ON THE BALANCE OF A SET OF RANKS Morris Zelditch ... - …

ON THE BALANCE OF A SET OF RANKS

Morris Z e ld itc h , J r . Stanford U niversity

Bo Anderson Stanford U niversity

May, 1S64

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ON THE BALANCE OF A SET OF RANKS

1. Introduction.

The purpose o f t h is paper i s to d ev elo p a th eory o f the b alan ce o f

a s e t o f ranks. A theory o f rank balance is concerned w ith situ a tio n s

in which a c to r s , s ta tu s e s , or c o lle c t iv e s are ranked in sev era l d iffe r e n t

ways which can be regarded as in c o n s i s t e n t Some exam ples a re: the

Negro p r o fe s s io n a l, the w ealth y Jew, the im poverished Boston Brahmin,

the $5,000 a year Harvard Ph?D. I t i s w id ely supposed th at d iscrep a n cies

o f t h is kind are a source o f s t r a in and th a t in d iv id u a ls w i l l attem pt to

bring th eir various ranks in to lin e ,

1 ,1 Homans6 Ledger C le r k s.

An i l l u s t r a t i o n o f t h is p ro cess i s rep o rted by Homans (1 9 5 3 , 1957,

1961) . The s t a t u s e s " led g er c lerk " and "cash p o ste r" in th e b i l l i n g

o f f ic e o f a p u b lic u t i l i t y are evalu ated by such c r it e r ia as s k i l l , r e

s p o n s i b i l i t y , v a r i e t y , incom e, autonomy, and s e n io r it y ? The led g er c le r k

i s regarded by a l l c le r k s in the o f f i c e as more s k i l l e d , more r e s p o n s ib le ,

more s e n io r , more autonomous, and in v o lv in g more v a r ie t y than cash p o s te r .

For variou s h is t o r ic a l reasons the two jo b s are

equal in income,, That

the le d g e r c le r k s are u p set by t h is i s shown in t h e ir com p lain ts to t h e ir

un ion , a g it a t in g for in crea sed w ages, and in th e ir h o s t i l i t y to mangement.

Cash p o s te r s , furtherm ore, sometimes refu se what the o f f ic e regards as

a "promotion" ra th er than become led ger c le r k

The "address f i l e cle r k " i s a th ir d s t a t u s in the b i l l i n g o f f i c e ,

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lower than cash p o ster on a l l c r it e r ia by which s ta tu s e s in the o f f ic e are ranked. Because they are a t the bottom o f the o f f ic e hierarchy the address f i l e c le r k s are not s a t i s f i e d w ith t h e ir jo b s , but th ey do not f e e l u n ju stly trea ted and are not as h o s t i l e towards management as the ledger clerk s. 1 *2 ? L e n s k i's c r y s t a l l i z a t i o n problem .

A second illu s t r a t io n i s reported by Leneki (1954, 1955). A sample of respondents in D etroit is ordered w ith resp ect to occupational p restig e, incom e, e d u c a tio n , and e t h n i c i t y . An in d ex o f d is c r e p a n c ie s among th ese ranks i s computed. Among resp on d en ts o f ap p roxim ately the same average socio-econom ic le v e l, those w ith the g r e a te st d iscrep a n cies are the most " lib era l" in socio-econom ic a t titu d e s , the most lik e ly to vote D em ocratic, the le a s t li k e l y to be s o c ia b le and the most li k e ly to p a r tic ip a te in community a s s o c ia tio n s fo r " u tilit a r ia n " purposes (such as " g e ttin g ah ead " ). Lenski in terp rets " lib era lism " as a d esire to change the s o c ia l stru ctu re, and low s o c i a b i l i t y a s w ithdraw al from u p s e ttin g s i t u a t i o n s . The respondents w ith no d iscrep a n cies in rank are c a lle d " c r y s ta lliz e d " 1 3 . D efin itio n of Problem.

In general such situ a tio n s have the follow in g c h a r a c te r istic s: 1) A ctors, s ta tu s e s , c o lle c t iv e s , or other elem ents o f a s o c ia l

system S may be ordered in k d i s t i n c t ways a cco rd in g to c r i t e r i a

V v*?v

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2) Standing on a c r it e r io n r, i s an evalu ated c h a r a c te r is tic in

S . T his means th a t members o f S, are d i f f e r e n t i a l l y ev a lu a ted

in d ir e c t p rop ortion to. th e ir rank on r^ , and p o sse ssio n o f

p o s it iv e ly ev a lu a ted stan d in g on jr. i s seen to be d esira b le

in S.

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3) A member o f who i s ordered in the same way w ith r e s p e c t to each o f h is k rankings i s sa id to be balanced; oth erw ise imb a la n c e d

One i s in t e r e s t e d in the b eh avior o f a c to r s w ith im balanced ranks and o f s o c ia l system s c o n ta in in g such a c t o r s .

Various synonyms fo r balance are ,,congruence", " c r y s t a lliz a t io n " , " c o n siste n c y " , any o f which may be p r e fix e d by e i t h e r " s ta tu s " , in the s c a la r s e n s e , or "rank". A synonym fo r " resto rin g balance" is " e q u i lib ra tio n " o f ran k s. I n t e r e s t in rank b alan ce g o es back a t l e a s t to Weber (s e e , for exam ple, Gerth and M ills , 1946, ch. v i i ) . A fundamental paper on the s u b je c t by B en oit-S m u llyan appeared in 1944 and s in c e th a t time a number o f in v e s t ig a t io n s have been rep o rted in w hich d is c r e p a n c ie s in ranks have been lin k ed to ob servab le p ro cesses ranging from p o l i t i c a l extrem ism (o f both th e r ig h t ( L ip s e t , 19 ) and l e f t (B arb er, 19 ) ) to p sychosom atic symptoms (J a ck so n , 1 9 6 2 ).

D espite a long h isto r y o f g rea t in t e r e s t in the problem the a v a ila b le evidence only weakly confirm s the c e n tr a l assum ption th at imbalanced ranks gen erate s t r a in and e f f o r t s to r e sto r e balance? C ontradictory r e s u lt s have been ob tain ed , supposedly p o s itiv e r e s u lts are sometimes q u ite in c o n c lu s iv e , and i t i s o f t e n n e c e ssa r y to in v e n t ad hoc p r in c ip le s to e x p la in p ecu lia r r e s u lt s in p a r tic u la r cases? This i s due le s s to the fa c t th a t the balance assum ption i s f a l s e , than to the incom plete and very

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vague form u lation o f th e th e o r y I t s assum ptions have n ot been made e x p lic it , the scope of the theory has not been c le a r ly d efin ed , several d i s t i n c t p r o c e s s e s have been g o in g under th e same name3 and many p o r tio n s o f the theory such as the p o ssib le response p rocesses--have not been thought out a t a l l .

In the p resen t paper what i s accom plished i s on ly a p a r tia l formu la t io n o f a th eory in p r o g r e s s . We do not even tr y to e x p la in e v e r y th in g th a t has gone under the name o f rank b a la n c e , but even w ith in the scope o f what we do in ten d to e x p la in , the th eo ry i s not com plete? The th eory i s narrow ly co n fin ed in scope to e v a lu a t io n s . I f the fo rm u la tio n we su g g e st is c o r r e c t, response to imbalanced ev a lu a tio n s depends on a comparison p ro cess. But comparison p rocesses are not y e t thoroughly understood. There are a l s o e v id e n t ly more o b serv a b le resp o n se p r o c e s s e s than have u s u a lly been m entioned in " te s tin g " the th e o r y , but we cannot y e t t r e a t them e x h a u s t iv e ly . I f we are asked to j u s t i f y such a p a r t ia l fo rm u la tio n , i t s p rin cip a l advantage is that i t s gaps point to the major unsolved prob lems o f the th eo ry more c l e a r ly than no fo rm u la tio n a t a l l . I t i s th e r e fore a more u s e f u l guide to fu r th e r work. 2? The S t r a t i f i c a t i o n o f S .

The s t r a t i f i c a t i o n o f a s o c i a l system S can be thought o f in the fo llo w in g way: the elem en ts o f ?5 (u^, fo r u n it s ) each have some g en era l

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sta n d in g or o v e r a ll e v a lu a tio n in --S (denoted "Ri.) which i s determ ined by some s e t o f c r i t e r i a (r ^ , r ? , . . . . ) . S in ce the c r i t e r i a may vary in

im portance, a s e t o f w e ig h ts (w^ *? ?

d eterm in es how much each

c r i t e r io n c o n tr ib u te s to th e v a lu e o f R_. . J u s t how th e w eigh ted v a lu e s

are added up i s d i f f i c u l t to s a y , but c e r t a in ly i s a m o n o to n ica lly i n

c r e a sin g fu n c tio n o f them. For s im p lic it y assume th a t R^ i s in f a c t a

linear function of

. . . For any g iv e n u. we have:

2 ?I* A ssu m p tion . SLi E q + ~2i 2 + * ' + ~k% k ** ~L

There w i l l be an e x p r e s s io n lik e 2 .1 fo r each elem en t in and the whole se t o f such ex p ressio n s d escrib es the system o f s t r a t if ic a t io n o f ?3 a s a w h o le.

Assumption 2 .1 says only that o v e r a ll standing is determ ined by adding w eigh ted sta n d in g s on v a rio u s c r i t e r i a r e le v a n t in S . What i s im p ortan t about i t i s n ot the lin e a r assu m p tio n , which we do not even b e li e v e , but the fa c t th at i t d e fin e s ?h at i s r e le v a n t and what i s n o t. I f sta n d ing on a g iv e n c r i t e r io n makes no d if f e r e n c e to o v e r a ll sta n d in g in S i t i s not an e v a lu a tio n , or rank, in S .

2 .2 . D e fin itio n . A rank i s any value on any c r iterio n ? w ith non zero w eight in ? or any function o f a combination o f such valu es.

In order to apply the theory form ulated here one must know, as a

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