Arizona’s Especially Worthwhile Electoral Reform Effort

A local group is pursuing a proposal that deserves nationwide recognition as well as success at home.

One of the most promising—and exciting—efforts at electoral reform in the United States right now is underway in Arizona. It needs to be more widely known—and supported—around the country as well as in its own state.

Sponsored by a homegrown organization called Make Elections Fair Arizona, this proposal would establish nonpartisan all-candidate primaries for elections in the state. As the organization’s slogan “Every voter. Every candidate.” succinctly puts it, the essential idea is that primary elections administered by the government would not be limited to candidates or voters belonging to a particular political party, but instead would involve all candidates and all voters regardless of party affiliation in the preliminary round of the government-run electoral process, which would determine which candidates would advance to the final round of voting in the November general election.

In this respect, the Arizona proposal is similar to California’s “top-2” or Alaska’s “top-4” primaries, both of which also involve all candidates and all voters regardless of party affiliation. In California’s case, the two candidates who receive the most votes in the primary advance to the November election, where voters choose which of the two they prefer. In Alaska, the four candidates with the most votes in the primary advance to the November ballot, which permits voters to rank the four in order of preference, and the state uses an “instant runoff” tabulation formula to determine the election’s winner based on all of the voters’ preferences on all of their ranked-choice ballots.

What is distinctive and especially important about the Arizona proposal is that it does not mandate either California’s system or Alaska’s; either alternative is an option, as indeed are others, as long as they include a primary that permits all voters to choose among all candidates regardless of party affiliation. If adopted, the Arizona proposal would put into the state’s constitution the requirement that this type of nonpartisan primary be used, while leaving it to the state legislature (or the secretary of state if the legislature fails to act) to determine which specific system consistent with this new constitutional requirement to employ.

Thus, Arizona’s legislature could pick California’s top-2 system or Alaska’s top-4, or the top-5 variation of Alaska’s system that Nevada is currently considering—or could design a new system that includes the requisite nonpartisan primary.

Even more significantly, the Arizona proposal does not specify which method of tabulating ranked-choice ballots the legislature (or secretary of state) must select. As I’ve discussed previously on Common Ground Democracy, there are different ways to identify an election’s winner from all the rankings on a set of ranked-choice ballots. Alaska’s “instant runoff” method is the typical way, but it suffers from the problem—especially when an electorate is highly polarized between two opposing parties—of eliminating consensus-building candidates who are not the first choice of either side but who are an acceptable second choice of both.

By contrast, the same set of ranked-choice ballots can be tabulated so that a candidate whom a majority of voters prefers to each other candidate (when each pair of candidates are compared one-on-one based on their relative ranking, higher or lower, on every ballot) is the election’s winner. Any tabulation method having this property of always electing a candidate whom a majority of voters prefer head-to-head over each other candidate is known in the scholarly literature as a “Condorcet-consistent” method, after the French philosopher who identified and explained the virtue of this property.

In the context of a polarized electorate, a Condorcet-consistent method will elect a candidate whom a majority consider acceptable—and preferable to each other candidate—when the voters are deeply divided as to which candidate is their first choice. The Arizona proposal would permit the state’s legislature (or secretary of state) to employ a Condorcet-consistent method of tabulating ranked-choice ballots, which would be especially suitable for a highly polarized state, as Arizona currently is.

Indeed, according to data compiled by Nate Atkinson and Scott Ganz for our co-authored article comparing Alaska’s “instant runoff” and Condorcet-consistent versions of ranked-choice voting, Arizona has one of the five most polarized electorates in the nation. Based on their analysis of data available from the Cooperative Election Study, Arizona’s voters are extremely polarized in the degree of their support for the two major political parties. If all of the state’s voters were plotted along a blue-purple-red spectrum of partisanship, the overall profile of the electorate would look something like this:

From this profile, one can see that there are relatively more voters who are intensely blue or red than there are who are purple or even moderately blue or red—although neither the intensely blue nor intensely red make up a majority of the electorate. This is what statisticians call a “bimodal” distribution—because there are two high points (“modes”) of the distribution at either polarized end of the spectrum, rather than a single high point (“mode”) as in a conventional “bell curve”:

When voters are divided into a bimodal distribution like Arizona’s, rather than forming a “unimodal” normal distribution (like a “bell curve”), it becomes a greater challenge to elect a candidate who best represents the collective preferences of all the voters in the electorate. Electing a candidate who corresponds to the position of one mode in the bimodal distribution, as a plurality-winner electoral system would do, would please the voters who position themselves at that same place on the partisanship spectrum—either intensely blue or intensely red—but it would displease a majority of the electorate, especially those voters who are at the opposite mode of the bimodal distribution, and who intensely disfavor the opposing political party and its candidates (as is the case when politics becomes tribalized by what political scientists call “affective” polarization).

By contrast, electing a candidate whose own position corresponds to the center of the bimodal distribution is a way to maximize the preferences, and minimize the displeasure, of the electorate overall. Even though in this highly polarized electorate there are fewer voters at the center of the distribution than there are at either of the two partisan poles, a candidate at the center—who shares the same position as the electorate’s median voter (where half are more to one side, and the other half are more to the other side)—is a compromise choice who can receive support from a majority of voters in comparison to any other candidate. In other words, the kind of candidate who would be elected in a Condorcet-consistent electoral system—the candidate whom a majority of voters prefers compared one-on-one to every other candidate—is the candidate most suited to represent a highly polarized electorate, and this is true even though there are relatively few voters who would pick this majority-preferred compromise candidate as their first choice.

After developing this profile of Arizona’s electorate, Nate and Scott conducted 100,000 computer-simulated elections using two different tabulation methods for ranked-choice ballots. The first method was the “instant runoff” that Alaska uses. The second method was Condorcet-consistent.

For both methods, Nate and Scott instructed the computer to pull four candidates randomly from the state’s overall profile of voters. Each of these 100,000 random four-candidate draws would correspond to one hypothetical exercise of Alaska’s top-4 nonpartisan primary. Then, modeling the tabulation method used in Alaska’s general election for the ranked-choice ballots with four candidates, and assuming that each voter would rank the four candidates in order of their proximity to the voter, the computer identified the 100,000 winners of these hypothetical general elections based on Alaska’s “instant runoff” formula. Similarly, given the same random selection of four candidates, and the same assumption that voters would rank these candidates in order of their proximity to the voters themselves, the computer identified the 100,000 winners of the hypothetical general elections using a Condorcet-consistent tabulation method for the ranked-choice ballots. (Nate and Scott did not need to specify which Condorcet-consistent method, because all Condorcet-consistent methods will reach the same result if voters rank candidates in order of proximity on a single dimension of partisanship, as Nate and Scott instructed the computer to assume.)

Not surprisingly, but very strikingly, these computer simulations produced noticeably different results depending on whether Alaska’s “instant runoff” or a Condorcet-consistent tabulation method was used. To be clear, the set of 100,000 four-candidate general elections is exactly the same for both tabulation methods, and the way that voter rank each of the four candidates in each of these 100,000 elections is exactly the same; thus, the only explanation for the difference in the two sets of 100,000 winners is the tabulation method itself. Here are the distributions of the 100,000 winners from these computer-simulated elections using, first, Alaska’s method (labeled “IRV” for Instant Runoff Voting) and, second, a Condorcet-consistent method; for ease of comparison, both of these follow, from left to right, the distribution of the voters in Arizona’s electorate (the same as depicted above):

Simply by looking at these three figures side-by-side, one can see the significant difference between how Alaska’s tabulation method and a Condorcet-compliant method perform in the context of the same hyperpolarized electorate. The Alaska method, while producing winners who are on average somewhat less polarized than the voters themselves, produces winners who are on average much more polarized the winners produced by the Condorcet-consistent method. The distribution of the Alaska method’s winners is another sharply divided bimodal distribution not unlike the extremely divided bimodal distribution of the electorate.  By contrast, the distribution of the Condorcet-consistent method’s winners looks much more like a typical “bell curve”—although it too has a bit of bimodality (but not nearly as severe as the other two distributions).

The reason for this sharp difference between the Alaska and Condorcet methods is the way the tabulation procedure of each applies in the context of highly polarized voter preferences. Alaska’s method operates by eliminating, one at a time, the candidate with the fewest first-choice votes based on all the ranked-choice ballots and then reallocating the ballots that ranked the eliminated candidate first to whichever candidate is ranked second on the ballot. The Alaska method repeats this elimination-and-reallocation procedure until one candidate has a majority of first-place votes among the remaining candidates.  With respect to a highly polarized electorate like Arizona’s, Alaska’s procedure tends quickly to eliminate more moderate (or “purplish”) candidates closer to the center of the electorate, leaving the instant runoff process to end up in a choice between a deep blue and deep red candidate. Sometimes the winner is far to one side of the bitter partisan divide and sometimes the winner is far to the other side, but the winner is rarely in the middle.

Conversely, the Condorcet-consistent method tends to elect candidates much closer to the middle of the same highly polarized electorate. This is because the Condorcet-consistent method will always elect a candidate whom more voters prefer to each other candidate. Thus, a candidate close to the center of the electorate will be preferred by the many voters on one side, plus the relatively few voters in the middle, to a candidate on the other side. Likewise, this centrist candidate will be preferred by the many voters on the other side, plus those same relatively few voters in the middle, to a candidate on the first side. In this way, the Condorcet-consistent method tends to elect a compromise candidate who, although the first choice of relatively few voters, is an acceptable backup choice for most voters on both sides—an outcome which, again, is the best that can be accomplished when the electorate is deeply divided between two rival parties, neither of which has a decisive majority of the entire electorate.

In addition to being able to see the significant difference between the Alaska and Condorcet methods just by looking at the graphs of the distributions, as presented above,we can quantify this difference by a simple calculation. First, we can measure the average distance of all voters from the electorate’s median voter. Let’s call this measure v.  The higher this number, the greater the electorate’s polarization. For Arizona, given the profile of the electorate that Nate and Scott have constructed, v is 0.292, which is the fifth highest among all fifty states.

Second, we can also measure the average distance of all the computer-simulated winners from the electorate’s median voter. Let’s call this measure w. Again, the higher this number, the more polarizing the electoral method—or, to put the same differently, the higher this number, the less depolarizing the electoral method. For Arizona, Alaska’s method has a w of 0.224, and a Condorcet-consistent method has a w of 0.148. The difference between these two values for w quantifies the greater dispersion of the Alaska method’s winners compared to the Condorcet-consistent method’s winners.

Moreover, to get a better sense of what these numbers mean, we can combine v and w into a single formula. How v and w relate to each other measures the extent to which an electoral method has a centrifugal (polarizing) or centripetal (depolarizing) effect, given the baseline degree of polarization of the electorate itself. Political scientists have advocated that highly polarized electorates need electoral systems that have a centripetal effect, thereby increasing social cohesion rather than tearing the polity apart. If w<v, then the electoral method has a centripetal effect, whereas if w>v, then the effect is just the opposite (centrifugal).

The most useful way to combine these two quantities is to define the “Centripetal Force” or C-Force of an electoral system as 1-(w/v). The reason for this definition is that if w=v, meaning that the average distance of the system’s winners from the electorate’s median voter is the same as the average distance of all the electorate’s voters from the median voter, then the electoral system’s C-Force is 0. In other words, when, w=v,the electoral system produces winners who are on average neither more polarized nor less polarized than the voters themselves.

Moreover, the smaller w is relative to v, the larger the electoral system’s C-Force will be. If all of electoral system’s winners were at exactly the same position as the electorate’s median voter, then w would be zero, and the electoral system would have a perfect C-Force of 1. Short of perfection, an electoral system is more centripetal—in other words, more depolarizing, or effective in combatting the polarization of the electorate—the closer the electoral system’s C-Force is to 1. Conversely, if w>v, then the electoral system will have a negative C-Force, below zero, indicating its centrifugal rather than centripetal effect.

Finally, for each electorate, one can calculate the difference between the C-Force of different electoral systems. For Arizona’s electorate, the C-Force of a Condorcet-consistent tabulation method is 0.494, whereas the C-Forceof Alaska’s tabulation method is 0.232, for a difference of 0.262. This difference for Arizona between the two methods in their C-Force is the third largest such difference among all fifty states, which reflects a basic relationship between the degree of polarization of the state’s electorate and the difference in C-Force between these two electoral methods: the more polarized the electorate, the more a Condorcet-consistent method outperforms Alaska’s method in having a centripetal (or depolarizing) effect.  We can see this basic relationship in this plot of the difference between the C-Force of the two methods, measured against the degree of the electorate’s polarization:

This analysis underscores the great merit of the flexibility of the proposed electoral reform for Arizona. It would enable the legislature (or secretary of state) to select a Condorcet-consistent method of tabulating ranked-choice ballots rather than Alaska’s method, while at the same retaining all the other features of Alaska’s top-4 electoral system, including its form of nonpartisan primary. A Condorcet-consistent method would be especially beneficial for Arizona, given how highly polarized its electorate is.

The state’s current U.S. Senate election also illustrates the difference that a Condorcet-consistent method would make in comparison to Alaska’s method. Kyrsten Sinema, the incumbent Senator who left the Democratic Party to become an independent, abandoned a reelection campaign because she could not win in the state’s current electoral system, given the degree of the electorate’s polarization. She is caught in the middle, without a home in either party. As a recent New York Times story described, a segment of the state’s electorate who supported Sinema likewise feel without a home in the state’s polarized political environment: “moderate voters said she spoke for a slice of the country that aches for compromise and feels alienated both from the Democrats and from the Republicans.” One voter bluntly stated: “There’s not room for people like us.”

Yet because of polarization, there are not enough of these moderate voters in Arizona for Alaska’s “instant runoff” system to have an effect. All the polling conducted before Sinema abandoned her reelection campaign showed that Sinema would have come in third, behind both major-party nominees. This means that in Alaska’s “instant runoff” system, Sinema would have been eliminated before either major-party nominee, leaving the election to end up a race between the two of them—just as in the state’s current electoral system.

But if Arizona had a Condorcet-consistent electoral system for this year’s U.S. Senate race, it is most likely that Sinema would have prevailed as a compromise candidate who was the first choice of neither partisan tribe but an acceptable second choice of both. In a three-way race with Sinema, it seems highly probable that neither major-party nominee would win a majority of first-choice votes, as Sinema would receive the first-choice votes of the small but significant segment of the electorate who are the moderates profiled by The New York Times. (This expectation accords with the profile of Arizona’s electorate assembled by Nate and Scott, which has voters in the middle of the distribution, although not as many as at either end.) A Condorcet-compliant electoral system would show that Sinema, by combining these first-choice votes from her own moderate supporters with second-choice votes from those ranked either the Democrat or the Republican first, would be preferred by a majority of the electorate to either of the two major-party nominees. Thus, Sinema almost certainly would win the Condorcet-consistent election, and yet she is shut out of the current system—and also Alaska’s “instant runoff” system.

In this way, this year’s Senate race in Arizona vividly exemplifies the importance of the proposed electoral reform, which would permit the state to employ a Condorcet-compliant method for tabulating ranked-choice ballots. (The proposed reform would not permit the kind of simple “top-3” system that Eric Maskin and I have developed, which does not require the use of ranked-choice ballots, as I’ve discussed previously on Common Ground Democracy. This is because the proposed reform requires the use of ranked ballots whenever more than two candidates advance from the nonpartisan primary to the November general election. Nonetheless, the proposed reform could achieve much the same effect by having a three-candidate November election with ranked-choice ballots, as long as a Condorcet-consistent method is used to tabulate the winner from those ballots. There are reasons why a Condorcet-consistent election with three candidates, rather than four (or five), would be simpler to administer even when using ranked-choice ballots rather than the direct head-to-head electoral method that Eric and I describe in our top-3 system.)

Given the advantage of a Condorcet-consistent system for a polarized state like Arizona, one might wonder why the reform proposal should give the state’s legislature (or secretary of state) the option of adopting any other system besides one that is Condorcet-consistent. The reason is a very important practical point: Arizona would be the first state to adopt a Condorcet-compliant system for its elections, and that novelty might be too much for its voters to embrace as part of a proposal that has the move to nonpartisan primaries as its main motivation.

From the perspective of a pragmatic reformer, it is better to achieve the more modest goal of enshrining nonpartisan primaries into the state’s constitution first and then advocate for a Condorcet-consistent version of ranked choice voting as a subsequent step, rather than have the whole reform effort go down to defeat by seeking too much too soon.

Moreover, the reform proposal permits the legislature (or secretary of state) to change the particular electoral method after six years. This also is a good feature of the proposal. It disallows too frequent changes, which might be manipulated by partisan politicians attempting to game the system to their short-term advantage. At the same time, it permits revision after a reasonable period of experimentation. If at first a Condorcet-consistent system is adopted, and it turns out to have unanticipated negative consequences, then without needing a new constitutional amendment the system can be adjusted to eliminate the problem that unexpectedly developed. Conversely, if at first some other system besides a Condorcet-consistent one is adopted, and it turns out not to have a meaningful effect in counteracting the problem of polarization—as is to be expected from the analysis above—then the state, without need of a constitutional amendment, can move to a Condorcet-compliant system as a second step of the reform process.

All in all, this reform proposal being pursued in Arizona is an excellent one, deserving of support. It must get enough signatures to secure a spot on the state’s ballot this November. Let us hope this signature-gathering effort is successful, and then that the voters of the state adopt it.

Furthermore, let’s also hope that other states—especially those with similarly hyperpolarized electorates, like Pennsylvania, Florida, and Ohio, among others—learn from Arizona’s leadership on this front. Many states could benefit from the kind of flexible, pragmatic reform that this Arizona effort is pursuing. It should be a model for multiple similar initiatives.