The case for approval voting

Citizens in many US states and cities in recent years have pushed for various reforms of voting methods. This raises the important question of which reform will best meet both normative and practical goals of representative democracy. While also evaluating criticisms of it, we make the case in this article that approval voting is the simplest actionable response. More specifically, we argue that approval voting offers distinct advantages, not only relative to the status quo of plurality voting, but also relative to alternative reforms. By giving voters the ability to support multiple candidates equally, approval voting grants true agency to the electorate to select strong winners among a candidate pool that is more competitive, diverse, and responsive to what voters want. As a low-cost yet high-impact electoral reform, the implementation of approval voting can create meaningful and lasting improvements in the quality of representation and policies.

64), the frustration and inefficacy felt by the American electorate when repeatedly faced with unsatisfactory electoral outcomes has heightened the salience of voting methods reform as an important political issue. This raises the question of what normative and practical considerations should be used to evaluate how well a voting method performs (e.g. Dunleavy and Margetts 1995;Powell & Powell Jr., 2000). The general consensus in prior literature is that no method perfectly meets all such criteria (Norris, 2004), ultimately requiring trade-offs (Reynolds et al. 2008). That said, some methods-particularly approval voting-stand out as being robustly good.
In this article, we make the case that approval voting is the best approach not only to address key normative principles of representative government but also to address relevant pragmatic concerns regarding administration and implementation. Both "simple [and] practicable" (Brams & Fishburn, 2007), approval voting is a low-cost, high-impact reform that can ultimately improve quality of representation and policy by providing consensus winners while accurately showing each candidate's support.

What is approval voting?
Approval voting is a single-winner voting method that allows voters to choose as many candidates as they wish. The candidate with the most votes wins. Each candidate's result is typically shown as the number of votes they received over the total number of ballots cast.
Approval voting's ballot style is nearly identical to traditional plurality ballots; it has a bubble or other selection option beside each candidate. The only difference is in the instructions where voters are instructed to, "Vote for AS MANY names as you approve of" or some variation.
Approval voting in its classic iteration is done in one round. It can, however, be done in other contexts, such as including a runoff to narrow the focus of the field or to placate traditional notions of the requirements of majority rule.
This piece focuses on single-winner approaches to approval voting, though the ballot style may also be applied in multi-winner contexts. This may be in the form of a bloc-style approach, where the most approved candidates are selected until all seats are filled. One caveat of this approach is that the candidates are likely to be similar. Alternatively, there are proportional approaches to approval voting that can be used when those choosing the election method want a more numerous body of winners that reflect the general makeup of the voters. These systems reweight ballots that contain winners, so that less-represented groups have the opportunity to elect winners in later rounds (Brams et al. 2019).

Background
Recent experimental research has found that, along with the electoral outcome and elite cues, voting experience is one of the primary influences on how voters perceive electoral integrity and form opinions about elections (Clark, 2021). This suggests that voting methods-particularly their transparency and accessibility-may matter more than ever, as elites continue to politicize the electorate and question the legitimacy of elections. To evaluate voting methods beyond their role in the voting experience, we consider other factors, including: (1) winner selection, (2) accuracy of measurement of candidate support, and (3) practicality of implementation.
In this article, we highlight approval voting as doing especially well across the board. By allowing voters to select as many candidates as they wish and not artificially limiting their choices, approval voting greatly enhances democratic choice and allows voters to "express themselves better at the polls" (Brams & Fishburn, 2007, 13). The candidate with the most votes wins in approval voting. This creates two immediate benefits. First, it means that approval voting is undisputedly simple and transparent in its process. It also means that approval voting is better insulated from typical ballot mistakes seen in plurality voting, such as overvoting.
In maximizing voters' options during the voting process, the increased expressivity offered through approval voting limits the need for strategic voting that is often seen in single-member plurality. As small parties are systematically underrepresented in single-member plurality, their supporters are motivated to strategically vote for one of the top two contenders, who have a greater chance of winning (Duverger 1951). Cox (1997) further develops this theory by specifying when we should expect strategic voting to take place. He suggests that a vote should be considered strategic when the voter is concerned with making their vote count. One might argue that a voting method's capacity to continue to select the optimal winner in spite of strategic voting should also be considered.
Voters are viewed as short-term utility maximizers who have information on the relative strength of various parties and candidates and then use that information to vote strategically (Cox 1997). This underscores the limitations of plurality voting in restricting competition to the top two contenders, which only reinforces the two-party system. By giving voters the ability to equally support multiple candidates in an election, approval voting can help adjust voter expectations of likely electoral outcomes. This ability to equally support multiple candidates diminishes voters' need for strategic behavior to make their vote count in the voting process. In particular, candidates with artificially low support-particularly non-major party candidates-get more accurate support under approval voting.

Winner selection
Importantly, approval voting does well at its most crucial job-selecting a strong winner. This applies regardless of how you qualify what a strong winner means, including the ability to elect Condorcet winners in honest conditions (Laslier, 2006;Igersheim et al., 2021), as well as under mixed strategy conditions (Smith and Kok n.d.a;Igersheim et al., 2021). More specifically, past research using utility scores to identify Condorcet winners shows that approval voting is one of the alternative methods capable of electing the Condorcet winner (Igersheim et al., 2021). Recent research using computer simulations under a Monte Carlo method demonstrates that approval voting also produces winners that reliably maximize voter satisfaction (; Quinn 2021).
More specifically, approval voting accomplishes this feat by allowing voters to not only choose their favorite candidate but also hedge their bets by selecting other candidates that they also deem viable. For example, a voter can choose a second candidate (or more) who is between their own favorite candidate and a less preferred candidate but still within their range of acceptability. This provides voters with meaningful expressiveness and agency in deciding where this range of acceptability begins and ends.
The ability of approval voting to select strong winners has been verified in multiple ways. The first of which is through the use of computer modeling (e.g. Smith 2006; Smith and Kok n.d.b.; Quinn 2021). While dependent on model assumptions, computational approaches have the benefit of simulating many more elections than one would traditionally have access to, overcoming the obstacles of limited samples when analyzing real elections. An additional benefit of computer simulations is their ability to account for varying levels of tactical voting, thereby more closely mimicing real-world elections.
Another methodological approach commonly used in prior research is polling. Studies have assessed how approval voting elections compare within German elections (Alós-Ferrer and Granić 2012) as well as multiple French ones (Laslier and Van der Straeten 2004, Baujard et al., 2011, Baujard et al. 2014, Baujard & Lebon, 2020. More recently, experimental polling has been conducted for US elections as well (Igersheim et al., 2021), testing how the winner selection of approval voting compared to the status quo plurality system as well as to other popular alternative methods.
Using a novel experimental approach, Igersheim et al., (2021) investigated how voting methods compared to a control measure, using the context of the 2016 US presidential election. This particular study used a within-subjects design to directly compare voting methods against honest assessments. This study used both a short and a long candidate list as well.
The underlying assumption is that voters' true candidate preferences should typically line up with the elected winner. In this study, approval voting was found to produce a virtual tie between the best and a slightly inferior candidate in a longer hypothetical candidate list (Igersheim et al., 2021). Other voting methods like instant runoff voting and plurality did much worse in their accuracy relative to voters' honest assessments. While range voting more clearly identified the best winner, approval voting showed clear promise and performed better than plurality and instant runoff voting.

Accuracy of candidate support
In addition to winner selection, an underrated yet important function of voting methods is to clearly capture the support of all the candidates. This is particularly important when considering the impact it can have on how candidates and their ideas are weighed throughout an election campaign. Without the ability to accurately capture the extent to which candidates are liked and supported by voters, some candidates may be dismissed erroneously, with their ideas having no chance to contributing meaningfully to the discussion. This often hapens with third parties (Igersheim et al., 2021;Brams and Fishburm 2007;Alós-Ferrer and Granić 2012;Rosenstone et al. 1996).
One way to test this support accuracy is to use polling and compare voting methods against a control measure. In addition to approval voting being compared in a 2016 US presidential election study (Igersheim et al., 2021), it was also compared against control measures for the 2020 US Democratic presidential primary (The Center for Election Science 2020a; 2020b). In each of these, there were minimal discrepancies between approval voting support and control measures. Approval voting was able to correct repeatedly for artificially low support as measured under plurality and instant runoff voting. In some cases, this meant correcting candidate support as much as ninefold, as with Green Party candidate Jill Stein under approval voting in the 2016 election.

Practical considerations
Approval voting has the advantage of being particularly easy to implement as well as avoiding administration concerns. This includes factors such as education, ballot design, voting machines, tabulation procedures, and risk-limiting audits.
Education campaigns for approval voting are straightforward. They simply involve letting voters know that they may choose as many candidates as they wish. Everything else about the voter experience is the same. Additionally, simple ballot directions give voters a reminder.
Ballot design for elections that use approval voting is extremely simple and only requires minute adjustments from currently used plurality systems. The name-bubble design commonly used in plurality elections across the U.S. is employed by approval voting, with the only change being that voters are instructed that they can select more than one candidate. This limits extra costs and strain on ballot printing, which is important in states and localities that rely on paper ballots. Similarly, the vast majority of voting machines in use in the U.S. are able to handle approval voting in their current software implementation. Practically speaking, the only adjustment needed in most voting machines and ballot marking devices is to allow them to cast "overvotes," which many are designed to prevent in their current operating software.
Similarly, tabulation procedures for approval voting are done precisely as they are in plurality elections; election officials simply need to add up the votes. The only difference inherent to approval voting is that more than one vote is possible from each voter.
Finally, there is nothing about approval voting that prevents risk-limiting audits from being conducted (Sarwate et al., 2011;Sarwate et al. 2013). Risk-limiting audits can and should be conducted following major elections that employ approval voting, and researchers describe extending plurality audits to approval voting as a "simple extension."

Addressing main critiques
Many of the critiques of approval voting involve the majority criterion, the later-noharm criterion, bullet voting, and voter expressiveness. We address each in turn.

The majority criterion
The concept of majority is a strange one in voting, as there is not always a Condorcet winner, and in an election with more than two candidates, there is not always a candidate who is preferred by more than half the voters to every other option (Gehrlein 1983). The majority criterion states that if there is a candidate who has more than 50% of first-choice preferences, then this candidate should be the winner. Approval voting fails this criterion since it is possible to create examples where this occurs among honest voters, such as the following: In this example A is preferred as first on 60% of the ballots and should be selected to pass the majority criterion. Yet, B is approved on all the ballots and would win with 100% approval. While there is a discrepancy, it raises the reminder that approval voting is not an ordinal method. The questions raised here are twofold: (1) whether candidate A is really better than candidate B and (2) how different candidates A and B are relative to the electorate's utility preferences.
A drawback of ordinal data is that there is no indicator of satisfaction from the ordered preferences. As a result, the ordinal data doesn't tell us the utility of the voters. For candidate B to be worse than candidate A in terms of voter utility would require certain assumptions. This would mean that the set of 60 voters would have to strongly prefer candidate A and barely find candidate B acceptable. And the remainder of voters would have to just barely disapprove of candidate A. To the degree that this is true, it's challenging to arrive at a plausible scenario where this violation has a meaningfully large utility discrepancy between candidates A and B.
It's important to remind ourselves that when using a criterion-based assessment, we must consider both the frequency of the violation and the degree to which the alternative winner is worse. If the frequency is uncommon and the violation causes the alternative candidate to be minimally worse (or even better), then the violation has trivial consequences.

The later-no-harm criterion
The later-no-harm criterion states that supporting an additional candidate who you prefer less than a preferred candidate should never cause the preferred candidate to lose. With approval voting, all approvals are counted equally. A vote for two acceptable candidates, one more preferred than the other, could cause the preferred candidate not to win if the contest is close with the other acceptable candidate.
Fortunately, this means that, at worst, a candidate who is acceptable to the voter still wins. Further, this violation refers to the individual voter or subset of voters and not to the electorate as a whole. A more appropriate question is whether the later-noharm violation worsens the winner for the entire electorate.

Bullet voting
A related critique of later-no-harm is that a fear of supporting additional candidates may cause voters to choose only one option-even when voters like additional candidates. That is, voters will "bullet vote" (Niemi 1984). Again, this should only bother us to the extent that this happens in practice and to the extent that this causes an inferior winner to be selected.
Fortunately, we have multiple polling experiments that test (1) whether voters would bullet vote under approval voting and (2) whether the presence of bullet voting materially alters the outcome. There is a general theme of the votes per ballot increasing with the number of candidates. In any case, we regularly see this number being significantly greater than one. In a German study with two scenarios, voters chose roughly two candidates per ballot when seven or eight candidates were present (Laslier and Van der Straeten 2004). In a survey associated with a French presidential election, we saw 3.15 votes per ballot with 16 candidates and 2.23 votes per ballot with 12 candidates for the 2002 and 2007 elections, respectively (Laslier and Sanver eds. 2010).
In a 2-seat election for the mayor of Fargo in 2020, we saw 2.3 votes per ballot with seven candidates, 0.5 more votes per ballot than usual years (The Center for Election Science 2020c). In a top-2 approval voting primary election in St. Louis, MO in 2021, we saw roughly 1.6 votes per ballot with four candidates (The Center for Election Science 2021).
All these data indicate that, in practice, we do not see pervasive bullet voting. And in fact, it does not take significant numbers of people selecting multiple candidates to make a material difference in close elections. Even if more than 75% of voters choose only one candidate, the fact that the remaining voters choose multiple candidates is more than enough to both change the winner and increase the accuracy of support for non-winning candidates.
These results should not be surprising. First, many voters may not actually approve more than one candidate, particularly in cases when there are few candidates to choose from. And for those who do approve of multiple candidates, it is often in their interest to say so on their ballot. Failure to support an approved candidate can risk an unacceptable candidate winning instead. The cost of accidentally causing an acceptable yet less preferred candidate to win, however, is a much lower cost. And, of course, this calculation of supporting additional candidates gets easier when one's preferred candidate shows little likelihood of winning compared to an acceptable alternative.
It's also worth asking whether the degree of bullet voting that takes place changes the outcome from the ideal winner or from an alternative voting method. If there is no difference in the winner-particularly compared to the ideal winner, then it is unclear what is actually problematic. It may also sometimes be that few candidates are worth approving or that voter support across candidates genuinely does not overlap.

Voter expressiveness
One final common critique is that approval voting is not sufficiently expressive. It is worth reminding the reader that approval voting uses a completely different kind of data than many other systems-cardinal rather than ordinal data. Since approval voting is both cardinal and binary, a voter can choose among 2 C possible ballots, where C is the number of candidates. 2 Compared to ordinal methods or cardinal methods going beyond a binary scale, approval voting has fewer possibilities. That said, approval voting still has a number of expressiveness advantages compared to many ordinal systems: 1. Approval voting can indicate equal support for candidates. 2. Approval voting ballots do not need to be truncated; voters can provide all their approvals without limit. 3. Approving candidates is simple and likely to be less susceptible to voter fatigue, so that voters do not reduce the information they put on the ballot.

Approval voting uses all voter data and never ignores ballot information any-
where in the tally (in contrast, for example, to instant runoff voting, which ignores all data on eliminated candidates later in the count). 5. Approval voting reveals a utility threshold, where voters separate the candidates they approve from those they do not approve, whereas ordinal methods show neither a threshold of support nor the degree of preference.

Current use
Approval voting is used in two places in the United States, and momentum is building for its expansion. In 2018, Fargo, North Dakota was the first city in the United States to pass approval voting for government elections (The Center for Election Science 2018). Fargo was previously plagued with vote splitting, as candidates claimed wins with less than 30% of the vote (Reform Fargo). The Fargo commission created a task force to study the issue. After six months, the task force recommended approval voting. The commission then ignored the task force for over a year, which eventually triggered Fargo citizens to file a ballot initiative (Reform Fargo).
In the 2018 ballot initiative, Fargo residents overwhelmingly supported the reform nearly two to one (Ballotpedia 2018). It cost the city no money to implement approval voting from a technical standpoint, as their voting technology was already equipped to handle approval voting. While approval voting's first use was to simultaneously elect two candidates to the commission, both candidates had over 50% approval (Center for Election Studies 2020c).
St. Louis is the most recent city to implement approval voting, having passed a ballot initiative by 68% in 2020 (Ballotpedia 2020). Its first use was in 2021, in the form of a nonpartisan open primary by approval, with a top-two general election where the primary election leader went on to win in the general election (Ballotpedia 2021). According to St. Louis election officials, the transition from plurality voting to approval voting was smooth and only required "a bit more education" and "chang[ing] the wording on the ballot and in the programming" (Rakich, 2021).
Beyond its use in Fargo and St. Louis, approval voting has been used in several private organizations for many years. Currently, it is used by political organizations such as the Texas Libertarian Party, the Texas Green Party, the Reform Party, as well as by the United Nations to elect the general secretary. Private organizations that use approval voting include the Mathematical Association of America, the American Statistical Association, the National Academy of Sciences, and the Institute for Operations Research and Management Sciences.

Discussion & conclusion
Approval voting is unique because it performs so well and yet is so simple, a feature even voting method experts appreciate (Laslier 2012). It does the core job of selecting a strong winner while accurately acknowledging the support of the remaining candidates. And it does all this while being transparent to voters and easing administrative burdens.
Even the main critiques against approval voting do not appear substantive, either on their face or in practice. What matters going forward is whether the best winner or true candidate support is compromised. And we do not see those issues with approval voting, albeit we still want to see use in more elections.
While approval voting does not walk away perfectly, it walks away better than alternatives such as plurality and instant runoff voting. And it does so without the fiscal or complexity costs of instant runoff voting. As more research is done to compare different voting methods-particularly against a control measure-it will be useful to see how approval voting fares. And it may take numerous elections to see enough complicated scenarios to show differences. But to the extent that approval voting at least ties any alternative method in winner-selection, its simplicity and transparency should act as the tiebreaker.
Approval voting has been late in its application to modern government elections, though its usage has taken a foothold. While advocacy continues, approval voting's simplicity will serve it well in spreading to further cities and states. With this exposure and minimal friction for implementation, approval voting sets itself up for use both throughout and beyond the United States. It holds great opportunity as the method to replace the repentant use of plurality voting.

Declarations
Competing interests Authors work for an employer that advocates for approval voting.
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