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19 Rutgers L. Rev. 317 (1964-1965)
Weighted Voting Doesn't Work: A Mathematical Analysis

handle is hein.journals/rutlr19 and id is 323 raw text is: WEIGHTED VOTING

John F. Banzhaf IIl*
In response to recent decisions requiring that both houses of state
legislatures be apportioned so that equal numbers of citizens have
substantially equal representation, weighted voting has been widely
suggested as an alternative to actual reapportionment. Weighted vot-
ing has already been adopted in at least three state legislative bodies,
including the New Jersey Senate; ordered by one federal district court;
considered in several other states; and used by one county governing
body for a number of years. In New Jersey and New Mexico, state
courts rejected, on state grounds, the weighted systems which had been
adopted.' Under such systems, in lieu of actual redistricting or reap-
* B.S.E.E., M.I.T., 1962. At present the author is president of Computer Program Li-
brary and an Editor of the Columbia Law Review at Columbia Law School.
The author is indebted to Martin Jacobs, Fairleigh Dickinson University, and Donald
Wardle, Columbia Law School, for their help in preparing this paper.
1. N.M. STAT. ANN. §§ 2-7-1 to 2-7-13 (Supp. 1964) established a weighted voting plan
for the New Mexico state legislature; this plan was later held to conflict with the state
constitution. Cargo v. Campbell, No. 33273, Dist. Ct. of Sante Fe County, N.M., Jan. 8,
TIONMENT 180 (1964). The New Jersey Senate passed a resolution creating weighted voting
in that body, but the resolution was subsequently invalidated for reasons of state law. See
Jackman v. Bodine, 43 N.J. 491, 205 A.2d 735 (1964).
Four reapportionment plans were passed by a special session of the New York legislature.
See Reapportionment Compliance Act and amendments, N.Y. Sess. Laws 1964, Second Ex-
traordinary Session, chs. 976-79 (McKinney Session Law News, Feb. 25, 1965). Two estab-
lished fractional voting, a type of weighted voting. Three of the four plans, including the
two based on fractional voting, were invalidated by a federal district court, which held that,
among other objections, fractional voting failed to equalize representation in areas other
than voting on the floor of the legislature. WMCA, Inc. v. Lomenzo, - F. Supp. - (S.D.N.Y.
1965). A state court subsequently invalidated all four plans on grounds which did not in-
volve weighted voting. See N. Y. Times, March 16, 1965, p. 1, cols. 1-3; id., April 18,
1965, p. 1, col. 8. Nassau County has had weighted voting for years, and New York State
law allows other counties to adopt it. N.Y. OPTIONAL COUNTY GOV'T LAW § 1006-a; see
Dutcher v. Hatch, 19 App. Div. 2d 341, 243 N.Y.S.2d 80 (1963). In the state of Washington
a federal court threatened weighted voting as a stop-gap but later retracted the order when
the legislature acted. Thigpen v. Meyers, 231 F. Supp. 938 (W.D. Wash. 1964), modified, No.
5597, W.D. Wash., Oct. 27, 1964, reported in XII NAT'L MUNICIPAL LEAGUE, COURT DE-
Several other courts have also briefly considered weighted voting with varying results.
Weighted voting has been cited with approval in only one case, Maryland Comm. for Fair
Representation v. Tawes, 228 Md. 412, 439, 180 A.2d 656, 671 (1962), where, in dictum, the
court suggested that it might be employed instead of reapportionment to achieve equality
of relative voting strength. The case was subsequently reversed on other grounds, 377 U.S.
656 (1964).
Two courts indicated that weighted voting would not be compatible with their state con-
stitutions. Fortner v. Barnett, No. 59965, Ch., Hinds County, Miss. (1962); Brown v. State
Election Bd., 369 P.2d 140, 149 (Okla. 1962).
One court initially considered it as a possible means of apportionment but rejected it
when counsel for both sides had conceded that weighted voting would be contrary to the


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