
    Ron DUDUM; Matthew Sheridan; Elizabeth Murphy; Katherine Webster; Marina Franco; Dennis Flynn, Plaintiffs-Appellants, v. John ARNTZ, Director of Elections of the City and County of San Francisco; City and County of San Francisco, a municipal corporation; San Francisco Department of Elections; San Francisco Elections Commission, Defendants-Appellees.
    No. 10-17198.
    United States Court of Appeals, Ninth Circuit.
    Argued and Submitted March 15, 2011.
    Filed May 20, 2011.
    
      James R. Parrinello, Christopher E. Skinnell, Nielsen, Merksamer, Parrinello, Mueller & Naylor, LLP, San' Rafael, CA, for the plaintiffs-appellants.
    Therese M. Stewart, Chief Deputy City Attorney, and Jonathan Givner, Andrew Shen, and Mollie Lee, Deputy City Attorneys, San Francisco, CA, for the defendants-appellees.
    
      Before: RICHARD A. PAEZ, MARSHA S. BERZON, and CARLOS T. BEA, Circuit Judges.
   OPINION

BERZON, Circuit Judge:

In 1873, Charles Lutwidge Dodgson, better known by his pen name, Lewis Carroll, spotted what he took to be an “extraordinary injustice”: using simple plurality voting to determine the winners of elections. 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 systems were designed to remedy that limitation, and are still praised today because they tend to elect candidates with widespread electoral support.

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.”

Over a century later, Dodgson’s wish remains unfulfilled. No perfect election system has been devised. Nonetheless, some governmental entities continue to experiment with innovative 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”) to replace the two-round runoff election system for the following city offices: Mayor, Sheriff, District Attorney, City Attorney, 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, candidates for a single office. The Department of Elections (the “Department”) then tabulates the voters’ preferences as follows: 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 “eliminated,” meaning that that candidate cannot win the election. 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 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 number of rankings on each ballot to three. San Francisco maintains, 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 untenable; 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 election; provide synopses of vote distribution during the tabulation process and of the final votes attributed to each candidate; and show the numbers of ballots “exhausted” as the tabulations proceeded. 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 practice.

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 unconstitutional, 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. 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 completed, sometimes in numbers greater than the final margin of victory. 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 structuring elections.” Burdick v. Takushi 504 U.S. 428, 433, 112 S.Ct. 2059, 119 L.Ed.2d 245 (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-choiee” 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, 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)(l); 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 disadvantages.” 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 system.” David M. Farrell, Electoral Systems: A Comparative Introduction 47 (2001).

For instance, in the familiar simple plurality system, sometimes 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 contests 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 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 Plurality-like Electoral Systems, in Electoral Laws and Their Political Consequences 193, 195 (Bernard Grofman ed., 1986), similarly has both significant strengths and troublesome weaknesses. In such a system, long used in many local elections and in some state races, voters select a single candidate 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 candidates who received the highest number of votes in the first round. 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 election at the runoff stage. Id. at 150. Also, an elected candidate 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 elections, id. at 149, and results in two different, albeit overlapping, 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 simple 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” — than does straight plurality voting, because votes that would otherwise be cast for losing candidates can be redistributed to candidates 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 elected. Whether that feature is a disadvantage or an advantage is, of course, debatable. Where, for instance, there is no candidate with a majority, and the vote spread between the top plurality 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 system, in contrast, provides voters that opportunity through a new round of balloting in a runoff election. Finally, both IRV systems are unfamiliar to many voters, and so some voters 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 winning. 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 candidates. 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

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 political beliefs, and the right of qualified voters, regardless of their political persuasion, to cast their votes effectively.’ ” Anderson v. Celebrezze, 460 U.S. 780, 787, 103 S.Ct. 1564, 75 L.Ed.2d 547 (1983) (quoting Williams v. Rhodes, 393 U.S. 23, 30, 89 S.Ct. 5, 21 L.Ed.2d 24 (1968)). At the same time, and even though “voting is of the most fundamental significance under our constitutional structure,” “States retain the power to regulate their own elections.” Burdick, 504 U.S. at 433, 112 S.Ct. 2059 (internal quotations omitted). As our short review has indicated, each available election system, “ ‘whether it governs the registration and qualifications of voters, the selection and eligibility of candidates, or the voting process itself, inevitably affects — at least to some degree — the individual’s right to vote.’ ” Id. (quoting Anderson, 460 U.S. at 788, 103 S.Ct. 1564).

Recognizing the need of States and municipalities “to assure that elections are operated equitably and efficiently,” id., we apply a “flexible standard” when considering constitutional 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 forward 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 plaintiffs rights.”

Id. at 434, 112 S.Ct. 2059 (quoting Anderson, 460 U.S. at 789, 103 S.Ct. 1564). When the burdens 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, 112 S.Ct. 698, 116 L.Ed.2d 711 (1992)). But voting regulations are rarely subjected to strict scrutiny. See Lemons 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 reasonable, nondiscriminatory restrictions.” Timmons v. Twin Cities Area New Party, 520 U.S. 351, 358, 117 S.Ct. 1364, 137 L.Ed.2d 589 (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 limitations inherent in restricted IRV. For instance, voters are unable to reconsider their choices after seeing which candidates have a chance of winning, and some voters might be unfamiliar with the system. Dudum does not, however, challenge 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 challenge, 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 “exhausted” 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 supported adoption of Proposition A stated in their official ballot argument that “[t]he ‘instant’ runoff works much like December’s ‘delayed’ runoff.”

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

In actuality, all voters participating in a restricted IRV election are afforded a single and equal opportunity to express 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. 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 candidate. 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 proceeds to the runoff election, that voter is still afforded an opportunity in the runoff election to select a different candidate, or not to vote at all. In a restricted IRV system, in contrast, if that voter chooses a successful candidate in one round, he is not afforded the opportunity to switch his vote to a different 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 Francisco and explains why the city supervisors compared the two. But restricted IRV does not replicate a two-round runoff system because, as we just explained, in two-round runoffs, voters cast ballots twice — that is, make and record their choices twice— whereas IRV allows only one chance to vote.

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 several 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 burden 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 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 instructive. In that case, after concluding that an election was defective, the state ordered a second curative election but limited participation to people who had voted in the original balloting. 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 interests 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 jurisdictions 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, 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 voters to participate in the second-round runoff election — albeit better than not participating at all.

If anything, properly understood, Dudum’s example highlights that IRV is not equivalent to two-round runoff elections: 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 candidate 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 preferences in the runoff election; the in-person voter votes twice using two ballots, but the absentee voter votes once using a single ballot. 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 ballots at the same time, and have their preferences calculated in the same manner.

In sum, the City’s restricted IRV system is not analogous 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 opportunities to cast ballots.

2.

Aside from characterizing San Francisco’s restricted IRV system as a limitation on casting ballots, Dudum tries a second 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, according to the Charter, voters whose ballots are “exhausted” do not have their ballots “counted in further stages of the tabulation.” 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.

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 conducted pursuant to the City’s IRV system can be elaborated so that the outcome is mathematically identical, yet the features 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 demonstrates 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 runoff 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 finish could continue to be reflected as a vote for that candidate in subsequent rounds. Votes that the candidate received from ballots with second- or third-choice candidates remaining 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 process 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 plurality 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. As this example illustrates, the restricted IRV system does not necessarily produce 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. Cfi 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 rephrasing makes explicit what is implicit in the current scheme: “Exhausted” ballots are counted in the election, they are just 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 candidate is eliminated may choose the winning candidate as their second- or third-choice pick. See Amy, supra, at 155.

All this is to say that “exhausted” ballots represent votes for losing candidates. “Exhausted” ballots are not disregarded 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, 665 N.E.2d 11 (1996), was an unrestricted form of preferential voting called the “single transferable vote.” Rejecting the argument that voting rights were seriously 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 election 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.” Id. at 652, 665 N.E.2d 11; see also Moore v. Election Comm’rs of Cambridge, 309 Mass. 303, 319, 35 N.E.2d 222 (1941) (reaching the same conclusion), abrogated on other grounds as recognized in McSweeney, 422 Mass, at 653-54, 665 N.E.2d 11.

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’ constitutional 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 Bd. of Estimate of New York v. Morris, 489 U.S. 688, 692, 109 S.Ct. 1433, 103 L.Ed.2d 717 (1989) (quoting Reynolds v. Sims, 377 U.S. 533, 565, 84 S.Ct. 1362, 12 L.Ed.2d 506 (1964)). 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.

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 preferences is not the same as providing additional votes, or more heavily-weighted votes, relative to other votes cast. Each ballot 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 provides 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 round every voter’s vote carrie[d] the same value.” Id. at 693.

Dudum attempts to distinguish Minnesota Voters’s rejection of the dilution claim by arguing that San Francisco’s system is different than Minneapolis’s, because the former restricts voters to choosing three candidates. Dudum’s observation, 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 progress (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 exacerbate them. And insofar as Dudum’s dilution argument shifts to a concern that the voters whose ballots become “exhausted” 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 Francisco’s and Minnesota’s systems (as considered in Minnesota Voters) therefore does not help Dudum’s dilution claim.

* * *

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 amalgam of advantages and disadvantages. The burdens Dudum identifies, however, are largely ephemeral, disappearing upon examination. The restricted IRV scheme does not provide disparate 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” feature 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 argument fails as well, because the ability to rank preferences sequentially does not affect the ultimate weight accorded any vote cast in the election.

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 governmental interests sufficient to justify that minimal at best burden under the flexible balancing analysis. See, e.g., Burdick, 504 U.S. at 487, 489, 112 S.Ct. 2059 (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”).

C. The Governmental Interests

Because restricted IRV does not impose severe burdens on voting rights, we do not apply strict scrutiny. See, e.g., Timmons, 520 U.S. at 358, 117 S.Ct. 1364; Pest Comm. v. Miller, 626 F.3d 1097, 1106 (9th Cir.2010). And here, the City’s “important regulatory 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, 117 S.Ct. 1364; Nader v. Cronin, 620 F.3d 1214, 1217 (9th Cir.2010).

1.

Before addressing the City’s proffered interests, we emphasize that the City is not required to show that its system is narrowly tailored — that is, is the one best tailored to achieve its purposes. See Timmons, 520 U.S. at 358, 117 S.Ct. 1364. Latching onto a phrase from Anderson v. Celebrezze, Dudum contends otherwise, insisting that the governmental restrictions must be “necessary to burden the plaintiffs rights,” 460 U.S. at 789, 103 S.Ct. 1564 (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 requirement that the rule is the only or the best way to further the proffered interests. See Timmons, 520 U.S. at 365, 117 S.Ct. 1364 (“[Bjecause the burdens the [challenged] ban imposes on the party’s associational rights are not severe, the State need not narrowly tailor the means it chooses to promote [its interests].”); Pest Comm., 626 F.3d at 1110 (holding that the district court correctly 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).

Such respect for governmental choices in running elections has particular force where, as here, the challenge is to an electoral 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 reviewing court can assess the likely effects of entirely eliminating the challenged rule. Cf. Burdick, 504 U.S. at 430, 112 S.Ct. 2059 (state prohibition on write-in voting); Anderson, 460 U.S. at 782, 103 S.Ct. 1564 (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 system 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 generally 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 restriction, then restricted IRV should be compared to election systems 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 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.

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 certification 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 ballots 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 restriction.

Assuming for the moment the constitutional validity of IRV systems generally, then, the three-candidate restriction furthers important interests in maintaining the orderly administration of San Francisco’s elections and in avoiding voter confusion. See, e.g., Eu v. San Francisco Cnty. Democratic Cent. Comm., 489 U.S. 214, 225-26, 109 S.Ct. 1013, 103 L.Ed.2d 271 (1989) (noting that “protecting voters from confusion” is a “compelling governmental interest”); Lubin v. Panish, 415 U.S. 709, 715, 94 S.Ct. 1315, 39 L.Ed.2d 702 (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, 92 S.Ct. 849, 31 L.Ed.2d 92 (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 (recognizing that avoiding voter confusion is an important state interest); Rubin, 308 F.3d at 1017 (acknowledging the “legitimate goal of achieving a straightforward, neutral, non-confusing ballot”). So, without more, Dudum’s challenge to the three-candidate restriction fails.

We could stop there, as Dudum purports to challenge only the three-rank restriction, not IRY generally. But even if we expand the comparative inquiry to other election systems, as Dudum would have us do, his challenge fares no better.

The City points to evidence that restricted IRV will save money compared to a two-round runoff system (the election system in place prior to IRV), as each runoff election costs the City between $1.5 million and $3 million. The interest in alleviating the costs and administrative burdens of conducting additional elections can be “a legitimate state objective” that also justifies the use of IRV, given the minimal at best burdens the system imposes on voters’ constitutional rights to vote. See, e.g., Bullock, 405 U.S. at 147, 92 S.Ct. 849; 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).

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, 94 S.Ct. 1274, 39 L.Ed.2d 714 (1974) (noting a state interest in “assurfing] that the winner 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 voters’ 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 necessarily majority support) tend to be elected, as compared to a traditional plurality system. See McSweeney, 422 Mass, at 654, 665 N.E.2d 11 (“[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 opportunity to express more than one preference among candidates.’ ” (quoting Moore, 309 Mass, at 331, 35 N.E.2d 222)).

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 wisdom 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. Happily, we are not required to engage in any such endeavor. We hold only that Dudum has not established that the City’s chosen system is unconstitutional.

AFFIRMED. 
      
      . See Charles L. Dodgson, A Discussion of the Various Methods of Procedure in Conducting Elections (1873), reprinted in 3 The Pamphlets of Lewis Carroll 33, 35 (Francine F. Abeles & Charlie Lovett eds., 2001).
     
      
      . 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).
     
      
      . 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).
     
      
      . 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 sometimes call this form of voting the "alternative vote system.” See, e.g., Samuel 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.
     
      
      . 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).
     
      
      . 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. Assn, 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 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 "exhausted” 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).
     
      
      . The parties stipulated that several thousand votes have been "exhausted” 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 ranked 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.
     
      
      . 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 "exhausted” 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.
     
      
      . The two-round runoff system is distinct from, yet similar to, party primaries, in which political parties select a nominee to run in a general election. See generally Cal. Democratic Party v. Jones, 530 U.S. 567, 572-82, 120 S.Ct. 2402, 147 L.Ed.2d 502 (2000) (discussing state regulation of party primary systems).
     
      
      . For example, in San Francisco's 2010 supervisorial election for District 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 candidate. 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/ d 10. html (last visited May 12, 2011) [hereinafter 2010 Election Results].
     
      
      . See Amy, supra, at 16 (“Wasted votes are votes that do not elect someone. If your candidate loses, you have cast a wasted vote.’’).
     
      
      . To illustrate: In San Francisco’s 2010 supervisorial election for District 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 supervisorial 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/ 2010U02/data/d6.html (last visited May 12, 2011).
     
      
      . A voting system called “Condorcet" voting addresses a related problem. In Condorcet voting, each voter ranks his candidate preferences, and the winner is determined by considering all pairwise contests between candidates. “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, Condorcet voting does not require two elections, and academics tend to like it because it selects candidates who are highly rated by the majority of voters. 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 candidates, 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 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, 103 S.Ct. 1564 ("[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.
     
      
      . 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 at, Introduction 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”).
     
      
      . We, of course, express no views on the constitutionality of this hybrid election system.
     
      
      . One might question why receiving a majority of the votes cast for non-eliminated candidates should be the triggering event ending the election. 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 redistributed?
      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 distributed. To see why that is so, consider an election in which, after several IRV tabulations, 100 ballots containing votes for non-eliminated candidates remain. Candidate A receives 51 of those votes. The votes attributable 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 denominator may be redistributed, but the denominator can never increase beyond 100 votes. Thus, even if no further votes are attributed to candidate 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.
      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 candidate 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 respective vote totals of each previously eliminated candidate can only decrease thereafter — they cannot obtain further votes, and some of the 1 st- and 2nd-rank votes that were attributed to them likely will have been distributed to the 2nd- and 3rd-choice candidates on those ballots.
     
      
      . 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 generally. Cf. Edelstein v. City & Cnty. of S.F., 29 Cal.4th 164, 183, 126 Cal.Rptr.2d 727, 56 P.3d 1029 (Cal.2002) ("Plurality rule is not anathema to the federal or state Constitutions.”).
     
      
      . 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 candidate rather than his third-choice pick. Such an objection would have little 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.
     
      
      . 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.
     
      
      . McSweeney went on to decide the case on different grounds, but its reasoning on the counting argument mirrors our own.
     
      
      . The “one person, one vote” cases involve instances in which citizens from heavily-populated districts select the same number of legislative representatives as voters from sparsely populated districts, with the result that their votes have less potential impact on the legislative process. See Reynolds, 377 U.S. at 563, 84 S.Ct. 1362. 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, 84 S.Ct. 1362; see also Bd. of Estimate, 489 U.S. at 693, 109 S.Ct. 1433 (discussing cases).
     
      
      . Other courts have reached the same conclusion. See McSweeney, 422 Mass, at 652, 665 N.E.2d 11 (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).
     
      
      . 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.
     
      
      . We express no views on any characteristics of restricted IRV beyond those discussed.
     
      
      . 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 alternative methods would advance the proffered governmental interests. Cf. Crawford v. Marion Cnty. Election Bd., 553 U.S. 181, 190 n. 8, 128 S.Ct. 1610, 170 L.Ed.2d 574 (2008) (opinion of Stevens, J.).
     
      
      . 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 minimal 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, 117 S.Ct. 1364.
      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 elections are aspects of the "feasibly accommodate" concern identified in Proposition A, not post hoc rationales.
     
      
      . See Lewis Carroll, The Hunting of the Snark: An Agony in Eight Fits (MacMillan Co. 1876).
     