Policy Studies Journal Vol. 9 No. 6

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Grofman, Lijphart, McKay, anC Scarrol

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REPRESENTATION AND REDISTRICTING ISSUES
Lexington, M: Lexington Books, i98e

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the Journal of the
POLICY STI.JDI ES ORGAN IZATION
Vol.9 Special #3. 1980-El No.6



AL lLirl',i^\ I lVts PUtlUiE,b l-UH
ACHTEVING THE GOALS

ALTERNA'TtVES TO SINGLE-MEMBER PLURALTTY DISTRICTS:
LECAL AND EMPIRICAL ISSUES*
Bernard Crofman, University of California, lrvine

INTRODUCTION. ln 1968, Paul Freund wrote that

While the moior outlines of the reopportionmcnt doctrine
moy be settled, there remoin o host of questions still
un'resolved: its opplicotion to locol government, the
legol stotus of gerrymondering, the limits on multimember
dlstricts, the use of weighted or froctionol voting in the
legisloture,

' (Paul A. Freund, Foreward to Dixon. 1968: vi)

The latter three of these issues remain largely unresolved,
and lt ls the last two issues on which this paper will focus.

While single-member districting (smd) is the most common
form of representation in the U.S., apportionment schemes at the
state and local level often make use of multimember districts
(Klain 1955; Jewell l97l), tlre polar type of which is, of course,
the at-large election; r alrd in one state (New York) weiqhted vot-
inq is tlre most common of the various systems ih use for courrty
go-vernment.2 ln the late 1960's and 70's such non-smd systems
6ave corne under increasing challenge as violating l4th Amendnnent

'requal protectiontt standards.

Of the lustifications advanced for deviations fronr the eqtral
population rule, the desire to preserve local political boundaries
is the most commonly voiced and the most frequently accepted.
However, if tlre desire to preserve political bounclaries is made a

major concern, then this leads to consideration of systenrs of '

representation other than simple single-member districting and
raises real constitutional issues as to what equal representation
consists of. (See Grofman and Scarrow, l98la forthcoming.) lf
political subunits are of discrepant sizes, in a single-member dis-
tricting system some small units will be denied their "own" reprs-
sentatives, whlte some larger units will be divided up. Political

t-
I
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l

*Thls research was supported by NSF Grant ISOC 77-24474,
Polltlcal Sclence Program. I am lndebted to the staff of the Word
Processing Center, School of Soclal Sclences, Unlverslty of Cali-
fornla, Irvlne for turning my handwrltten scrlbbles lnto flnlshed
copy, to Sue Pursche for btbllographic asslstance and to l{oward
Scarrow for helpful discusslon of a number of the lssues consldered
ln thls paper.

A methodologlcal appendlx, dlscusslng ln detall seventeen
recent emplrlcal studles of at-large vs. ward distrlcting, ls avall-
able upon reguest from the author.

875



bounlt'aries can be fully preserved only by (t) allowing for
multiple-member districts (vrhictl tnay use plurality voting, or some

'forrn o[.proportional representation), or (2) using weighted voting
to compensate for population differences across political subunits.

A REVIEW OF RECENT COURT CASES ON MULTIMEMBER DIS-
lans

f sentatives to a district in
direct proportion to that district's population, in the aftermath of
the Supreme Court's entrance into the "political tlricketI of reappor-
tior':ment, the constitutionality of multimember districts and at-large
elections has recently been challenged on several grounds related
to |tone r€n, one voteti issues.

First, multimember distrlcts are sald to submerge potitical ,
especla!ly racial, minorities.

The nwinner-toke-olln chorocter of the typicol election
schene creotes the possibility thot o specific moiority
will elect oll the representatives from o multimember
distt'ict whereos the outvoted minority might hove been
oble to elect some representotives if the multimember
district hod been broken down into severol single-
member districts . ( T ribe, 1978: 750) .

A second accusation against multimemlter districts is based on
a mathematical argument advanced by Banzhaf (1956) which shows
that resiclents of smaller districts are being denied equal represen-
tation because residents in the larger districts who are electing
representatives proportional to their numbers have a more than
proportionate chance of affecting election outcomes.

A third and related challenge against multimember districts
is based on the alleged propensity of representatives from such
districts to act as a bloc. Chosen from the same constituency,
almost certainly of the same party, the identity <if interests arrrng
such represenratives could be expected to be greater than those
chosen from the same population divided up into plural distinct
districts.

A fourth claim ls that as the number of legislative seats
within the district increases, the difficulty for the voter in making
intelligent choices among candidates also increases. Ballots tend to
become unwieldy, confusing, and too lengthy to allow thoughtful
consideration.

A final charge brought against at-large elections ls that,
when candidates are elected at large, residents of particular dis-
trlcts may feel that they have no rePresentative especially re-
sponsible to them (see'Chopmon v. Meier il9751).'

L'lultlmember districts have, however, not been without their
defenders. Around the turn of the century replacing district sys-
tcms wlth at-large elections was the goal of municlpal reformers
anxicue :c b!"eak the power or trY.'ardtr politlclanr. Slmllarly, Brycc

(1889: 463-6{; citecl in Klain, 1955: l'l lB) deplored tlre. sprcad of

single-memller districts, holding; the.m resl:onsible .for.th.e decline

ir' irriltv of state t;;iJl"t;;r." ,'Thu area of clroice being smaller,

inferior men are choi'err'" Tlris charge has begr-r-en5l95ed by both

p"fiili-lr.r-and potitiJai scientists (seJ Klain, 1955: l l lB, no. 30) '

The claim has also been macle by some political .scientists tlrat
;;;;;-;;p;j"r",',totio't is teclrnically more feasible with multiple dis-

trictsr' (Klain, 1955: 1117; and see referetrces cited in Klain' 1955:

ll17, no. 26; also see cititions in lUlritcontb v' Chovis'-i UV which

is meant the statisti."r osilr""tion that the fewcr tlre clistricts the

;;;i"; ii is to design districts so as to obtain exact population

equallty among them).

ln the first of the post-8oker -cases cl'rallenging multimember

districts {Fortson v, Dorsey t 19551 ) 
6 the complaint was tltat voters

in the Ceorgia legisiatureis'single-member cli stricts could elect their

own representatives; wlrile votJrs in the multimember districts (who

elected representatives at large but with the candidates required to

beresidentsofasubclistrict,witheachsubclistrictallocatedexact.
ly one representative) were, it was pioposed' being .cleniecl 

their

o'*n ."pt!tentative, since voters Irom outside the subdistrict
truip"J'to .J]ooru the subclistrictrs representative' "The Court up-

held Georgia's districting system, concluding that voter.s in multi-

rnember districts oii-i"alui elect their own representatives--the
,up[t"ni.iives of 

'Gu 
.,,t'ty, rutlgf than of the srrbdistrict in

which they happert"A tn resicle" (Tribe, 1978: 752).' emphasis

ours). ln Fortson tf,u S"pt"*e tourt lreld (as it had in Reynolrls

i. l'inrr7) that "equal proiection does not rrecessarily require for-
,"ti"n of alf single-member districts in a staters legislative appor-

tionment schemel" However, the Court had not yet been con-

fronted with the full range of arguments against-multim.ember dis-

i;[ii;;. 
"in 

parti.rtur, It nuO not yet been confronted with an

;ii;;;;'tir" n'ry or ,"usuring citizen "weiqltt'r in an apportionment

system lnvolving districts of different sizes'

lnthenextcasetocomeuponthisissue,Btlrltsy.
Richordson (1965), tttu Co"t reiierateds tl're standard advanced in

rrrirrr! ir.,ui ,,tt o leqislative clroice of mul timember districts is

trbll.l tq constitutional challenge only upol ? showing tlrat tlre
plan was designed to or would 6perate to minimize or cancel out

the voting strength of racial 9.f political group-s.'' ll. Burtts'
Kitgortin et ol, v. uitt t1954)r0 and in Wiitcomb v' Chovrs the

C;;;i'maiority held no iuch showing was made' However' the

t"foi"g ih wiitco^a aisLrtea that "Ihe validity of m.u-ltimember

districts is iusticiall;;ii and it "left open th.e possibility not only

il;i';';";iilrir, ,riiir"ru"r district migt.rt be slrown -to 
cancel

out the voting power of a minority group-but also that multimem-

ber districts mighi-i"entuatty be deilared illegal per se if sonrc of

the indictments leveled ot such districts -g-cnerolly-could 
be es-

tobtished by more'piisuosive evidencett (1ribe, 1978: 753, n. 18,

emphasis ours).

ln Whitcomb the Court squarely confronted -for the first time

thelssueoftheallegedoverrePresentationofresidentsofthe
iii.iiirrfiimemUer distrlcts as measured by their abitity to affect

877

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election outcomes. ln Whitcombl2 the Court reiterated its views ln
.Reynblds y. -srms on rvhat is required for full and effective par-
tlcipaticn ln the pol itical process, to wit:

Filt ond effective porticipotion by otl citizens in stote
government requires, therefore ., that eoch citizen hove
on equolly effective voice in the election of members of
ffihasisours).r3
The chaitenge to the multimember apportionment scheme in

ltlhitcomb rested on two quite dlstinct. bases. The first was the
assertion that the Marion County district rrillegally minimizes and
cancels out the voting power of a cognizable racial minority in
Marion county.ttlq This claim, as we noted above, was rejected by
the Court on the grounds of arr inadequate showing as to the
facts. The second was the claim (based on the argument in
Banzhaf, 1966) that "voting power does not vary inversely with
the size of the district and that to increase legislative seats in
proportion to increased population gives undue voting power to
the voter ln the multimember district since he has more chances
to determine election outcomes than does the voter in the single-
member distrlct."15 Thls claim was also reiected by the Couit.
(See note 3.)

lf minority votes are not needed to win elections and there
are no districts in which minorities predominate, minorities may be
frozen out completely. The Supreme Court held this to have
occurred for Blacks in Dallas County, Texas, and Mexican-Ameri-
cans in Bexar County, Texas (ltlhite v. Regester). rG ln White
the Court found the Democratic party organization in Dallas County
"did not need the support of the Negro community to win elections
in the county, and it did not therefore exhibit good faith @ncern
for the politlcal and other needs and aspirations of the Negro
community.tr Also, the Court in White upheld the lower court
findings that "the Black community had been effectively excluded
from fartlcipation ln the Democratic primary selection process.t'17
The Supreme Court ln White similarly upheld District Court find-
ings that Bexar Countyrs "multimember districts invidiously ex-
cluded Mexican-Americans from pol itical participation" and that
single-member districts were 'rrequired to remedy the effects of
past and present discrimination against Mexican-Americans." r0

ln l/hite the Court revealed that the hints, offered ln
Fortson and Whitcomb, that a properly mounted challerige to multl-
member Cistricts (mmds), when sustained by an historicql record of
discrimination, could in fact succeed, were not idle ones. Other
mmd schemes have subsequently been struck down by the federal
courts. For exampl e, ln Kruiclenic v. McCutlochrs an ll-member
distrlct was held unconstitutlonal; while in two lmportant parallel
casee, Aroves v. Bornes (1972)20 and Graves v, Bornes (1974),21
mixed slngle and multlmen:ber dlstrlcting for the Texas state legls-
lat':re vras repudlated as discriminatory against Mexican-Americang
and Blackg ln a number of the most populous Texas counties.
Il,loreover, in Connor v. Johnson (1971)22 and Chopmon v. Meier
(1975), tha Supreme Court struck down ludlcially created appor-
t!r,nn:nl schemes lnvolvlng muttlmember dlstrl:ts, rrcreatlng a

virtuailyperseruleagairrstcourt-orclerec|multimenlberclistrict
olans in the absence oi exigcnt circumstances" (Tribe' 1978: 755'

;;il;;;;;;.;t." Ftrrtherirore, the Justice Delxrtment' under

ifr,i Vrti"g Rights Act of 19G5, has, in effect, prevented arry iur-
isdiction covered by that act from chonginq to a pure at-large
system.

As of 1970 "more tlran 60 percent of ttre cities (and one

third of the counties) in this country elect their legisla-tive bodies

ui iu,'gtu ratlrer ft,niitv districts-, and the proportio.n.of tlrose lras

;;;; d;";ing" (Jeweli, rgzr: 52!. At the municipal level' it has

U"u" i'tg""ithat at-large elections-!L""t acted to discriminate

"g"i"tt 
?acial,nO otn"t"minorities (lYashington'. l97l; .Karnig and

wil.r.,, l978; Heitig, I97B; Jones, 1976). lvith incr.easing frequency

since'ttre ,ia tgZOIs federal courts have been l'rearing cases

chaltenging local electoral structure--cases often arising ottt of the

V"iin; hijr,tr e.t. Until the le80 ruling in.City.of lttobile'
Alobonn v, Bolden2h (see discussion below) it had appeared that

tft"-r";o. arena of , apportionnlent cha.llenges in tlte 1980's would

have been with respect to at-large electiotrs' "

ThattheSupremeCourtwoulcJeventuallyc|eclareat-large
districting u,tconsiitutional on its face was in our vierv never at

"iiiiX"l,," 
since the Court had proceeded quite catrtiously with t'e-

spect to multimember districts, anci in an aside in Lucos v'
AG;ri, Cencrot Assembl5' (1964)26 tl're Court csserted that'
despite certain undesirabie features of multimernber elections,

"pplttiontent 
sctremes which provide for the at-large electiorr of a

number of legislators from a county, or any political.-subdivision'
are not "preiumptively constitutionally defective.'' . (-See also Seer

,. 
- 

U. j. i r gze l) . " l'ionetheless, where a substantial racial
minorityexistsandwherethereisaclear-cttthistoryofpastdis-
criminaiion, at-large elections had successfully been challenged
under standards enunciated in 1973 by the Federal Court of
Appeal, Fiftlr Circuii in Zimnrcr v. UclXeithen ( 085 F. 2d 129.7) 2c

lnZintnrcritwasheldthatunconstitutionaldiscrimirration
could be demonstrated throuclh a preponderance of evidence in-
cluding (1) lack of access of minorities to tlre nonlinatioll process,
(2) ttre unresponsiveness of legislators to tlre particularized in-
ieiests of mirrorities, (3) a tenuotrs state policy underlying the
preference for multimember or at-large.distric.ting' or.(4) tlre
!rirt",.,.e of past cliscrimination preclucling effectiv_e.-m.inority par-

ticipation in itre election system. .l.n Zimnrcr, the Fifth Circuit
Co,irt also enunciaiecl crit6ria which would Pr:ovide indirect evi-'

dence of discrimination--inclucling large distrlcts, a maiority vote

requlrement, provisions prolribit'rlng "bulletrt 1r'5inQle-s5ot") voting.

"nd 
tft" lacf of geographically linked posts' However,- the suffien-

cv of these stanclurJ, i"t now (1980) been reptrdlatecl by the

Slrpreme Court in the Mobile case,

ln Mobile, the Supreme Court enunciatecl a new and much

stronger requirement. tt is no lpnger enough to demonstrate that
i givEn at-lirge districting js discriminatory in its effccts, but
rather one must Jro if,o"-that it ls discriminatory in rntent. 2t The

879

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discrlmlnatory purpose doctrirre ln Mobile was derived from two
qartier Uecisions, llloshingtcn v. Dovis ( 1976) 30 and Arlingtott ,. ,,
Heigltts v, lletropctiton kousing Development Corp. (19771 .:'L'31'"

ln Llobite, a decision marked by the absence of a maiority
opinion and a plethora of competing views, tlre only thing wlrich
ii sure is that the Court no longer acknowledges the dual standard
enunciated in Fortson (emphasis ours) that a plan is subiect to
constitutional challenge upon a showing that the plan. r'wos desig.ned
to or would operote t*o mi'nimize or cancel out the voting strength
of racial or political grouPs. r' 3q lndeed, quite remarkably, Jus-.
tices Stewari, Burgei. Powell,and Rehnquist argue in Mobile $ that
the court has never had such a dual standard of intent or impact,
and that the larlguage in Fortson (repeated in Burnsl doesn't mean

what it obviously says. For an instructive example of legal double-
think,note l3 in-Mobile can harclly be bettered. (See, in this con-
text, l,/tarshallrs stinging dissenting opinion in Mobile.l

The principal consequence of the tlobile decision is that it
will be extremety difficult to mount a successful challenge to an
at-large election system, no matter how invidious may be its dis-
criminatory impact on the representation of racial or linguistic
minorities. The only optimistic note that can be sounded in the
light of tlobite is. that lhe Alobile decision cloes not (directly) affect
tlie constiiutional tegitimacy of Justice Department action (under
the Voting RiChts Act) to forestall chonges to at-large districting.

AT-LARCE ELECTIONS AND MINORITY REPRESENTATION:
A E IffiNeE. fhe suPreme

t challenges to
the constitutionai ity of multimember districts and of at-large elec-
tions, inctuding ones based on game theoretic arguments (see
Grofman and Siarrow, l98la, for detaitsl . However, the only
chatlenge that the Court has accepted as legitimate grounds for
overturning an apportionment scheme is evidence that the plan
t'was designed to or would operate to minimize or cancel out the
strength 6f raci-l or political groups" (Fortsonl.36

Confining ourselves to the issue of at-large vs. ward elec-
tions (the analysis for multimember vs. single member distrlcting
ls anatogous) , there are four different ways the question of lm-
pact on-racial representation has been approached.

First, a priori theoretical arguments have been advanced to
show why minorities are less likely to be successful in at-large
rather than district-level competitions. Second, historical evidence
has been amassed for a particular unit of government to demon-
strate that Blacks (or Mexlcan-Americans), although a substantial
minority, have not been proportionally successful in electing rep-
resentaiives of thei r own kind--evictence which seems particularly
telling when coupled with an historical record of racially polarized
votin!. Third, before-and-after case studies have been done of
citics wl:ich switched from at-large to ward elections or vice versa.
Fourth, cross-sectional analysis has been done comparing Propor-
tior:allty of raclat and Hispanlc representatlon ln cities wlth varlous
typee of eiest::'al systernr.

Let us first examirre the tl.reoretlcal Brclume,rts on the relt-
tionship between electiorr system and equity of minority represen-
tatlon: According to Tribe ( 1978: 755, n. 26)

well-eitoblislrcd mothentoticol principles ntake clcor
thot the likelilrcod of o minorityts bcing oble to elcct o

reprcsentotive clecreoses os district sizc incrcosc-s. Since
the use of multimembcr districts leods, for ony given size
of the tegisloture, to o higher overoge populotion
per district, it exocerbotes the olwoys presenl likelihood
thot o minority will be left completely tt'itl'tout represen-
totion.

We would wish to qualify Tribe's assessment because, as,
suggested by our discusiion betow, it leaves out the politics of
thJ*situation. Following Grofnran and scarrow ( 1978) we can, how-
ever, make Tribe's statement above (and analogolrs remarks in
Comment [ 1970: 1587-l5BBl arrcl el sewhere) consi<Jerably more pre-
cise by looking at the notion of thresholds of representation and
exclusion. The threshold of representotrbn, Tp (Rokkan, 1968;
Rae, Hanby ancl Loosemore, 1971- Crofman, 1975) is the minimum
support necessary to earn a group its first legislative seat. The
thrcshold of exclusion , TE (Loosemore and Harrby, l97l; Ct'ofman,
1975),on the other hand, Ts t5e maximum support whiclr can be

attained by a group and nonetlreless fail to win it even one seat.
Both those indices are rooted in the notion of an election as an
n-Person game.

lf we let m be the number of representatives elected from
the district and the number of candidates contesting tlre race, and
posit the minority group to run one candidate, then if all voters
cast a1 the votei t6 which they are entitled, the threslrolds of
representation and exclusion became as in expression (l) below:

ri
a

I

mmTl=-'E m + I ' 'R 
9"

Hence, for single-member district pl urality elections Tq = 7 and

,* = *. clearly ,+, ] rot m > l; and o. 9.

;"" 'q 2

lform> Il.mt

( l)

Hence, for a minority constituting a fixed percentage of the poptt-
lation irr each distriit, tl're maximum strenqth (under tlre worst of
circumstances) tlrat a mirrority group (fielding one candiclate) carr

have and still be excludcd fronr representation is higher under
mmd plurality (bloc) voting than uncler smd plurality voting; and
the lninirnun strength (under the most favorable of circumstances =
all groups other than your own being of the same size) needed to
gairi a first seat is also higher unclei mmd bloc voting than under
imd plurality. Thus, whether the best of circtrmstances or the
,orsi, under the specified assumption as to distribtrtion of miltor-
Ity strength across districts and as to voter behavior, for plurality
elections,'smds are always better for minority representation than
mmds.

ln addition to these purely analytic arguments, lt has also
been noted that:

881



ln district roces . . ., due to rcsidentiol segrcgultorr'.Blockcondidotcstettdtohoveonelectorotetultichisot
leost primorily Btock; given lhe niinority slotu.s.of Blocks

. in most Amer'icon cilie{, Block ospironts in all but a few
ot-lorgerocesmustcontendwitholilhiteelectorolmoiority,
ond Wnirc voters ore less opt to vole for Block condidotes
than o fellow Btock would be. filoreover, ot-lorge contests
oltegedly increose compoign costs, tend to require endorse-
,"it Oy civic ossociotioni ond lhe medio, ond ore bosed

often on nome recognition--otl elements which putotively
rleduce the chonces of Block elcctorol success' (Karnig
and tYelch, 1978: 2)

Turning now to the empiricSl approaches,.we find a pattern
of markedly iontradicting claims.3' Ai the municipal level, it has

been argued that at-larg-e electio_ns have traditionally been used

to discriminate against iacial and other minorities (Karnig and

Vlelch, 1978; Heiiig , 1978; Jones, 1976; Washington, l97l) ' lt
should also be notid that, although many I'at-large systems may

not rrave been adopted wiih the jpecific intent of weakening Black

political influence, there are documented instantg.t -*h:f" cities
irave changed to at-large systems as tactics to dilute Black potitical

influence[ 
-(Jones, 1976-: 34'6; see also Heilig, 1978; Sloan and

French, l9?l).

Ylhile we fincl intuitively plausible Malcolm Jewell's view that

',it is cii fficult to see how any local legislative body--city, county,
or metroPot itan--can be perceived as giving afee.yate voice and

vote to minorities if it i; elected in at:large elections without any

forrn of districting or proportional repr-esentationrr (Jewell , 1971"

53; cf. Dixon, lgil: 33-3ll); the empirical evidence on thls point

is iar from clear.

On the negative slde:

(l) ln Lakeland (a Pseudonymous satellite city near Detroit)
wlrich shifted from ward to at-targe elections with dei;ignated rep-
resentatives,Sloan(1969)foundnochangeinBlackrepresenta-
tiorr. 3o

cross-sectional methods, Cole (l97tl) has shown

Jersey cities Black representa-tion is not signifi-
by the presence of at-large elections'

(2) Using
that in 15 New
cantly affected

(3)MacManus(1978)inlookingat2ll3centralcities,has
,rgr"d' that once conirols'are introd-uced for socioeconomic and

ottier factors, the impact of district elections on Black city 
-

council representation vanlshes. Moreover, MacManus (1978)

iir,gtes ori thor" cities whlch experlenced a change ln election
iyti", durlng the past decade and finds no significant-.difference
i; th; propoition"liiy of Black.representation between those cltles
yrhictr inifiea from'viarA to ,t-larbe and those which shifted the
otherway.atthoughthemeaningfulnessofthlscross.sectional
;;rp";i;; rc "iiiiieo 

by the stTong ceteris paribus assumptlon

lmpticitly required.

882
883

(4)lVelclraltclKarrrig(19/8:2)1':r'ovrclcCv-irlclrctllrr(lr((ltrrlg
that sihoot districts with a-t-iarge contests actually have. greater

;i;;k ;"ptesentatiol i'r school 6oard elections' though their

limited sample or .iiiu, *iin oirtri.t-based representation makes

confident generalization impossible'

On the Positive side:

( l) Raleigh, North Carolina, and Charlotte' North Carolina'

recently, via refer"nJ,', shifted from at-large to ward elections;

and Mundt (1979) finOt rft't in Clrarlotte' Blacks no1-h9ld 27'31

of council seats as lornput"a to 5'q?-between 1945-1975 (see also

Heiliq, 1978), alttrougtr'in Rutuign, Btack representation remains

unchinged. 3e

(2) ln Fort Worth and San Antonio the 1977 change from at-

large io'ward elections lead to a ,'dramatic increaseil in Mexican-

American representalion in botlr cities (Cotrell and Fleischman'

le79).
( 3) Using the same cross-sectional data base of 273 central

cities as MacManus-1iszet, Robinson and Dye !]-97.q) co.me to quite

different conclusions. i6 'f n"y assert ( .1978: 137) that "Black
,"pr"r"ntution is significantly gr.eater in cities with ward elections

than in cities with it-l,tg" elections and further assert (1978:

ilc, iqo, emplrasis ours)-that "at-large election is tlre single most

influential independent variable" and that "reformed government

structures signiricaniiy "na inctepenclent/y contributc to Black

under rePresen tat ion . rr

(4) Using the same data base as both lllacManus (1978) and

Robinson and Dye ( 1978), Taebel ( 1978) ' who challenges the

suitability of the rrtio 'u""re of inequity used by Rob.inson and

ov"-irgzhl uno usu, instead the difference measure oI lvlacl\lanus

(1978), nonetheleslirot that botlr for Blacks and 1{ispanics there

ls a relationship ult*u"" at-large elections and inequity of minority

;;pr;;;i;tion,' altirorsr, 1r'1.t rJlationship is :tlonge.r for Blacks

t1,ln ior Hispanics [eJpecially when controlled for size of city'
council) . rl

(5) ln the study which we believe to be tlre most impressive

in its methodologii"iligot. wl'rich looks at the 264 American cities

with population over zi,ooo and with at least terr percent Black

poprrlation, ,no *t i.t, ftcuses on the 66 cities which combine dis-

trictwithat_large...up,."'u.'t"tion,KarnigandWelch(1978)show
thatincitieswittra-mixedsystem,thedistrictcomponentisalnrcst.
p".hlily proportional in its racial reDresentation while the at-

i;g;;";ionint ir'l"r'iro, equitabte (N = 66); an9 that in cities

using district systems Black representation is nearly proportional

to gi""k poputaiion (.sz on the difference measur€' -l'38 on the

ratio meaiure IN = OZ]); while in pure at-large cities^representa-
tfon is quite inequitiUie'(.G2_on.,the ratio mealure, -9.61 on the

differenie measure IN = llll)."

The nlne studies
this area) suffer from
tlons.

we have cited above (and other studies in
a variety of methodologicat flaws or limita-



Althouqh the case studies are longitudinal, in none ol tlre
case siudies -are there any cotrtrol groups, so that we can't be

sure that changes in patterns of minority rePresentation are
cousolly linked to changes in type of electoral system--minority
representation may be ihanging due to other factors' ln the
cross-sectional studies (with the exception of the within-city
comparisons for mixed systems in Karniq and welch -[19781), we

have the usual difficulty of causal inference. lf cities with at-
targe elections differ in systematic ways from- those with ward
eleftions (not captured by the control variables used), thet't
differences (or absence of differences) in equity of minority rep-
resentation rnay be artifactual. Moreover, the cross-sectional
studies differ in their operationalization of equity of representa-
tion, some using a ratio measure (Robinson andDye, 1-978; Welch

and Karnig; l9r8), some a difference measure (Cole, 1974;

McManus, -1978; Taebel, 1978). These differences in operationali-
zation can lead to differences in result. (See footnote 41.) Only
Karnig and welch (I978) and crofman (in an unp-ublished retabu-
lation'bf data in Sloan Il9G9J)make use of both the ratlo and the
difference measures.

Tlte cross-sectional studies also differ in which other
varlahrles (e.g., city council, council size, percent Black popula-
tion, city poful"rticn, city median income level , city manager vs'
maycr vi. 'comrirission, etc.) are controlled for and in the fineness
of ca,tegorization of type crf electoral system, used, w.ith most

authcrJ usinq a trichotomous classification (ward, mixed, at-large)
but some studies (MacManus, 1978; Karnig and lllelch, 1978) intro-
drrcing othrer potentially significant distinctions, e' g' , as between
at-lar[e elections wit6 and without designated rePresentatives.
Also, ihe cross-sectional studies vary tremendously-in the data

ir"ini e.*erninecl , with sample bases ranging from cities over 25,000,

to centra! citie,; exclusiveiy, to central cities excluding those with
miniinat Black populations, to very large cities (populations over
25C, 000.,

orre ornission common to all the cross-sectional studies is that
(for those cities with explicit or implicit partisan contests) they do

not differentiate between cities under Republican control and those

under Democratic control. This is an inrportant omission because

we would anticipate that Black representation would be compara-
tively lower in Republican-controlled areas because Blacks are
customarily pa.t of the Democratic party constituency. Finally,
and we beiieve most importantly, the cross-sectional studies do

noi (fUactrlanus I t97Sl and Taebel I l978] are partial exceptions)
loo-r'at guogruphi. concentration of minorities in the cities they
i"""tiiq;t".' ilearty, the nature of political .and demographic
realitiei wil! determine the extent to which single-memtrer or
multimember districting will help or hinder particular minorities'
lf a minority is reasoiably large and geographically concetrtrated,
it may expect to get its I'own" representalive(s) in a single-member
distritt ULt mignt-be swamped by other grouPs lf fo59eO to compete

foi representaiion in a very large multimember district' On the
other 'hand, lf a minority ii not-geographlcatly conce-ntrated and

ii-ii tr"i sohe politlcal rttout,'iimay be far more effective ln a

88{

larger mutimenrtrer unlt, whcra lt may be grantcd sorne reprcScntr-
tion, perhaps evetl rePresentation proprcrtional to its numbers,
than engaoed in fighting ond losing a ntrmber of struggles for
control of 

-single-member districts. (See discussion in Carpenetti,
1s7 2 .1

Nonetheless, if we look to the representation not of any
particular minority grouP, but of minorities in getreral, tlren an
argumerlt can be made on behalf of sinclle-member districts as

opposed to at-large elections wlrich we find to be compelling. - At-
large elections put minority representation at tlre discretion of
the majority. tn polarized situations, this is likely to leave minor-
ities completely unrepresented.

WEIGHTED VOTING. As of 1960, nrost New York counties used a

@fortheircountyboardsofsupervisorsinwhich
each town/city ward was qiven one representative. This scheme
was, not surprisingly, struck down in Croltom v, Boord of Super'
visors of Erie County (1967). ''3 ln the l960rs, in response to the
voiding of unit-votinq systems, nearly half of New Yorkrs 57

counties souglrt to preserve townsl'rip-llased representation while
still complying with Court directives oll "one man, one vote" by
shifting to rveiqhted votino schemes similar to that in use in Nassau
County (a county which, since 1917, had used weighted voting).
Two cases involving such counties (Saratoqa County and lYaslting-
ton County) were combined and decided by the New York Court of
Appeals in an important decision, lonnucci v. Boord of Srrpervisors
of the County of llloshington. ln that case, the Court held that
weighted voting was permissible only if the weights led to Banzhaf
power values for eacl'r legislator proportional to the population he/
she represented. (See Banzhaf, 1995r_ 1966; Brams, 1975; Lucas,
1974; drofman and Scarrow, 1980.) brr'rrs We shall quote tlre Courtrs
opinion at some length:

Atthouglh the smoll towns ii o county vould be seporotely
representcd on the boord, eoch nright octuolly Lre /css
oble to offect the possoge of legislotion tltott if tlte county
were dividecl into drsfrrcts of equol populotion with equol
rcpresentotion on the boord ond severol of the smoller
towns werc ioined together in o single district. (See
Bonzhof 1965: 317) . . The significortt stondorg! fol
meosuring o legislotor's voAng poYi,ni ill. U.onzhqf . .poiil; ouT:i;l;ol t6e nunrfcrniirqction of ve!9:-which
6e nti
@ent. of o meosure, And he
goes on to demonstrote thot o weighted voting plon,
while opporcntly distributing this voling power in pro-
portion to populotion, moy octuolly operote to dcprive
tlrc smoller .towns of tvltot little voting powcr tlrcy
possess, to such on extent thot some of thcm miqht be
comptetety disenfronchised ond rendercd incopoble of
offecting ony legislotion.- (lonnucci, emphasis ours) 15

r

885



' .The principle of one mon-one vote is viololcd, ttowever,
u,hen the power of. o representotive to cffect the possoge
of legistotion by his vote, rother thctn by influencing his
colleigues, does not roughty correspond to the proportion
of tlti populotion in his ionstituency, Thus, for exomple,
o porticulor weighted voting schcmc wottld be involid if
60;% of the populotion were represented by o single legis-
lotor who wos entitled to cost 60ea of the votes, Although
his vote would opporently be weighted ortly in proportion
to the populotion he represented, he would octually
possess 100q, of the voting powbr wltenever o simple'moiority 

wos oll thot wos necessory to enoct le.gislotion'
Simitoriy o plon would be invotid if it wos moth.e-moticolU
impossibte for o porticutor legislotor representing soy 5\
of tfie populotion to ever cost o clecisive vote' ldeolly, in
ony we:ioitted voting plon, it should be mothemoticolly
po'ssible for every member of the legislotive body to'iost 

the decisive vote on legislation in the some rotio
which the poputotion of his constituency beors to the
tolol poputotion. Only then woulri o nrember represent-
ing 5% of the populotion hove,'ot leost in theory, thc
sime vcting power ( 5o) under o weighted votin.g.plon
os he woutd hqve in o legistotive body which did not
use weighted voting--e.g., os o member of .o 2}-member
body with eoch member entitled to cost o single vote'
Tnii is whot is meont by the one mon-one vote principle
os opplied to weighted voting plons for municipol govern-
menis. A tegistoTor's voting power, meos.ured. by the
mothemoticol possibititv of his costing o decisiue uo!9,

lo-
ture which did not employ weighted voting.-

(lonnucci, emPhasis ours) *'

The Court then went on to confess itself unable to determlne
whether the plans before it met the criterion proposed, and
asserted that the Boards are not entitled to rely'on the presump-
tlon that their legislative apportionments are constitutional.
Rather,

. .with respect to weighted voting. , ,o considered
ludgment is impossibte iithout computer onolyses o.nd,
occordingly, if the boords choose to reopportion them'
selves Oy tne use of weighted votinq, there iJ n9,ol-
iir"iiii aui ti requireihem to ,oi, 6F*oFiFW

ses on

lIlth these words the court ushered ln the age of computer-
lzed weighted voting in New York county- government. . The ex-
perlencei of the 24-New York counties which have used weighted
vcting offer a number of useful lessons to leglslatures .considerlng
opl.iois cther than simpte single-member districting and a number
oi lessons in terms of 

'evaluating the ability of lawyers and iudges
to understand sophistacsted mathematlcal arguments ln the xons

!1t3ll, (,r.c voterl ar88. 
6oE

plons.
Tdi-nucci, emphasis ours) 18

First, in many counties weightecl voting has c;i.ren rise to
situations in wlriclr a coalition of i very few of the large;>olitical
units can wielcl major-ity control . Second, by allowinq. modified
weightecl voting, without recorltrizing that representa.tives from the

,u**o ditttict elected by the same constituency are likely to vote

as a bloc, the courts have inaclvcrtcntly allowed the largest unit
in one New York county a disproportionate share of the plower

iCrofman and Scarrow, 1981b, forthcoming) ' Tlrircl, in general'
weighted voting systems fail to satisfy tlre criterion of equalizing
t,peison powern; i.e., tSey do pot allocate a trttmber of reltresen-
tatives pi.oportional to the population representccl , thtrs failinq to

recogniie that legislators perform services which have notlring t-o

ao witn voting ar.rO tnhi.h reqrrire personal attention. (See Grof-.

man ancl Scarrow, l9BIa, forthconling.) For'rrtlr, New York courts
have unknowingly shifted the method of measurentcnt ttsed to

measure tlre fai-rness of power apportionments in weigSted voting
schemes, so as to apply an extrenrcly weak standard wlriclr is at
variance with that used by the U.s. strprenre court for luclging
single-member district scltemes. Fifth, the court-inrposed require-
.nnt of computer caiculations to obtain optimal weiglrt assignments
for weig;hteci voting systems has prove^ largely unnec.essary; i'e',
the ass'lgnment of weights according to si mple population propor-
tions wo-uld have prod'-rrced power icores which matclred population
proportions almost exactly. (For extended discussion, see Grofman
and scarrow, 1979, 1980, 1981 forthcoming, l98lb fortlrcoming' ) re

ln sum, it does not appear to me that weighted voting ought
to be looked to as a means of provicjing particular geographic units
(or geographically concentrated racial or linguistic minorities) a

,uun", oT ,ep.ur".,tation proportiorral to population. lYhile weighted
voting.".,6u used to accomplislr this end, I believe that its draw-
backs" more than outweight its benefits, especially as its constitu-
tionality has never yet -been subiect to suprente court- test. None-

theless, if clistrict jires arc permitted to vary only sliglrtly from
equipopulation, weighted voting nright be a useful way of recOr':il-
ing i,one person, oie vote" standards lvith maintenance of politic:al

suiunit bounclaries and witltout requiring much of any decennial
shifting of district bouncJaries (Lee Papayanopoulos, personal
communication, June 14, l9B0).

PROPORTIONAL REPRESENTATION.

f-

The Hare System. slightly over two dozen U.S. cities have made

ilse-ofurofirfional rep-resentation (in the form of the Hare single
transferabie vote) for their city council elections at some time
during tlris century, primarily during the periocl l9l5- 1946 (l1oag

and fiallett, 1925; Hallett, 'lgtl0). Most of these cities used PR

for only a few elections, but seven cities (Ashtabula, Bottlder,
Cincinnati. Lowell, New York, Toledo, t{hcel irrg), used PR for at
least a decade, and one city (Canrbridge) is still usirrg PR and
has done so since shortly after lY}llt, while New York began in
the lg70's to use PR for school board elections. Until the early
60rs, the Nationat Municipal League had PR as one of the compo-
nents of its rnodel citY charter.

no,



The chief obiections to PR were that ( l) the Hare system

was too compl icated for voters to understand, (2) the Hare system

$/as too complicate<J for voters to use, leading to lower turnout
and a high proportion of spoiled ballots, (3) PR made stable

maiority Tule government impossible, and (q) PR made it possible

for r,undesirables" e.g., kooks, communists, Negroes) to be

el ected.

The first charge is partly true but largely-.false.' Certainly
the Hare vote transf"er procedure is rather compl icated to explain,
but most voters could readily grasp the basic idea that any grtup
*r,i.t composed a certain prbp6rtion of the electorate woul d be

able under the Hare system to elect a representative of its choice.

Moreover, it seems ,.,fiL"ty that Americans who can tell you. how

many games the Phillies are out of third in the division would

r""jit/ be unable to comprehend the idea of rank-ordering their
candidate preferences.

I nere ts no evidence to supPort the second charge and

little eviclence to support the thirct charge, either {s-ee esp. Dodd,

lg76). Nonetheles., 
'l]orro. stories about the instability of Euro-

pean countries whic-h used (party list) PR were used by PR

opponents to attack the Hare system as malefic and trn-American'

The fourth assertion, that PR led io the election of "un-
desit'ables,r'was resjonsiUie for the demise of PR in a number of
instances. The election of atleged "irresponsibles" in Ashtabula,
the election of communists in N-ew York City, and the threatened

"ru.tio" 
or a Blacl< mayor in cincinnati were key factors in the

referendutn repeals of PR in those cities'

The repudiation of PR by all but one of the American citi€s
which uscd ii hus oflen been alleged to demonstrate its unsuita-
bility for use irr the U.S. Actually, as far as we are aware' in
those cities rvhere the Hare system was usecl it worked well' and

its "unrlesirable" conseqtlences were mostly in .the. eyes of the
previously impregnably entrenclred maiority beholders'. Whether

ih" pr"r"nt d'ay lontext of concern for effective minority repre-
sentation can "ilo* PR to make a "comeback" is an open question'
There are a few signs of its present day resuscitation' e'9" use

of the Hare Syster-in thu tgiO's for school board elections in New

ioit 
-City, 

un'a tt',o ieplacement of winner-take-all primaries with a

form of pioportionat representation in the Democratic Party nomi-

nating process. (See Lenqle, this volume')

ccrrnulative Voting. Voting for the llllnols ceneral Assembly has,

ffi''periodofstatehood,madeuseofcumulative
,oting. cumulative voting in lllinois takes place in three-member
distriits, in which voters nny cast three votes for a single candi-
aaie o. one and a half votes for each of two candidates or one

vote apiece for three candidates.

' One consequence of cumutative voting as it has been prac-
ticed ln llllnois ii tfrat virtually all districts have elected one

mlnorlty party and two maiortty party rePresentatlves, since (for a

Rnn

two-Party contest) only wlrere tlre rniority Party lras 751 or nnre

of the voting strcngtlr (and can expect its loyalists to vote a

struijftt pariy tict<ei) .un that party capttrre all three seats in a

ai ,trtt. ' Thus, the Republican clownstate rtrral districts clect

some Democratic representatives to tlre lllinoi s llouse and ttre
Ctli.rgo Democratic districts elect some Republican.r'epresentatives'
This crossover prevents the urban-rural split in lllinois frorn being

defined in PurelY Parti san terms'

A proposal for the repeal of cumulative voting was made as

part of a referendum to redtrce the size of the lllittois Assembly-.

Thi s referendum carried overwhel mingly in 1980 for reasons that
had little or nothing to clo with support/opposition to cumulative
voting.

lnourview,thelllinoisexperiencedemonstratesconclusively
that the effect of a particular voiinq system catr be- understood
only in the context of the politics in which it is embedded' ln
lllinois, cumulative voting has operated within the context of a

t.ril.,o.-'iri,it-party system.- ln lllinois, cumulative voting has not

i;J t, i prolifelation of single-issue candidates or parties. More-

over, in lllinoi s, for a variity of reasons, the prol itical parties
have not run wlrat (in retrospect) can be shown to be the optimal

number of candidates. ln particular, the maiority party in each

district plays it very safe. Even in cases where ttre maiori ty
putty tut"iied over 60? of the vote--cases where it can be shown

if,"t'it could not hurt for it to lrave run three candidates--over
808 of the time only two candiclates were run (Brams, 1975: 120). sc

ln tllinois, cumutative voting has certainly not destroyed
two-party government nor has it been accompanied by an unusual
proliferatioi of "special interest'r representatives--charges often
ieveled against PR systems. Furthermore, it has usually given
rise to a vert,5looO i.it between a party's vote share. and its share
of legislative'seats. On balance, ihe cumulative voting record in
lllinoTs lvas a quite favorable otre (Sawyer and MdcRae,. 1962;

Blair, 1973; Epstein and Crofman, work in progressl ' "r

NOTES

l.Forexample,atpresent(accordingtotheCouncilof
State Governments) the upper house in 13 states and the lower
house in 22 states utilize some multirnember districts'

2.NewYorkhas24ofits62countiesusingsomeformof
welghted voung within the county legislature and l2 electing
repiesentattvei from a comblnation of s-ingle- and.nrultiple-inem[er
dtitrlcts or multlple-member cllstricts of various sizes'

3. In two articles whlch appeared ln Amerlc.'tn law journals

ln the mld I960's, a lawyer named John Banzhaf tll (B.lnzhaf ,

1965, 1966) proposed to evaluate representatlon systems in terms
of the extent to whlch they allocatedrrpower" falrly. . Banzhafrs
analysis makes use of game-theoretic notions ln whlch power ls
eguated wtth the abflity to affect outcomes.

r
I

889



' Conslder a group o{ sltlzens choostng between two opposlng
'. candtdates. To calculate the power of the tndlvldual voter, we

generate the set of all posslble voting coalltlons among the dls-
trlctrs elg_ctorate. If there are N voters in the distrlct, then there
will be 2N posslble coalitions. Then we ask, for each of these
posslble coalitlons, whether a change ln an lndlvidual voterrs cholce
from Candidate A to Candtdate B (or from Candldate B to Candl-
date A) would alter the electoral outcomc. If so, that voterrs
ballot ls said to be declslve, A voterrs power is deflned as the
number of tlmes, tnTif possible coalltlons, that his vote could be
declslve, and can best be expressed'as a percentage--1.e., the
number of hls declslve votes dlvlded by the total number of all
the declslve votes of all the voters (lncludlng himself). The
hlgher the percentage of voter coalitions ln whlch hls vote is
declslve, the htgher a voterrs power score. The BTn'zhaf lndex
E,IFGsiderable lntultlve appeal; power ls based on abllity to
affect cutcome. However, the Banzhaf calculatlons also rest on
the not so reasonable propositlon that all voting comblnatlons are
equally likely.

For slngle-member dlstrlct systems, each dlstrict having
equ.J populations, all voters have ldentical power; the abtlity of
the votcr ln one distrlct to affect his distrlctrs electoral outcome
Is lden'rlcal wlth the abillty of another voter ln a nelghborlng
district to affect the outcome there. But what about the case of
multiple-member dlstrlcts, with some distrlcts of one slze and
others of another size? Here, slnce the voters who elect k repre-
sentatives have k tlmes as much importance as voters who can
elect only one representative, we might expect that to equallze
voter power we should asslgn the districts with k representatlves
k tlmes as mar:y voters as well , since wlth all votes of equal
welght, intuitl..'ely, we would expect a voterts ablllty to declslvely
affect outcomes sl'rould be lnversely proportlonal to distrlct size.
Banzhaf ( 1966) polnted out that thls argument ls mathematlcally
lncorrect and tlrat actually the voters have declslve power propor-
tlonal to the square root of dlstrlct slze.

Thls lssue and the mathematlcs underlylng thls argument are
dlscussed at length ln Lucas ( 1974) and Grofman and Scarrow
(I98la, forthcomlng).

4. Chapman v. Meler (1975) 420 U.S. at 15-16.

5. Whltcomb v. Chavls (1971) 403 U.S. 124 at 157-158,
n. 38.

6. Fortson v. Dorsey (1965) 379 U.S. 433.

' 7. Reynolds v. Slms (1964) 377 U.S. 533 at 57.

8. Burns v. Rlchardson (1965) 384 U.S. 73, at 74.

9, Fortson v. Dorsey (1965) 379 U.S. at 439.

10. Burns, Kllgarlln et al. v. Hlll (1964) 386 U.S. 120.

ll. whttcomb v. chavts (1971i 403 u.s. 124 at I25.

12. Whttcomb v. Chavts (197I) 403 U.S. 124 at I4l.
13. Reynolds v. Slms (1954) 377 U.S, 533 at 565.

14. Whitcomb v. Chavls (197i) 403 U'S' at 144'

15. Wlritcomb v. Chavis (1971) 403 U'S' at 144-145'

16. Whlte v. Regester (1973) 412 V 'S' at 767'

17. White v. Regester (1973) 412 U 'S' at 767'

18. White v. Regester ( 1973) 412 U'S' at 769'

19. Kruidenic v. McCulloch ( ) 142 N'W' 2nd 355'

ZO. Graves v. Barnes (19721 373 F' Supp' 704 (W'D"
Texas).

21. Graves v. Barnes (1974) 378 F' Supp' 640 (W'D"
Texas).

22. Connor v. ]ohnson (1971) 402 U'S' 690'

23, In.East carroll Parish school Board v. Nlarshall (1976)

424 U.S. 636 the court held that single-member dlstricting ls the
ippropriate remedy for federal courts to lmpose where a-t-large

"in"tion 
schemes have been found to unconstitutionally dilute the

;;;;; "i."nsth 
of Black nrinorities. In iurlsdictions @vered

";e;; tne V6ttng Rishts Act of 1965 (as lnterpreted by the U.S.
Suprerne Court ln the Petersburg and Richmond cases (see belol),
slnce 1973 the Justice Department.has had a ban on changes from
ward to at-large districting.

24.CityofMoblle,Alabamav.Bo]den(1980)48L.w.4436.
25. It appears as lf a new wave of reformers has taken up

district elections as a "reform" to replace the at-large elections
whlch were a reform of an earlier generation of reformers. In
addition to court challenge to at-large electlons, referenda to
replace at-large with district elections have taken place ln a num-

Uei of cities;1nd faced with the prospect of court challenge' a

number of cities had voluntarily shifted from at-large to district
elections. By one or the other of those mechanisms, at-large.
electlons have been replacecl with district syste$s in such cities
as Albany, Georgia; Charleston, South Carolina; Forth Worth'
te*a.s; Mo'Uit", Alabama; Aberdeen, Mississippi; Raleigh, Virginla;
San Antonlo, Texas; San Franclsco, California; and Waco' Texas
(Heilig, l97B; Cotrell and Fleischnnn, t979; Mundt, 1979) '
lf"rtn"i polltrcal nor legal challenges against at-large elections or
systems whlch mix district and at-large elections |Bvs,_however,
bten u'tformly successful. (See Karnig and Welch, 19782 2;

Cotrell and Flelschrnan, 1979, note 8.)

26, Lucas v. Colorado General Assembly (1964) 377 U'S'
713, n. 2.

27. Beer v. U.S. (1976) S. Ct. 1357.

28, Zlmmet v. McKeithan (1973) F. 2d 1297. At-large elec-
tlons for school board and -rollce Jurles ln Louisian.r Parlsh
(courry) were repudiated irr Zimmer, dcspite thc fact that 46t
of the registered voters in thE-F;iGh were Black and some Black
candlclatei had been elected in the previous at-large elections--
lncluclng one candldate whc md been defeated when runnlng ln
nt oo:n-ward when ward-bastd elections were ln effect. (This

r
i

891



case ivas afftrnted, albeit on otlrer grc'unds, as East CarroLl Parlsh
'.School Board r'. l"larshall [19761 424 U.S. 636. See discussion ln

Dolgorv, 1977: 173-475. ) In Wallace v. House (515 f . 2d 619 [ sth
Clr. 19751), at-large mutricipa! elections were inv.:tlidated ln
Ferriday, Louislana, although a plan combining mixed single-mem-
ber dlstricts and at-large electlons was upheld. (In that city,
although Blacks constltuted nearly fifty percent of the voters,
under the at-large scheme they had controlled not one of lts
aldermanlc seats.) A number of other at-large electlons have
been struck down, but ln other Jurlsdlctlons at-large electlons
were sustained agalnst legal challenge. (See e.9., Hendrix v.
Joseph ll977l 559 F. 2d 1265 and Davld v. Gamson I 1977] 553
F. 2d 923.)

In Richmond, Vlrglnla, a shift from at-large to ward elec-
tlons for city councll was the prlce the city was required (by the
Justlce Department) to pay if lt wished to annex a suburban area
which vras predomlnantly White--an annexatlon which would have
kept the city population maJority White. The Justice Departmentrs
authorlty to lmpose such a requlrement under the Voting Rights
Act of 1965 and 1975 was sustalned by the U.S. Suprerne Court
tn Clty of Ricirmond, Vlrglnia v. United St.rtes (1975) 422 U.S.
358. (See also City of Petersburg, Vlrglnia v. United States
I I973j 410 U.S. 926.) See also Beer v. U.S. (1976) 76 S' Ct.
1357, ln which the at-large component of a proposed change ln
electlon procedures for the New Orleans Clty Council election
was exempted from Justice Department scrutiny because the at-
large features remained unchanged from earlier election laws and
thus were not held to be subject to review under the Voting
Rlghts Act of 1965.

29. Thls result was antictpated ln an earlier case before
Flfth Clrcult, Nevitt v. Sides (1978) 571 F.2d 209, in whlch the'
claim was reJected that at-large dlstrtctlng for a clty council
in a raclally polarized clty was per se dlserlminatory, and a show-
lng of "lntenticnal" discrimlnatlon found to be necessary. In
Nevltt the court referred to at-large districting as "racially neu-
i?ilIon its face," and the court asserted that I'absent other
evidence lndlcating the existence of lntcntional discrimination,
state laws provldlng for at-large distrlctlng are entitled to the
Ceference accorded any other statute; thelr means need only be
reasonably related to ends properly withln state cognizance.rl
However, ln Nevltt (at 22ll the Court held that a plan, rrraclally
neutral at its ad-optlon" may be unconstltutional lf it furthers
t'preexlstlng dlscrlmlnatlon" or ls used to [malntain" lt. More-
over, and most lmportantly, ln Nevitt the Fifth Circult court
maJorlty waTTEid-EiEEiI-Throug6-ilEEt we regard an lngenlous
loglc chopplng, to reconclle the proof of lntent requlrement
enunclated by the U.S. Supreme Court ln Washlngton v. Davls
as belng fully compatlble wlth lts own prevlous rullng ln Zlmmer
v. McKetthen.

30. tTashlngton v. Davls (1976) 426 U.S. 229.

'31. Arllngton Helghis v. Metropolltan Houslng Development
Corp. (19771 429 U.S. 252. Arllngton Helghts lnvolved a zonlng
ordlnance prohrbltlng multlfamily dwelllngs, whtch was challenged

on the ground that the orcllnance hatl a raelally dlscrlntltlatory'
effect. washlrrgton v. Davis involvcd the constitutiollolity of a

;;ltt;; pui-"onnlt test which Blachs vrct'e fottr tint's mote lil:elv
to fail than whites. Roth the orrlin.rttce arrd tho tcst werc fotrnd

io U" O"uoid of any racial overtones which would require Court

intervention on constitutional grounds, sit.tcc in ncither casc was

itLie touncl any intent to engage in racial discrimittation.

g2, The difference between the purpose doctritre .tnd earlicr
rulnds can be sl.rown with a quote from the holclings ilr Graves v.
Barnis (1974) 378 F' Supp. 640 (emphasls ours):

Civen generol conclitions incticoting rocio-|. di.scrimi-
nolionthot-hosstuntcrltheporticipotiottofBlocksond
Mexicon-Americons in tife of stote, plointiffs who cloim
thotntulti-nlemberlegislotivedistrictsdiscrinlinoted
igotinst.such minorit'y necd ottly proYe o.n ogsregote of
fictors inctuding restrt'ctel occess of minority groups
lo sloting of coididotes for porticulor porty nominotions,
consisteit use of rqciol corypoigrt toctics to dcfeot
minority conclidotes or tlrosc chompioning minority con-
ccrrts, indifference or hostility of district-wide represen-
totives to porticulorized minority interests, ond inobil!t.y
of minority groups to-oQ!o.in rgprcsen.totlon in proportion

,

Sg. Ur" *nfr, also note that in Kirksey v' Board,-of Super-
visors of Hlnd iounty, Mississippi (19771 544 F' 2nd 139' a 1977

case which also reached the U.S. Court of Appeals, Fifth Circuit,
wedge-shaped single-member districts which cut up the Black
populatlon so as to deprive them of maiority cotrtrol of any riis-
irict were rejected as discriminatory even though direct discrimi-
natory intent was not proved; while ln City of Rome, Georgia 'r'
Unitei States (August 9, 19791 472 F. Supp 221 lU.S. District
Court, District oi Columbia, a change of election sys-tem which

ln ioalcea runoffs, nunrbered posts, and staggered elections was

held to violate the votlng Rights Act even though no intent to
discrlminate was proved. In Kirksey there was 'rn cstablished
history of previous discrimin.rtion and a holding that incquality of
u""u." to tire political process was an inference which flolfed from
existence of economic and educational inequalities suffered by
minority inhabitants of the county. In the words of Iudge
Godbold ln that opinion, ,,nothlng suggests that where purposeful

and lntentional discrimination already exists it can be constitu-
ttonally perpetuated into the future by neutral official action.rl

34. Fortson v. Dorsey (1965) 379 U'S' 433 at 439'

35.CttyofMobile,Alabamav.Bolden(1980)48LW4436'
Note 13.

36. Fortson v. Dorsey (1965) 379 U'S' 433 'rt 439'

37, Karnlg and Welch (1978: 2-4) review a nurnber of these
studles arrd the reasons why findlngs dlffer' We draw upon their
iniiv"r"l* our dlscussion below. A detailed discussion of over a

dozen studles (lncluding all those clted below) ls available upon
request from the author.

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r38. Sloan ( 1969; Table 3, 1967) d<.res find that, under at-
" Iarge elections with deslgnate,d reprresentatives, when two Blacks

run against each other, the Black preferred by other Blacks is
defeatcd ln the city-balloting. Thus, while the percentage of
BlEEEEpresentation may remain unchanged, tlre-frETii6-of that
representatlon may have changed dranratically. We regard thls as
an extremely lmportant polnt. A number of mlnority representa-
tlves propoitlonal to mlnorlty population ls not a suffl?teilftffill-
Gi-for proportlonate representatlon of minorlty interestff and
lndeed lt may not evenl6-E-nEEe33E-ry one. We share the vlew of
Trlbe (1978: 658-659) that 

--.:-To speok of o group's electing "its" represcntotive is,
ofter oll, on oiersimptificotion. -Vorious condidotes
oppeol in vorying degrees to oll populotion groups.
Thus o minority might insure some representotion cven
in o district where it could not come close to electing o
condidote who espoused its views without reservotion;
the minority could help elect the condidote whose views
were leost obnoxious to its members. OI course, if
there were cleorly dichotomized minorities ond moiori-
ties--ortd if voters never cost r,voyword bollots--tlte
minority ttright still be completely denied representotion.
But these foctuol ossumptions defy lhe focts of politicol
life: there ore mony types of lnterests ond mony grodo-
tions of opinion, *,ith the result thot o process of
occontmodotion is generolly undertoken in which even
srnoll minorities con successfully vie for influence.

39. Irlclr'lanus ( 1978) , Taebel ( 1978) , and Robinson and Dye
(197E) look at the same cities. However, the exact data each look
at ls sllqhtly different. See lvlacManus (1979).

40. lr4unilt ( 1979) has looked at Rlchrnond. In response to
leqa! clrailenge to a proposed annexation of White suburbs whlch
v:culd h(-rve reduced the percentage of Black population below 508,
there lvas a Justlce Department-imposed shtft frorn at-large to dls-
trlct electlons in whlch four distrlcts were created with a clear
Black majorlty, four wlth a clear lVhlte maJority, and one dlstrlct
rvhich was a "slvlngt'dlstrlct. T'he swing district has been won by
a Black candldate, creatlng Black majority control.

41. All but turo of the (cross-sectional) studles concluding
that at-large electlons impede Black representatlon have employed
the ratlo approach (exceptlons are Taebcl, L978, and Karnlg and
Welch, 1978), and both of the cross-sectlonal examinatlons un-
coverlrrg no relatlonshlp between Black electabtlity and electoral
form have utlllzed the dlfference approach (Cole. 1974; MacManus,
1978).

42. Karnlg and Welch find the most lnequttable Black
representatlon ln cltles uslng at-large elecUons wlth deslgnated
representatlves (.44 on the ratlo measure, -t{.0E on the dlfference
measure, N = 27).

{3. Graham v. Board of Supervlsers of Erl County (1967)
267 N.Y.S. Znd 383.

44. Iannuccl r'. Board
tlrashinqlton ( 1967) 2BZ N. Y.
tlon of the Banzhaf Index'

of Supervlsors of the County of
2nd 502. See Footnote 3 for a detr,ti-

' 45. So lond as each legislator has.r sirrgle Yf,A or NAY vcte
on issues conring beforc the legislature, the qrtestlon of legisl.:ttlve
power does not ltave to be explicitly addressr:d. Thus, irr tho
ieading apportionment cases wltich havc come before thc U'S'
Supreme Court, all of which h.lve involvcd single- or multiplc-
member districts with each electcd rcprcsclltative cligible to cast a

single vote, it seclns to be sirnply assum€ that thc jttstific.rtion
for exantlnlng the number of persons contairred withln each (listrict
ls the fact tliat their elected representatives by thcir vote wie'ld

equal declsion-making powcr in the affairs of the polity; and that
equality of apportionment thus indirectly results in equality of
policy-maklng power among citizens.

But what about weighted voting schemcs (also fractional
voting schemes) where, say, a legislator fronr a district with
20,00-0 population casts two votes, while a legtslator from a distrlct
with 10,000 population casts only one vote? Again, it was John
Banzhaf III who polnted out the fallacy of such "common sense"
apportionment schemes. Consider, f<-rr example, a three-member
committee, with members A ancl B with two votes, arrd mernber C
with only one vote. Despite the fact that vote shares (weights)
are not Lqual , from the stanclpoint of BanzEEf-k copcept of decisive
votes all commlttee members have equal power (l/3, l/3, I/3) when
a majority (3 of 5 votes) is needed. Wh;; a two-thirds vote is
necur"uty for passage, the power scores change. Now member C
has no power at all (in the language of game theory, he is a

dummy), while the other two members each hold 50 pcrcent of the
power. Banzhaf 's argument is simply that when vreighted voting
schemes are designed, weights should be assigned in such a way
that a legislator's power (as contrasted with the number of l'otes
he wields) should 6E-ni5de proportional to the number of citizens
tn hls distrlct.

46. Iannucci v. Board of Supervisors of the Country of
Washington (1967) 282 N.Y.S. 2nd 502 at 507.

47. Iannucci v. Board of Supervisors of the Country of
Washlnston (1967) 282 N.Y.S. 2nd 502 at 508.

48. Iannucci v. Board of Supervisors of the Country of
Washlngton (1967) 282 N.Y.S. 2nd 502 at 510.

49. New York courts have also failed to rccognize the
mathematlcal identity between wclghted votinq systcms and multl-
member dlstrict systems 1n which dlstrlct represcllt.ltives vote as a
bloc. This ls an ,mportant omlsslon becattsc partisan politics in
New York makes bloc voting at the district Ievel thc rcallty ln
most New York political units with multimember distrlcts.

50. Among the reasons why parties did not purstle an
Ioptlmal'r strategy are (a) electoral uncertaintles with them wtrich
prevent the clear identification of an optinnl strategy (Brams,
1975: I20); (b) understanding opposite numbers ln the other
party--sweetheart deals which preserve lncumbents and ellmlnate
iwo-barty competltlon (Sawyer and MacRae, 1962: 939-945);

89s

r
I



(ci gc.Itrol by the partyts lnclrmbents ln the district of the number
\if candidates to be slated. Incumbents are reluctant to see addl-
tional candldates on the ballot. Candidates who aren't certaln of
election may act as ittdividuals rather than as part of a party
slate, thus potentially jeopardizing the electoral success of the
partyrs other candlclate(s). In particular, they may jeoparclize
the electoral success of the incumbent(s) running for reelection.
(David llpstein, Parliamentarian, Illinois House of Representatives,
Personal communicatlon, July 1I, 1980); and (d) since the early
70rs, a clause ln the Illlnots constitution compels political parties
to nrn no fevrer than two candidates ln each district. With a hand-
ful c,f exceptions, thts provtslon has been complied wlth throughout
the state.

51. in November 1980 cumulatlve voting for the Illlnols
House was abollshed as part of a referendum to reduce the slze of
the leglslature.

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BLAIR, G. (1973) rrCumulative voting: An effective eiectoral
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BRYCE, f . (1889) The Amerlcan Commonwealth, Vol. l, London.

CARPENETTI, W. (l9T2l "Legislative apportionmerit: Multimember
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COLE, L. (1978) rrElectlng Blacks to munlcipal offlce: Structural
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HOAG, C. ancl G. HALLETT (1926) Proportional Representation.
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JEWELL, M. (1970) "Commentary on rthe court, the people' and
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IONES, B. ( I976) "Distributional considerations in models of
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KARNIG, A. and S. WELCH (1978) "Electoral structure and Blar:k
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LtiCAtI, W. (lg74l "Measurlng power ln welghted votlng systens'rl

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( 1978)
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wAS!iINGToN,R.(1971)|lDoestheConstltutionguarahteefalr
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scficof 

'boards,x 
Soclal Sctence Quarterly 59: 162-I71.

t-
)



Flgure I

Relatlonshlp getween Vote percentage and Seat Percentage ior a Slngle-ilen6er Dlstrlct Leglslaturc
I

lthose Equlpopulatlon Dlstrlcts Hrve'Been Randomly Drawn

1..,

1.0

.9

'.8

SEATS (S)

.7

.6

.5

.{

.3

.2

.l

0

'0.1.2.3.4.5.6.7-8.91'0
YoTES (V)

?

\ ..-r

o Blnomla'l
Approxlmatlon

n_-sl- I.
Ocublc: \S/ \

XSlmulatlon of
Randomly Drrwn
0lstrl cts

R.R,
.o

x
ox

I
u

x
o

6
x
o

*66