able, and also al­low rea­soned as­sess­ment of so­cial wel­fare.

So­cial choice the­ory has thus be­come a broad dis­ci­pline, cov­er­ing a va­ri­ety of dis­tinct ques­tions. Un­der what cir­cum­stances would majority rule yield un­am­bigu­ous and con­sis­tent de­ci­sions? How ro­bust are the dif­fer­ent vot­ing pro­ce­dures for yield­ing co­gent re­sults? How can we judge how well a so­ci­ety as a whole is do­ing in light of its mem­bers’ dis­parate in­ter­ests? How, more­over, can we ac­com­mo­date in­di­vid­u­als’ rights and lib­er­ties while giv­ing ap­pro­pri­ate recog­ni­tion to their over­all pref­er­ences? How do we mea­sure ag­gre­gate poverty in view of the vary­ing predica­ments and mis­eries of the di­verse peo­ple who com­prise the so­ci­ety? How do we ar­rive at so­cial val­u­a­tions of pub­lic goods such as the nat­u­ral en­vi­ron­ment?

Beyond th­ese ques­tions, a the­ory of jus­tice can draw sub­stan­tially on the in­sights and an­a­lyt­i­cal re­sults emerg­ing from so­cial choice the­ory (as I dis­cussed in my 2009 book The Idea of Jus­tice). Fur­ther­more, the un­der­stand­ing gen­er­ated by so­cial choice the­o­rists’ study of group de­ci­sions has helped some re­search that is not di­rectly a part of so­cial choice the­ory – for ex­am­ple, on the forms and con­se­quences of gen­der in­equal­ity, or on the cau­sa­tion and preven­tion of famines.

The reach and rel­e­vance of so­cial choice the­ory is ex­ten­sive. Rather than un­der­min­ing the pur­suit of so­cial rea­son­ing, Ar­row’s deeply chal­leng­ing im­pos­si­bil­ity the­o­rem, and the large vol­ume of lit­er­a­ture that it has in­spired, has im­mensely strength­ened our abil­ity to think ra­tio­nally about the col­lec­tive decision-mak­ing on which our sur­vival and hap­pi­ness de­pend.

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