Dudum v. Arntz

                  FOR PUBLICATION
  UNITED STATES COURT OF APPEALS
       FOR THE NINTH CIRCUIT

RON DUDUM; MATTHEW SHERIDAN;           
ELIZABETH MURPHY; KATHERINE
WEBSTER; MARINA FRANCO; DENNIS
FLYNN,
              Plaintiffs-Appellants,
                v.                           No. 10-17198
JOHN ARNTZ, Director of Elections             D.C. No.
                                           3:10-cv-00504-RS
of the City and County of San
Francisco; CITY AND COUNTY OF                  OPINION
SAN FRANCISCO, a municipal
corporation; SAN FRANCISCO
DEPARTMENT OF ELECTIONS; SAN
FRANCISCO ELECTIONS COMMISSION,
             Defendants-Appellees.
                                       
       Appeal from the United States District Court
          for the Northern District of California
       Richard G. Seeborg, District Judge, Presiding

                 Argued and Submitted
        March 15, 2011—San Francisco, California

                    Filed May 20, 2011

      Before: Richard A. Paez, Marsha S. Berzon, and
               Carlos T. Bea, Circuit Judges.

                 Opinion by Judge Berzon




                            6661
                           DUDUM v. ARNTZ                           6665
                             COUNSEL

James R. Parrinello, Christopher E. Skinnell, Nielsen, Merk-
samer, Parrinello, Mueller & Naylor, LLP, San Rafael, Cali-
fornia, for the plaintiffs-appellants.

Therese M. Stewart, Chief Deputy City Attorney, and Jona-
than Givner, Andrew Shen, and Mollie Lee, Deputy City
Attorneys, San Francisco, California, for the defendants-
appellees.


                              OPINION

BERZON, Circuit Judge:

   In 1873, Charles Lutwidge Dodgson, better known by his
pen name, Lewis Carroll, spotted what he took to be an “ex-
traordinary injustice”: using simple plurality voting to deter-
mine the winners of elections.1 Dodgson, celebrated for his
whimsical classics Alice’s Adventures in Wonderland and
Through the Looking Glass, was also a mathematician who
developed election systems—meaning, simply, methods for
translating preferences, or votes, into winners of elections.
Dodgson disliked simple plurality voting because, in fields
with several candidates, it can elect a candidate who receives
the most first-place votes but is strongly disfavored by a
majority of the electorate. Dodgson’s innovative election sys-
tems were designed to remedy that limitation, and are still
praised today because they tend to elect candidates with wide-
spread electoral support.2
  1
    See Charles L. Dodgson, A Discussion of the Various Methods of Pro-
cedure in Conducting Elections (1873), reprinted in 3 THE PAMPHLETS OF
LEWIS CARROLL 33, 35 (Francine F. Abeles & Charlie Lovett eds., 2001).
  2
    See, e.g., Francine F. Abeles, Introduction to the Political Pamphlets
and Letters, in 3 THE PAMPHLETS OF LEWIS CARROLL, supra, at 1, 21-22;
Douglas J. Amy, BEHIND THE BALLOT BOX 187-89 (2000); Samuel Merrill,
MAKING MULTICANDIDATE ELECTIONS MORE DEMOCRATIC 70 (1988).
6666                        DUDUM v. ARNTZ
   While Dodgson preferred his systems to simple plurality
voting, he recognized that his innovations were themselves
imperfect. In a letter accompanying one of his pamphlets,
Dodgson lamented: “A really scientific method for arriving at
the result which is, on the whole, most satisfactory to a body
of electors, seems to be still a desideratum.”3

   Over a century later, Dodgson’s wish remains unfulfilled.
No perfect election system has been devised. Nonetheless,
some governmental entities continue to experiment with inno-
vative methods for electing candidates. At issue here is one
such system, used by San Francisco for the election of certain
city officials.

        FACTUAL AND PROCEDURAL HISTORY

   In March 2002, San Francisco voters approved a ballot
measure, Proposition A, amending the City Charter to adopt
a new electoral system for certain municipal elections. Before
adoption of Proposition A, most city officials were selected in
a two-round election: The city first held a general election.
Then, unless one candidate won an outright majority in the
first-round election, the two candidates who had garnered the
most votes faced each other in a runoff election. Proposition
A implemented instant runoff voting (“IRV”)4 to replace the
two-round runoff election system for the following city
offices: Mayor, Sheriff, District Attorney, City Attorney,
  3
     See Charles L. Dodgson, Circular Accompanying A Method of Taking
Votes on More Than Two Issues (1877), reprinted in 3 THE PAMPHLETS OF
LEWIS CARROLL, supra, at 59, 59 (emphasis omitted).
   4
     San Francisco Charter § 13.102, which codifies Proposition A, refers
to the City’s voting system as both “instant runoff” voting and “ranked-
choice” voting. See S.F. CHARTER § 13.102. Election experts also some-
times call this form of voting the “alternative vote system.” See, e.g., Sam-
uel Issacharoff, et al., THE LAW OF DEMOCRACY 1095 (2d ed. 2002). We
refer to the City’s system using the initialism for instant runoff voting,
although, as will become clear, the label is somewhat misleading.
                          DUDUM v. ARNTZ                        6667
Treasurer, Assessor-Recorder, Public Defender, and members
of the Board of Supervisors. See S.F. CHARTER § 13.102(b).

   IRV allows voters to rank, in order of preference, candi-
dates for a single office. The Department of Elections (the
“Department”) then tabulates the voters’ preferences as fol-
lows: First, all first-choice rankings indicated on the ballots
are counted. If a candidate wins a majority of these first-
choice votes, he wins the election. Id. § 13.102(c). If not, the
candidate who received the fewest first-choice votes is “elimi-
nated,” meaning that that candidate cannot win the election.5
The second-choice votes on the ballots that had selected the
eliminated candidate are then distributed to those voters’
second-choice candidates. Some candidates’ vote totals, as a
result, now reflect a combination of first- and second-choice
votes. Id. If all candidates ranked by a voter are eliminated,
that voters’ ballot is “exhausted,” meaning that it is not
recounted as the tabulation continues. Id. § 13.102(a). As long
as no candidate receives a majority of the votes from the
“continuing” ballots—that is, the nonexhausted ballots—the
process of eliminating candidates, transferring preferences,
and “exhausting” ballots repeats. A candidate is declared
elected when he receives a majority of the operative votes on
the “continuing” ballots. Id. § 13.102(d).

   San Francisco’s Charter provides that IRV ballots are to
allow voters to rank a number of candidates equal to the total
number of candidates running in an election. Id. § 13.102(b).
For instance, if ten candidates are running for mayor, then
voters are to be able to rank all ten of them. But the Charter
also provides that if the voting system or equipment used by
the Department cannot “feasibly accommodate” ranking that
many choices, the Director of Elections can limit the number
  5
    Two or more candidates can be “eliminated” at the same time if the
total number of votes they receive is less than the number of votes
received by the next-lowest ranked candidate. See S.F. CHARTER
§ 13.102(e).
6668                        DUDUM v. ARNTZ
of candidates voters may rank to no fewer than three. Id. We
refer to this variant as “restricted IRV.”

   As it has turned out, in all of the City’s IRV elections since
Proposition A passed, the Department has restricted the num-
ber of rankings on each ballot to three. San Francisco main-
tains, and the plaintiffs, several San Francisco voters
(collectively “Dudum”), do not dispute, that this choice is one
of necessity: The voting machines currently in use are not
equipped to tabulate unlimited rankings; cost and logistical
concerns make accommodating the unlimited option untena-
ble; and providing a ballot on which voters may rank every
candidate in a large field could result in confusion, voter
error, and inaccuracies in vote calculation.

   The Department makes publicly available on its website
tables showing the election results for the City’s past IRV
elections. These tables tally the total ballots cast in each elec-
tion; provide synopses of vote distribution during the tabula-
tion process and of the final votes attributed to each
candidate; and show the numbers of ballots “exhausted” as
the tabulations proceeded.6 See, e.g., City and County of San
Francisco Dep’t of Elections Website, Elections Archives by
Year, available at http://www.sfgov2.org/index.aspx?
page=1671 (last visited May 12, 2011). These tables provide
helpful illustrations of how restricted IRV has worked in prac-
tice.
  6
    In an order filed simultaneously with this opinion, we grant Dudum’s
request for judicial notice of the City’s official election results as posted
on the Department’s website. See Fed. R. Evid. 201(b) (allowing a court
to take judicial notice of a fact “not subject to reasonable dispute in that
it is . . . capable of accurate and ready determination by resort to sources
whose accuracy cannot reasonably be questioned”); Daniels-Hall v. Nat’l
Educ. Ass’n, 629 F.3d 992, 998-99 (9th Cir. 2010) (taking judicial notice
of official information posted on a governmental website, the accuracy of
which was undisputed); United States v. Camp, 723 F.2d 741, 744 n.**
(9th Cir. 1984) (taking judicial notice of a verifiable public record).
                            DUDUM v. ARNTZ                             6669
   Dudum filed suit in federal court seeking injunctive relief
against San Francisco and its election officials (collectively
“San Francisco” or “the City”). Principally, Dudum maintains
that when more than four candidates run for a particular
office, the restricted IRV system precludes some groups of
voters from participating to the same extent as others. That
argument is premised on an analogy: It would be unconstitu-
tional, Dudum asserts, to prevent qualified voters from casting
ballots in a runoff election; “exhausting” the ballot of a voter
who would have ranked more than three candidates if allowed
to do so, Dudum contends, is no different.7 Dudum also points
out that the City’s Charter declares that “exhausted” ballots
are “not counted in further stages of the tabulation,” S.F.
CHARTER § 13.102(a) (emphasis added), and argues that not
including the votes of certain voters in the later tabulation
stages once all three of their chosen candidates have been
eliminated is similar to disenfranchisement of those voters,
and so unconstitutional. In support of those arguments,
Dudum points to several recent elections in which significant
numbers of ballots were “exhausted” before tabulation was com-
pleted,8 sometimes in numbers greater than the final margin
  7
     Dudum challenges only the three-candidate limitation, including the
corollary to that limitation that ballots are treated as “exhausted” when
three ranked candidates on a ballot are eliminated. Ballots can also be “ex-
hausted” for tabulation purposes under unrestricted IRV. For instance, in
both systems, ballots can be “exhausted” when a voter chooses to rank
fewer candidates than the system permits and the ranked candidates are
eliminated. Likewise, a ballot is “exhausted” if a vote of a given rank
would otherwise be attributed to a candidate, but the voter indicated that
same rank for more than one candidate. See S.F. CHARTER § 13.102(a).
   8
     The parties stipulated that several thousand votes have been “exhaust-
ed” in each of various elections between 2004 and 2008. For example, in
the 2004 supervisorial elections for District Five, 16.2% of all ballots cast
were “exhausted” as a result of the elimination of the three candidates ran-
ked on those ballots. The City suggests that the 2004 District Five race
was an outlier, pointing to the 2008 supervisorial race for District Nine
and the 2006 supervisorial race for District Six. In those races, only 3.4%
and 0.2% of ballots were “exhausted” as a result of the elimination of all
the candidates ranked on the ballots.
6670                      DUDUM v. ARNTZ
of victory.9 Dudum maintains that as a result of the mandatory
“exhaustion” feature and its impact, the restricted IRV system
violates the First Amendment, the Equal Protection and Due
Process clauses of the Fourteenth Amendment, and the Civil
Rights Act, 42 U.S.C. § 1983. He requests declaratory and
injunctive relief prohibiting the City from using the system in
future elections.

   Agreeing that material facts are not in dispute, the parties
filed cross-motions for summary judgment. The district court
granted summary judgment for the City on all claims. Dudum
appealed.

                           DISCUSSION

                           A.   Overview

   “Common sense, as well as constitutional law, compels the
conclusion that government must play an active role in struc-
turing elections.” Burdick v. Takushi, 504 U.S. 428, 433
(1992). As a way of “structuring elections,” San Francisco’s
IRV system is fairly innovative in the context of American
elections, yet has a historied pedigree.

   First developed in the 1870s by W.R. Ware, a professor at
the Massachusetts Institute of Technology, instant runoff (or
“ranked-choice” or “alternative vote”) systems have been
used in the United States and elsewhere at various times since
then. See Issacharoff, supra, at 1095; Jeffrey C. O’Neill,
  9
    Dudum again points to the 2004 race for District 5 Supervisor, in
which 22 candidates were on the ballot and the winner was determined in
the 19th stage of tabulations. By that stage, 37.44% of ballots cast had
been “exhausted.” Of those, voters had exercised all three available
choices on 16.2% of the ballots. Because the margin of victory in that
election was only 311 votes, the argument goes, those involuntarily “ex-
hausted” ballots may have affected the outcome had they not been limited
to the three ranks and so not been “exhausted” before the tabulation was
complete.
                        DUDUM v. ARNTZ                      6671
Everything That Can Be Counted Does Not Necessarily
Count, 2006 MICH. ST. L. REV. 327, 334. Australia, Ireland,
and London use IRV for certain elections, see Issacharoff,
supra, at 1095, and several U.S. cities use versions of the
restricted IRV system at issue here, including Oakland and
Berkeley, California, and Minneapolis, Minnesota, among
others. See CHARTER OF THE CITY OF OAKLAND, § 1105(k)(1);
BERKELEY MUNICIPAL CODE § 2.14.030(A); MINNEAPOLIS
MUNICIPAL CODE § 167.30.

   Like all electoral systems, including widely-used systems
such as plurality voting and two-round runoff elections, IRV
offers a “package[ ] of potential advantages and disadvan-
tages.” Issacharoff, supra, at 1089. Dodgson’s disappointed
“desideratum” observation, made in 1877, remains true. To
this day, “there is no such thing as the perfect electoral sys-
tem.” David M. Farrell, ELECTORAL SYSTEMS: A COMPARATIVE
INTRODUCTION 47 (2001).

   For instance, in the familiar simple plurality system, some-
times called “first-past-the-post” elections, voters chose one
candidate, and the winner is the candidate with the most
votes. See id. at 19. Plurality voting is widely used in the
United States for single-office elections, including races for
mayors and governors. See Amy, supra, at 142.

   Plurality voting has the benefit of simplicity: It is easy for
voters to use, and also easy for voters to understand how their
votes are tabulated and the winning candidate determined. Id.
at 143. Plurality voting also avoids the expense and burden of
holding a runoff election. Id.

   But the system has less auspicious features as well. In con-
tests with several candidates, it privileges candidates with a
robust and organized core of support, even if they are strongly
disapproved of by most of the electorate. Id. at 144; Farrell,
supra, at 21-26. Likewise, plurality voting allows a candidate
to win with a small minority of the total votes cast when many
6672                         DUDUM v. ARNTZ
candidates are on the ballot. Amy, supra, at 144; Farrell,
supra, at 26.

   A two-round runoff system, sometimes called a “double-
ballot” election, see Peter C. Fishburn, Social Choice and Plu-
ralitylike Electoral Systems, in ELECTORAL LAWS AND THEIR
POLITICAL CONSEQUENCES 193, 195 (Bernard Grofman ed.,
1986), similarly has both significant strengths and trouble-
some weaknesses. In such a system, long used in many local
elections and in some state races, voters select a single candi-
date in the first round of voting, much like plurality voting.
If no candidate receives a majority of the vote, a second round
of voting is held, in which voters choose between the two can-
didates who received the highest number of votes in the first
round.10 See Amy, supra, at 147. Two-round runoff systems
result in the election of candidates with majority support of
those voters who turn out for the second election. Id. at 148.

   That majority support, however, is misleading in some
respects. When the second- and third-place candidates, or
second-, third-, and fourth-place candidates, are relatively
close in a first-round election, a runoff scheme can arbitrarily
eliminate a candidate who might otherwise have won the elec-
tion at the runoff stage.11 Id. at 150. Also, an elected candidate
   10
      The two-round runoff system is distinct from, yet similar to, party pri-
maries, in which political parties select a nominee to run in a general elec-
tion. See generally Cal. Democratic Party v. Jones, 530 U.S. 567, 572-82
(2000) (discussing state regulation of party primary systems).
   11
      For example, in San Francisco’s 2010 supervisorial election for Dis-
trict 10, the top five candidates received the following percentages of all
first-choice votes: Lynette Sweet, 12.07%; Tony Kelly, 11.80%; Malia
Cohen, 11.78%; Marlene Tran, 11.51%; and Steve Moss, 11.06%. Cohen
received only 5 fewer first-rank votes than Kelly. But, in a two-round run-
off system, Cohen would not have proceeded to the runoff election. As it
turned out, Cohen won the election under the City’s IRV system, because
she garnered more second- and third-choice votes than any other candi-
date. See City and County of S.F. Dep’t of Elections Website, Official
Ranked-Choice Results Rep., Nov. 2, 2010 Consolidated Statewide Direct
Primary Election, Bd. of Supervisors, Dist. 10, available at
http://www.sfelections.org/results/20101102/data/d10.html (last visited
May 12, 2011) [hereinafter 2010 Election Results].
                             DUDUM v. ARNTZ                             6673
will likely receive support from voters who strongly preferred
candidates eliminated in the first-round election, as voters
may choose between the two candidates left standing on a
“lesser of two evils” basis. And, of course, the system
requires the expense and burden of holding two separate elec-
tions, id. at 149, and results in two different, albeit overlap-
ping, electorate pools, the relative sizes of which can be
affected by the choice of dates for the runoff round. Id. at
149-50.

   Unrestricted and restricted IRV systems eliminate the need
for a separate runoff and ordinarily will result in the election
of a candidate with more widespread support than would sim-
ple plurality voting. See id. at 55; Farrell, supra, at 65. IRV
systems also tend to produce fewer votes cast only for losing
candidates—in academic parlance, “wasted votes”12—than
does straight plurality voting, because votes that would other-
wise be cast for losing candidates can be redistributed to can-
didates with a chance of winning. Likewise, IRV systems
“allow[ ] the voters more say over who they want to represent
them: if it is not to be their first choice, then they can choose
a second.” Farrell, supra, at 65.

  Under restricted or unrestricted IRV, a candidate who did
not receive the most number of first-choice votes can be elect-
ed.13 Whether that feature is a disadvantage or an advantage
  12
      See Amy, supra, at 16 (“Wasted votes are votes that do not elect
someone. If your candidate loses, you have cast a wasted vote.”).
   13
      To illustrate: In San Francisco’s 2010 supervisorial election for Dis-
trict 2, Janet Reilly won the highest percentage of all the first-choice votes
(41.08%), and Mark Farrell received the second highest percentage of
those votes (40.26%). Farrell ultimately won the election, because he
received more second-choice votes in the second (and final) calculation
stage than did Reilly. See 2010 Election Results, Bd. of Supervisors, Dist.
2, available at http://www.sfelections.org/results/20101102/data/d2.html
(last visited May 12, 2011). In other instances, the plurality winner after
the first stage will eventually be elected. For example, in the 2010 supervi-
sorial election for District 6, Jane Kim received the highest percentage of
all first-choice votes (31.40%) and was eventually elected, after twelve
stages of calculation. See 2010 Election Results, Bd. of Supervisors, Dist.
6, available at http://www.sfelections.org/results/20101102/data/d6.html
(last visited May 12, 2011).
6674                        DUDUM v. ARNTZ
is, of course, debatable. Where, for instance, there is no candi-
date with a majority, and the vote spread between the top plu-
rality candidates is small, the more nuanced IRV systems can
be seen as better tests of the depth of voter support for each
candidate than a simple first-past-the-post plurality system.
Additionally, while both IRV systems allow voters to rank
their preferences, neither system allows voters to reconsider
their choices after seeing which candidates have a chance of
winning. In other words, voters must submit their preferences
before polls close, and, even though they might have chosen
differently with more specific information about other voters’
selections, they are not provided an opportunity to revise their
choices. See Farrell, supra, at 173. A two-round runoff sys-
tem, in contrast, provides voters that opportunity through a
new round of balloting in a runoff election.14 Finally, both
IRV systems are unfamiliar to many voters, and so some vot-
ers might not entirely understand how their votes will affect
the election. See Amy, supra, at 156.

  Moreover, all voting systems in elections with more than
two candidates can be manipulated through strategic voting.
See Farrell, supra, at 171-74; Fishburn, supra, at 198;
O’Neill, supra, at 340-41. In a plurality voting scheme, a
voter might choose a candidate who is not his first-choice
preference, but who he believes has a realistic chance of win-
  14
     A voting system called “Condorcet” voting addresses a related prob-
lem. In Condorcet voting, each voter ranks his candidate preferences, and
the winner is determined by considering all pairwise contests between can-
didates. “For example, for three candidates (A, B, and C), there are three
pairwise contests (A-B, A-C, and B-C). The winner is the candidate who
wins all of her pairwise contests.” O’Neill, supra, at 335. Like IRV, Con-
dorcet voting does not require two elections, and academics tend to like
it because it selects candidates who are highly rated by the majority of vot-
ers. But it has problems as well: It allows for the election of a candidate
with few first-place votes. Moreover, when there are more than two candi-
dates, the system can fail to produce a winning candidate (e.g., A beats B,
B beats C, and C beats A). See Amy, supra, at 188-89; Merrill, supra, at
15; O’Neill, supra, at 337-38 & 337 n.64.
                         DUDUM v. ARNTZ                       6675
ning. In a two-round runoff system, a voter might cast a vote
in the first-stage election for a weak candidate, so that his
actual first-choice candidate will face that weak candidate in
the runoff. See Fishburn, supra, at 199. The risk of strategic
voting exists in IRV but is less severe than in plurality voting
or the first stage of a runoff election: Voters are more free to
vote their true preferences, because they face less of a threat
of having their votes entirely “wasted” on unsuccessful candi-
dates. See Amy, supra, at 52; Merrill, supra, at 105; O’Neill,
supra, at 340.

   In sum, restricted IRV, like every election system, offers a
menu of benefits and limitations. But that observation does
not mean it is a constitutionally acceptable system, so we now
turn to Dudum’s constitutional objections to the City’s
restricted IRV system.

                 B.   The Burden on Voters

   [1] Restrictions on voting can burden equal protection
rights as well as “interwoven strands of ‘liberty’ ” protected
by the First and Fourteenth Amendments—namely, “ ‘the
right of individuals to associate for the advancement of politi-
cal beliefs, and the right of qualified voters, regardless of their
political persuasion, to cast their votes effectively.’ ” Ander-
son v. Celebrezze, 460 U.S. 780, 787 (1983) (quoting Wil-
liams v. Rhodes, 393 U.S. 23, 30 (1968)). At the same time,
and even though “voting is of the most fundamental signifi-
cance under our constitutional structure,” “States retain the
power to regulate their own elections.” Burdick, 504 U.S. at
433 (internal quotations omitted). As our short review has
indicated, each available election system, “ ‘whether it gov-
erns the registration and qualifications of voters, the selection
and eligibility of candidates, or the voting process itself, inev-
itably affects—at least to some degree—the individual’s right
to vote.’ ” Id. (quoting Anderson, 460 U.S. at 788).

  Recognizing the need of States and municipalities “to
assure that elections are operated equitably and efficiently,”
6676                       DUDUM v. ARNTZ
id., we apply a “flexible standard” when considering constitu-
tional challenges to election regulations:

       A court considering a challenge to a state election
       law must weigh “the character and magnitude of the
       asserted injury to the rights protected by the First
       and Fourteenth Amendments that the plaintiff seeks
       to vindicate” against “the precise interests put for-
       ward by the State as justifications for the burden
       imposed by its rule,” taking into consideration “the
       extent to which those interests make it necessary to
       burden the plaintiff’s rights.”

Id. at 434 (quoting Anderson, 460 U.S. at 789). When the bur-
dens on voting imposed by the government are “severe,” strict
scrutiny applies, and the “regulation must be ‘narrowly drawn
to advance a state interest of compelling importance.’ ” Id.
(quoting Norman v. Reed, 502 U.S. 279, 289 (1992)). But vot-
ing regulations are rarely subjected to strict scrutiny. See Lem-
ons v. Bradbury, 538 F.3d 1098, 1104 (9th Cir. 2008). We
have repeatedly upheld as “ ‘not severe’ restrictions that are
generally applicable, even-handed, politically neutral, and . . .
protect the reliability and integrity of the election process.”
Rubin v. City of Santa Monica, 308 F.3d 1008, 1014 (9th Cir.
2002). Where non-severe, “[l]esser burdens” on voting are at
stake, we apply “less exacting review, and a State’s important
regulatory interests will usually be enough to justify reason-
able, nondiscriminatory restrictions.”15 Timmons v. Twin Cit-
  15
    Dudum does not suggest separate analyses for his First Amendment,
Due Process, or Equal Protection claims. The Supreme Court has
addressed such claims collectively using a single analytic framework. See
Anderson, 460 U.S. at 787 n.7 (“[W]e base our conclusions directly on the
First and Fourteenth Amendments and do not engage in a separate Equal
Protection Clause analysis. We rely, however, on the analysis in a number
of our prior election cases resting on the Equal Protection Clause of the
Fourteenth Amendment.”); LaRouche v. Fowler, 152 F.3d 974, 987-88
(D.C. Cir. 1998) (using “a single basic mode of analysis” for such claims).
We do the same here.
                        DUDUM v. ARNTZ                      6677
ies Area New Party, 520 U.S. 351, 358 (1997) (internal
quotations omitted); see also Caruso v. Yamhill County ex rel.
Cnty. Comm’r, 422 F.3d 848, 859 (9th Cir. 2005).

   We have already explained some of the structural limita-
tions inherent in restricted IRV. For instance, voters are
unable to reconsider their choices after seeing which candi-
dates have a chance of winning, and some voters might be
unfamiliar with the system. Dudum does not, however, chal-
lenge those inherent features of the City’s IRV system.
Instead, Dudum concentrates on challenging the three-rank
restriction aspect of San Francisco’s system. We consider
below the characteristics of restricted IRV Dudum does chal-
lenge, to determine the degree to which those features burden
voters’ constitutional rights, if at all, and if so, whether the
burdens are so severe as to trigger strict scrutiny.

                               1.

   Dudum first contends that the treatment accorded “exhaust-
ed” ballots as the vote tabulation proceeds under the City’s
restricted IRV scheme is akin to prohibiting certain voters
from voting in an election, and so imposes a severe, or at least
a serious, burden on voters’ constitutional rights. To support
that characterization, Dudum points out that IRV replaced a
two-round runoff system, and that explanations of how IRV
works often analogize the successive vote calculation steps to
a series of elections. For instance, the supervisors who sup-
ported adoption of Proposition A stated in their official ballot
argument that “[t]he ‘instant’ runoff works much like Decem-
ber’s ‘delayed’ runoff.”

   But the analogy is just that—an analogy. Upon examina-
tion, the analogy is off the mark in describing the real impacts
of restricted IRV on voters’ opportunities to cast ballots.

   [2] In actuality, all voters participating in a restricted IRV
election are afforded a single and equal opportunity to express
6678                        DUDUM v. ARNTZ
their preferences for three candidates; voters can use all three
preferences, or fewer if they choose. Most notably, once the
polls close and calculations begin, no new votes are cast. To
determine the winner of the election based on that single set
of votes cast, restricted IRV uses an algorithm.16 The ballots,
each representing three or fewer preferences, are the initial
inputs; the sequence of calculations mandated by restricted
IRV is used to arrive at a single output—one winning candi-
date. The series of calculations required by the algorithm to
produce the winning candidate are simply steps of a single
tabulation, not separate rounds of voting.

   In contrast, a two-round runoff system involves at least two
rounds of voting, or inputs, explaining why it is sometimes
referred to as a “double-ballot” election. See Fishburn, supra,
at 195. For instance, in a two-round runoff system, even if a
voter’s chosen candidate in the first round successfully pro-
ceeds to the runoff election, that voter is still afforded an
opportunity in the runoff election to select a different candi-
date, or not to vote at all. In a restricted IRV system, in con-
trast, if that voter chooses a successful candidate in one round,
he is not afforded the opportunity to switch his vote to a dif-
ferent candidate as the tabulation progresses. That is so
because restricted IRV considers only one round of inputs,
i.e., votes.

   Restricted IRV, of course, can be used in place of a two-
round runoff election, which is what occurred in San Fran-
cisco and explains why the city supervisors compared the two.
But restricted IRV does not replicate a two-round runoff sys-
  16
     An algorithm is “any well-defined computational procedure that takes
some value, or set of values, as input and produces some value, or set of
values, as output. An algorithm is thus a sequence of computational steps
that transform the input into the output.” Thomas H. Cormen, et al., INTRO-
DUCTION TO ALGORITHMS 5 (2d ed. 2002); see also 1 NEW ENCYCLOPAEDIA
BRITANNICA 266 (15th ed. 2007) (defining algorithm as a “systematic
mathematical procedure that produces—in a finite number of steps—the
answer to a question or the solution of a problem”).
                       DUDUM v. ARNTZ                      6679
tem because, as we just explained, in two-round runoffs, vot-
ers cast ballots twice—that is, make and record their choices
twice—whereas IRV allows only one chance to vote.

  [3] Dudum’s contention that restricted IRV threatens to
exclude some voters from voting is therefore incorrect. The
contention sidesteps the basic fact that there is only one round
of voting in restricted IRV.

   Aside from his two-round analogy, Dudum points to sev-
eral cases in which qualified individuals were denied an
opportunity to vote on certain issues and the resulting burden
on the right to vote was treated as significant. But because
restricted IRV involves only one round of voting, those cases
are inapplicable here.

   Partnoy v. Shelley, 277 F. Supp. 2d 1064 (S.D. Cal. 2003),
for example, concerned a requirement that, unless voters
voted either “yes” or “no” on the recall of a governor, their
votes on any successor candidates for governor would not be
counted. Id. at 1071. The defendants argued that the recall and
the successor issues were part of one compound question, and
no one was prevented from voting on that one question. The
court disagreed, reasoning that the voters were faced with two
separate questions and holding that it would be a severe bur-
den to force voters to choose between either voting on an
issue upon which they did not want to vote or having their
votes for a gubernatorial successor not counted. Id. at
1074-75. The court held the requirement unconstitutional,
because it concluded that the state failed to advance narrowly-
tailored compelling interests to justify it. Id. at 1079.

   Assuming it was correctly decided—which we do not
determine—Partnoy is not instructive here. In that case there
were two questions before the voters: Should the governor be
recalled? If so, who should succeed him? Those two questions
were conceptually separate; a voter could wish to express a
view on only one of the questions, or have a strategic reason
6680                    DUDUM v. ARNTZ
to vote on one but not the other. In contrast, voters in the San
Francisco elections are asked to cast a vote on one issue: Who
should be elected to the particular office?

   Nor is Ayers-Schaffner v. DiStefano, 37 F.3d 726 (1st Cir.
1994)—again, assuming without deciding that we would
decide it the same way as did the First Circuit—at all instruc-
tive. In that case, after concluding that an election was defec-
tive, the state ordered a second curative election but limited
participation to people who had voted in the original ballot-
ing. Id. at 727. The court held that the state’s restriction
imposed a severe burden on the excluded voters’ right to vote,
id. at 728, and, as the state failed to advance compelling inter-
ests justifying the limitation, it was unconstitutional. Id. at
730.

  The problem in Ayers-Schaffner was that otherwise eligible
voters were not allowed to vote in a determinative election.
Here, to reiterate, voters who participate in the restricted IRV
system are not excluded from any election or opportunity to
vote, so no comparable burden is imposed on voting rights.

   Finally, Dudum notes that in two-round runoff elections,
some jurisdictions use an IRV-like system to tabulate the
votes from certain absentee ballots. See ARK. CODE § 7-5-406;
S.C. CODE § 7-15-405. According to Dudum, IRV must be
equivalent to a series of elections, because in those jurisdic-
tions absentee voters have votes counted using an IRV-like
approach in more than one election.

   This example is not particularly relevant, as it concerns a
hybrid system which, unlike the San Francisco IRV scheme,
does treat groups of voters differently with regard both to
numbers of ballots cast and to the method of tabulating the
ballots. The hybrid system, in effect, adds together apples and
oranges: Absentee voters, a small subset of the electorate,
must rank their choices among a large pool of candidates on
a single ballot; in-person voters, in contrast, cast two ballots,
                            DUDUM v. ARNTZ                           6681
and in the runoff round choose between only two candidates.
The hybrid system is one of convenience given the time
delays. But it is a less-than-perfect way for the absentee vot-
ers to participate in the second-round runoff election—albeit
better than not participating at all.

   If anything, properly understood, Dudum’s example high-
lights that IRV is not equivalent to two-round runoff elec-
tions: In the hybrid system, each in-person voter has the
opportunity to vote differently in the runoff, even if he voted
in the first-round for a candidate who continues to the second
round; in contrast, an absentee voter who voted for a candi-
date who makes the runoff has his vote automatically cast
again for that candidate, even if he would now prefer the other
candidate. In other words, the absentee voter is not afforded
the same opportunity as in-person voters to reassess his pref-
erences in the runoff election; the in-person voter votes twice
using two ballots, but the absentee voter votes once using a
single ballot.17 Pure IRV systems, like the City’s, do not
involve any such differential treatment of voters. All voters
can rank up to three choices on a single ballot, cast those bal-
lots at the same time, and have their preferences calculated in
the same manner.

   [4] In sum, the City’s restricted IRV system is not analo-
gous to limitations on voting in successive elections, because
in San Francisco’s system, no voter is denied an opportunity
to cast a ballot at the same time and with the same degree of
choice among candidates available to other voters. Neither
Dudum’s analogies nor the cases he relies upon persuade us
that the City’s election system imposes any serious burdens
on voters’ constitutional rights by providing unequal opportu-
nities to cast ballots.
  17
    We, of course, express no views on the constitutionality of this hybrid
election system.
6682                    DUDUM v. ARNTZ
                               2.

   Aside from characterizing San Francisco’s restricted IRV
system as a limitation on casting ballots, Dudum tries a sec-
ond tack: He maintains that the tabulation scheme under San
Francisco’s system burdens voters’ constitutional rights to
vote by effectively discarding, rather than counting, the votes
from “exhausted” ballots.

   In support of this characterization, Dudum points to the text
of two provisions in the San Francisco Charter: First, accord-
ing to the Charter, voters whose ballots are “exhausted” do
not have their ballots “counted in further stages of the tabula-
tion.” S.F. CHARTER § 13.102(a). Second, a candidate wins the
election when he receives “a majority of the votes from the
continuing ballots,” meaning the nonexhausted ballots. Id.
§ 13.102(c) & (d) (emphasis added). Dudum reads this text as
meaning that “exhausted” ballots are discarded, and so not
counted, in determining the election’s ultimate outcome.

   [5] An examination of how restricted IRV works, however,
indicates that the supposed inequity Dudum has identified is
one of surface appearances and semantics, not substance. The
algorithm used to determine the winner in an election con-
ducted pursuant to the City’s IRV system can be elaborated
so that the outcome is mathematically identical, yet the fea-
tures forming the basis of Dudum’s characterization of the
system as not counting some votes disappear. In essence, a
more complete explication of the tabulation process demon-
strates that “exhausted” ballots are counted in the election,
they are simply counted as votes for losing candidates, just as
if a voter had selected a losing candidate in a plurality or run-
off election.

  To illustrate, the tabulation scheme could be spelled out
and recorded more fully than it is now as follows: When a
candidate receives the fewest votes in a stage, any ballots that
would otherwise be “exhausted” by that candidate’s last-place
                             DUDUM v. ARNTZ                              6683
finish could continue to be reflected as a vote for that candi-
date in subsequent rounds. Votes that the candidate received
from ballots with second- or third-choice candidates remain-
ing would still be transferred to the second- or third-choice
candidates. In other words, even though last-place candidates
could no longer mathematically win the election, and could
not obtain further votes, one could clutter the tabulation pro-
cess by showing their votes on the tabulation tables even after
they had been proven incapable of prevailing. The winner
could then be defined as the candidate who receives a plural-
ity of the total votes cast (including votes cast for candidates
mathematically eliminated in prior stages), as long as he also
receives a majority of the votes cast for candidates who were
not mathematically eliminated previously.18 As this example
   18
      One might question why receiving a majority of the votes cast for
non-eliminated candidates should be the triggering event ending the elec-
tion. That is, why shouldn’t the final step occur when all the recorded
votes have been distributed in accord with the tabulation rules, with the
winning candidate being the person with more votes than the other
remaining candidate after the losers are eliminated and their votes redis-
tributed?
   The answer is that, if a candidate receives a majority of the votes cast
for non-eliminated candidates, it is mathematically impossible for that
candidate to lose if the tabulation is extended until all ranked votes are dis-
tributed. To see why that is so, consider an election in which, after several
IRV tabulations, 100 ballots containing votes for non-eliminated candi-
dates remain. Candidate A receives 51 of those votes. The votes attribut-
able to him can be thought of as the numerator, and that number plus the
remaining 49 votes (spread over the other non-eliminated candidates) the
denominator. In later stages of tabulation, the votes counted in the denom-
inator may be redistributed, but the denominator can never increase
beyond 100 votes. Thus, even if no further votes are attributed to candi-
date A, he will always have at least 51% of the votes cast for non-
eliminated candidates. And, in fact, the denominator could very well
decrease as candidates are mathematically eliminated, and last-ranked
votes continue to be recounted for those eliminated candidates (rather than
being redistributed to non-eliminated candidates and retained in the
denominator). Of course, if the denominator decreases, or if more votes
are distributed to candidate A, his majority position can only increase.
6684                         DUDUM v. ARNTZ
illustrates, the restricted IRV system does not necessarily pro-
duce a majority result; a plurality of the total votes cast can
prevail, as the majority is only of the last stage of calculation,
when many candidates have been mathematically eliminated.19
Cf. Merrill, supra, at 13 (characterizing IRV as a plurality
system).

  This “show your work” alternative—to quote many high
school teachers—is more cumbersome than San Francisco’s
actual tabulation regime, but it accomplishes precisely the
same result. As pertinent to Dudum’s challenge, the rephras-
ing makes explicit what is implicit in the current scheme:
“Exhausted” ballots are counted in the election, they are just

   It is true that further rounds of tabulation might affect the ultimate vote
distribution for non-winning candidates. Imagine that candidates B, C, and
D have 24, 13, and 12 votes respectively (totaling 49 votes) when candi-
date A receives his 51 votes. If, after candidate D is eliminated, every vote
attributed to him is redistributed to candidate C, then candidate C will
have one vote more (25 votes) than candidate B (24 votes). But no matter
how the non-elected candidates are ranked, candidate A wins. Thus, there
is no practical difference (in terms of who will be elected) between ending
the tabulation when only two candidates remain or when any candidate
receives a majority of the votes cast for non-eliminated candidates.
   Moreover, in addition to maintaining a majority of the votes cast for
non-eliminated candidates, candidate A will always have a plurality of the
total votes cast: As we just explained, his 51 votes will always be more
than any of the non-eliminated candidates. Likewise, each previously
eliminated candidate at some point received the fewest votes in a stage,
meaning, of course, fewer votes than candidate A. Moreover, the respec-
tive vote totals of each previously eliminated candidate can only decrease
thereafter—they cannot obtain further votes, and some of the 1st- and 2nd-
rank votes that were attributed to them likely will have been distributed
to the 2nd- and 3rd-choice candidates on those ballots.
   19
      Dudum does not dispute the legality of plurality systems. Rather, he
presents simple plurality voting as a preferable alternative to restricted
IRV. We are aware of no successful challenge to plurality voting gener-
ally. Cf. Edelstein v. City & Cnty. of S.F., 29 Cal. 4th 164, 183 (Cal. 2002)
(“Plurality rule is not anathema to the federal or state Constitutions.”).
                             DUDUM v. ARNTZ                               6685
counted for losing candidates in the tally of total votes. In the
terms used by election experts, these are “wasted” votes, not
because they aren’t counted, but because they were cast for
candidates not ultimately elected. Notably, both IRV and
restricted IRV tend to result in fewer entirely “wasted” votes
than plurality voting, because voters whose first-choice candi-
date is eliminated may choose the winning candidate as their
second- or third-choice pick. See Amy, supra, at 155.20

   [6] All this is to say that “exhausted” ballots represent
votes for losing candidates. “Exhausted” ballots are not disre-
garded in tabulating election results, and the result of not
“counting” them is identical to counting them while explicitly
recognizing that the system often produces a winner who
attains a plurality, not a majority, of the total votes cast. Given
this substantive equivalence, Dudum’s objection that votes
may not be “counted” at the determinative tabulation steps
reflects only the Charter’s current phrasing, not any actual
burden on voting rights.

   The only court to have addressed a similar argument has
reached the same conclusion. At issue in McSweeney v. City
of Cambridge, 422 Mass. 648 (1996), was an unrestricted
form of preferential voting called the “single transferable
vote.”21 Rejecting the argument that voting rights were seri-
  20
      A voter might regard as objectionable San Francisco’s IRV system,
even as thus more fully reticulated, because he would prefer to have his
vote recorded in the final step of tabulation in favor of his first-choice can-
didate rather than his third-choice pick. Such an objection would have lit-
tle force, as the election results reported by the City would reflect the first-
choice vote up until the tabulation stage in which the designated candidate
received the fewest votes and so could not prevail. Alternatively, a voter
could decide to vote for only one candidate, and the ballot would be
recorded as a vote for that candidate throughout the tabulation process and
in the final election report.
   21
      The “single transferable vote” system resembles IRV but it is used to
elect multiple candidates to a representative body, whereas IRV is used to
elect a single candidate to office. See Issacharoff, supra, at 1096.
6686                      DUDUM v. ARNTZ
ously burdened because “exhausted” ballots are not counted
in the election, the court noted that “[exhausted ballots] too
are read and counted; they just do not count toward the elec-
tion of any of the nine successful candidates. Therefore it is
no more accurate to say that these ballots are not counted than
to say that the ballots designating a losing candidate in a two-
person, winner-take-all race are not counted.”22 Id. at 652; see
also Moore v. Election Comm’rs of Cambridge, 309 Mass.
303, 319 (1941) (reaching the same conclusion), abrogated on
other grounds as recognized in McSweeney, 422 Mass. at
653-54.

   [7] In short, Dudum’s contention that the City’s system
discards votes is incorrect. Instead, the system “counts” all the
ballots, but the final tabulation recognizes that some of the
ballots ranked only losing candidates. Like his inaccurate
comparison of the algorithm used in restricted IRV to a series
of elections, Dudum’s “counting” argument reveals an at most
minimal—and perhaps nonexistent—burden on voters’ con-
stitutional rights.

                                 3.

   Dudum’s final contention regarding the voting burden
imposed by the restricted IRV system is that even if restricted
IRV does not prevent some voters from voting (it doesn’t, as
we explain above), and even if all votes are counted (they are,
for the reasons just given), San Francisco’s restricted IRV
system is nonetheless unconstitutional because it results in the
dilution of certain votes. Specifically, Dudum maintains that
“some voters—those who vote for continuing candidates—
only have one vote counted in ‘the election’; other voters,
however, have votes counted for three different candidates.”
Therefore, the argument goes, the City’s IRV system violates
the equal protection guarantee of “one person, one vote.” See
  22
    McSweeney went on to decide the case on different grounds, but its
reasoning on the counting argument mirrors our own.
                             DUDUM v. ARNTZ                             6687
Bd. of Estimate of New York v. Morris, 489 U.S. 688, 692
(1989) (quoting Reynolds v. Sims, 377 U.S. 533, 565 (1964)).23
At its core, Dudum’s argument is that some voters are literally
allowed more than one vote (i.e., they may cast votes for their
first-, second-, and third-choice candidates), while others are
not.

   [8] Once again, Dudum’s contention mischaracterizes the
actual operation of San Francisco’s restricted IRV system and
so cannot prevail. In fact, the option to rank multiple prefer-
ences is not the same as providing additional votes, or more
heavily-weighted votes, relative to other votes cast. Each bal-
lot is counted as no more than one vote at each tabulation
step, whether representing the voters’ first-choice candidate or
the voters’ second- or third-choice candidate, and each vote
attributed to a candidate, whether a first-, second- or third-
rank choice, is afforded the same mathematical weight in the
election. The ability to rank multiple candidates simply pro-
vides a chance to have several preferences recorded and
counted sequentially, not at once.

   Several courts have rejected variants of Dudum’s dilution
argument. Most recently, Minnesota Voters Alliance v. City of
Minneapolis, 766 N.W.2d 683 (Minn. 2009), was a challenge
to an IRV scheme on the ground that voters whose first-
choice candidates were eliminated were afforded multiple
opportunities to affect the election. See id. at 690. The court
rejected that argument, reasoning that votes for continuing
candidates were counted throughout the process, and “in each
  23
     The “one person, one vote” cases involve instances in which citizens
from heavily-populated districts select the same number of legislative rep-
resentatives as voters from sparsely populated districts, with the result that
their votes have less potential impact on the legislative process. See Reyn-
olds, 377 U.S. at 563. To rectify that “dilution” problem, the Supreme
Court has interpreted the Equal Protection Clause to require that the seats
in state legislatures “must be apportioned on a population basis.” Id. at
568; see also Bd. of Estimates, 489 U.S. at 693 (discussing cases).
6688                        DUDUM v. ARNTZ
round every voter’s vote carrie[d] the same value.”24 Id. at
693.

   Dudum attempts to distinguish Minnesota Voters’s rejec-
tion of the dilution claim by arguing that San Francisco’s sys-
tem is different than Minneapolis’s, because the former
restricts voters to choosing three candidates.25 Dudum’s obser-
vation, however, either cuts against his dilution claim or
exposes the dilution argument as just a rehash of his “not
counting” argument.

   If the purported problem is that some voters have votes
counted for more than one candidate as the tabulations prog-
ress (although never for more than one at any tabulation
stage), then restricting the number of candidates voters can
rank should reduce Dudum’s dilution concerns, not exacer-
bate them. And insofar as Dudum’s dilution argument shifts
to a concern that the voters whose ballots become “exhaust-
ed” have their votes diluted because their votes do not “count”
in the determinative calculation stages, we have already
explained that that is so only because their candidates have no
chance of prevailing. Any distinction between San Francis-
co’s and Minnesota’s systems (as considered in Minnesota
Voters) therefore does not help Dudum’s dilution claim.

                                  ***
  24
      Other courts have reached the same conclusion. See McSweeney, 422
Mass. at 652 (noting, in the context of an unrestricted preferential voting
scheme, that “it would be misleading to say that some ballots are counted
two or more times. Although these ballots are examined two or more
times, no ballot can help elect more than one candidate.”); Stephenson v.
Ann Arbor Bd. of Canvassers, No. 75-10166 AW (Mich. Cir. Ct. Nov.
1975) (same).
   25
      As the parties recognize, the Minneapolis election system actually
does limit voters to ranking three candidates. But the court in Minnesota
Voters did not address that limitation.
                          DUDUM v. ARNTZ                         6689
   Again, “every electoral law and regulation necessarily has
some impact on the right to vote.” Weber v. Shelley, 347 F.3d
1101, 1106 (9th Cir. 2003). The City’s restricted IRV scheme
is no different. Like every electoral system, it offers an amal-
gam of advantages and disadvantages. The burdens Dudum
identifies, however, are largely ephemeral, disappearing upon
examination. The restricted IRV scheme does not provide dis-
parate opportunities for any voter to cast additional ballots or
votes. The appearance that some votes are not “counted” is
just a product of how the algorithm operates for efficiency’s
sake; the result would be identical were the “exhaustion” fea-
ture eliminated, and the “exhausted” ballots recorded and
counted throughout the process for what they are—votes for
losing candidates. As the votes from “exhausted” ballots are
taken into account in the election, as much as “wasted” votes
ever are, the practical burden on voters is no different than in
other election systems. Finally, Dudum’s vote dilution argu-
ment fails as well, because the ability to rank preferences
sequentially does not affect the ultimate weight accorded any
vote cast in the election.26

   [9] Therefore, if the characteristics of the City’s system
Dudum has identified impose any burdens on the right to
vote, they are minimal at best. For the sake of completeness,
we shall assume some burden is imposed, however limited,
and so consider whether the restricted IRV system serves gov-
ernmental interests sufficient to justify that minimal at best
burden under the flexible balancing analysis. See, e.g., Burd-
ick, 504 U.S. at 437, 439 (holding that “any burden imposed”
by the challenged regulation was “a very limited one,” but
nonetheless considering the governmental interests
advanced); Lemons, 538 F.3d at 1104 (weighing the pertinent
governmental interests, even though the burdens imposed
were “minimal”).
  26
    We express no views on any characteristics of restricted IRV beyond
those discussed.
6690                        DUDUM v. ARNTZ
                C.    The Governmental Interests

   Because restricted IRV does not impose severe burdens on
voting rights, we do not apply strict scrutiny. See, e.g., Tim-
mons, 520 U.S. at 358; Pest Comm. v. Miller, 626 F.3d 1097,
1106 (9th Cir. 2010). And here, the City’s “important regula-
tory interests” are more than substantial enough to justify the
minimal at best burdens imposed by the City’s chosen system.
Timmons, 520 U.S. at 358; Nader v. Cronin, 620 F.3d 1214,
1217 (9th Cir. 2010).

                                     1.

   Before addressing the City’s proffered interests, we empha-
size that the City is not required to show that its system is nar-
rowly tailored—that is, is the one best tailored to achieve its
purposes. See Timmons, 520 U.S. at 358. Latching onto a
phrase from Anderson v. Celebrezze, Dudum contends other-
wise, insisting that the governmental restrictions must be
“necessary to burden the plaintiff’s rights,” 460 U.S. at 789
(emphasis added). But later cases refute Dudum’s reading of
Anderson, making clear that when a challenged rule imposes
only limited burdens on the right to vote, there is no require-
ment that the rule is the only or the best way to further the
proffered interests. See Timmons, 520 U.S. at 365 (“[B]ecause
the burdens the [challenged] ban imposes on the party’s asso-
ciational rights are not severe, the State need not narrowly tai-
lor the means it chooses to promote [its interests].”); Pest
Comm., 626 F.3d at 1110 (holding that the district court cor-
rectly applied the flexible balancing test and “was not obliged
to consider whether Nevada’s system could or should be more
narrowly tailored”); Caruso, 422 F.3d at 862 (same).27
  27
     We note that a sliding-scale balancing analysis, rather than pre-set
tiers of scrutiny, apply to challenges to voting regulations. Thus, there may
be instances where a burden is not severe enough to warrant strict scrutiny
review but is serious enough to require an assessment of whether alterna-
tive methods would advance the proffered governmental interests. Cf.
Crawford v. Marion Cnty. Election Bd., 553 U.S. 181, 190 n.8 (2008)
(opinion of Stevens, J.).
                        DUDUM v. ARNTZ                      6691
   Such respect for governmental choices in running elections
has particular force where, as here, the challenge is to an elec-
toral system, as opposed to a discrete election rule (e.g., voter
ID laws, candidacy filing deadlines, or restrictions on what
information can be included on ballots). Discrete election
rules generally further limited identifiable interests; a review-
ing court can assess the likely effects of entirely eliminating
the challenged rule. Cf. Burdick, 504 U.S. at 430 (state prohi-
bition on write-in voting); Anderson, 460 U.S. at 782 (state
early-filing deadline); Rubin, 308 F.3d at 1011 (regulation
prohibiting a candidate from designating himself a “peace
activist” on the election ballot). In contrast, the City must use
some overall system for casting ballots, tabulating votes, and
determining the outcome of elections. It cannot select a sys-
tem that best serves all the multiplicity of interests implicated
in an election, as no such system exists. Moreover, given the
need to adopt some overall election system, we cannot as a
practical matter assess the likely effects of eliminating one
election system without considering what system would
replace it, and what new burdens that replacement choice
would likely impose.

   Dudum challenges only the three-candidate limitation, not
IRV generally. In light of that limited challenge, one would
expect Dudum to argue that the interests advanced by the City
in favor of the three-candidate restriction are inadequate. But
Dudum does not contest those specific justifications. Instead,
he argues that the interests advanced in favor of IRV gener-
ally can be served just as well by either a plurality system or
a two-round runoff scheme. Dudum’s logic seems to be that
if the three-candidate limit imposes a burden on voting rights,
and if the City maintains that it cannot eliminate that restric-
tion, then restricted IRV should be compared to election sys-
tems whose constitutionality is not in question.

  In the end, then, Dudum is effectively asking the court to
choose between electoral systems (i.e., between restricted
IRV, plurality voting, or two-round runoff elections). As
6692                   DUDUM v. ARNTZ
explained, however, electoral systems serve diverse interests
with various degrees of success. That is why, absent a truly
serious burden on voting rights, “it is the job of
democratically-elected representatives to weigh the pros and
cons of various [election] systems.” Weber, 347 F.3d at 1107.

                               2.

   The City advances several interests justifying the minimal
at best burdens of which Dudum complains. Some of those
interests concern the three-candidate restriction, and some
support IRV as compared to the two-round runoff system it
replaced.

   [10] First, the City adduces evidence that (1) the current
voting machines cannot process ballots allowing unlimited
ranking, and (2) permitting voters to rank more than three
candidates might exceed the memory capacity of the
machines now in use. The City maintains that the state certifi-
cation necessary for new voting software or hardware or for
redesigned ballots could take months or years, so allowing
unlimited choices would disrupt the City’s preparation for
upcoming elections. Moreover, contends the City, (1) because
some elections include many candidates, allowing unlimited
rankings would require either extremely large, confusing bal-
lots or multiple ballots for each voter; (2) multiple ballots
could lead to calculation errors; and (3) in testing, voters
regarded ballots offering four choices as confusing. Notably,
Dudum introduced no evidence suggesting that San Francisco
could conduct unrestricted elections without running into the
problems identified, and does not now argue that the City’s
interests are inadequate to justify the three-candidate restric-
tion.

   [11] Assuming for the moment the constitutional validity
of IRV systems generally, then, the three-candidate restriction
furthers important interests in maintaining the orderly admin-
istration of San Francisco’s elections and in avoiding voter
                            DUDUM v. ARNTZ                             6693
confusion. See, e.g., Eu v. San Francisco Cnty. Democratic
Cent. Comm., 489 U.S. 214, 225-26 (1989) (noting that “pro-
tecting voters from confusion” is a “compelling governmental
interest”); Lubin v. Panish, 415 U.S. 709, 715 (1974)
(“[K]eeping . . . ballots within manageable, understandable
limits is of the highest order,” because “ ‘laundry list’ ballots
discourage voter participation and confuse and frustrate those
who do participate.”); Bullock v. Carter, 405 U.S. 134, 145
(1972) (“[T]he State understandably and properly seeks to
prevent the clogging of its election machinery [and] avoid
voter confusion.”); Pest Comm., 626 F.3d at 1107-08 (recog-
nizing that avoiding voter confusion is an important state
interest); Rubin, 308 F.3d at 1017 (acknowledging the “legiti-
mate goal of achieving a straightforward, neutral, non-
confusing ballot”). So, without more, Dudum’s challenge to
the three-candidate restriction fails.28

   We could stop there, as Dudum purports to challenge only
  28
    Dudum objects that the interests the City now relies on were not
advanced upon adoption of Proposition A and so are impermissible post
hoc rationales. We are far from sure that the normal ability of litigants to
advance arguments justifying their out-of-court behavior is suspended in
election challenges where, as here, the burden imposed on voting is mini-
mal at best. For instance, in Timmons v. Twin Cities Area New Party, the
Court expressly relied on a state interest admittedly not advanced in its
briefs, but mentioned during oral argument, implying that the interest also
was not advanced prior to the litigation (or else the Court presumably
would have noted that fact). See 520 U.S. at 366 n.10.
   In any event, the post hoc rationale point doesn’t matter in this case, as
the City’s justifications for the three-candidate limit were set forth in the
text of Proposition A itself. Proposition A explained that the Director of
Elections may limit the number of choices a voter may rank if “the voting
system, vote tabulation system or similar or related equipment used by the
City and County cannot feasibly accommodate choices equal to the total
number of candidates running for each office.” S.F. CHARTER § 13.102(b).
The interests in avoiding changes to the voting system and equipment that
would be confusing or risk seriously disrupting the administration of elec-
tions are aspects of the “feasibly accommodate” concern identified in
Proposition A, not post hoc rationales.
6694                    DUDUM v. ARNTZ
the three-rank restriction, not IRV generally. But even if we
expand the comparative inquiry to other election systems, as
Dudum would have us do, his challenge fares no better.

   [12] The City points to evidence that restricted IRV will
save money compared to a two-round runoff system (the elec-
tion system in place prior to IRV), as each runoff election
costs the City between $1.5 million and $3 million. The inter-
est in alleviating the costs and administrative burdens of con-
ducting additional elections can be “a legitimate state
objective” that also justifies the use of IRV, given the mini-
mal at best burdens the system imposes on voters’ constitu-
tional rights to vote. See, e.g., Bullock, 405 U.S. at 147;
Lemons, 538 F.3d at 1104 (holding that the minimal burden
imposed by a state’s system for verifying referendum petition
signatures was justified by the “administrative burden”
another system threatened to impose); Weber, 347 F.3d at
1106 (recognizing a state’s interest in saving money).

   [13] Further, restricted IRV advances the City’s legitimate
interests in providing voters an opportunity to express
nuanced voting preferences and electing candidates with
strong plurality support. See Storer v. Brown, 415 U.S. 724,
732 (1974) (noting a state interest in “assur[ing] that the win-
ner is the choice of a majority, or at least a strong plurality,
of those voting”). Unlike a two-round runoff election,
restricted IRV will not always produce a candidate with
majority support. But restricted IRV also does not limit vot-
ers’ choices to only two candidates, and so it allows voters to
express a wider range of preferences. Moreover, in practice,
the ability to express more nuanced preferences means that
candidates with greater plurality support (although not neces-
sarily majority support) tend to be elected, as compared to a
traditional plurality system. See McSweeney, 422 Mass. at 654
(“[A] preferential scheme, far from seeking to infringe on
each citizen’s equal franchise . . . seeks more accurately to
reflect voter sentiment . . . [and] ‘to enlarge the possibility of
a voter[ ] being represented therein by giving the voter an
                          DUDUM v. ARNTZ                        6695
opportunity to express more than one preference among can-
didates.’ ” (quoting Moore, 309 Mass. at 331)).

   [14] In sum, we have no difficulty holding that these
important governmental interests are more than sufficient to
outweigh the extremely limited burdens—if any—that the
restricted IRV features Dudum challenges impose upon San
Francisco’s voters.

                         CONCLUSION

   If the aspects of the City’s restricted IRV scheme Dudum
challenges impose any burdens on voters’ constitutional rights
to vote, they are minimal at best. Moreover, the City has
advanced valid, sufficiently-important interests to justify
using its system. We, of course, express no views on the wis-
dom of using IRV, restricted IRV, or any other electoral
method. There is no perfect election system, and our search
for one would prove no more successful than a hunt for the
mythical snark.29 Happily, we are not required to engage in
any such endeavor. We hold only that Dudum has not estab-
lished that the City’s chosen system is unconstitutional.

  AFFIRMED.




  29
   See Lewis Carroll, The Hunting of the Snark: An Agony in Eight Fits
(MacMillan Co. 1876).