II. Theory

III. Cases of Mixed-Member Majoritarian Electoral Systems

Table 1 lists countries using mmm electoral systems divided into three categories: pure mmm, mmm with partial compensation, and mmm with majority-assuring provisions. All mmm systems allocate seats in two separate tiers, but some mmm systems try to reduce the size of the bonus accruing to large parties by adopting what is known as “partial linkage” based on vote transfers.Footnote ²⁹ These systems adjust the number of votes used to determine a party’s seat allocation in one tier by the number of votes it receives in the other, with the goal of redistributing seats away from larger parties toward smaller ones. Because partial linkage reduces large parties’ seat bonuses to a much lesser degree than linkage based on seats under mmp systems, Matthew Shugart and Martin Wattenberg call these systems “mmm with partial compensation.”Footnote ³⁰

Table 1

Countries using a Mixed-Member Majoritarian Electoral System for Lower House Elections^a

Sources: ACE 2013; International Institute for Democracy and Election Assistance 2017; Kollman et al. 2019; Inter-Parliamentary Union 2016; Carr 2021; Shugart and Wattenberg 2003b; Jastramskis 2019; and Hicken 2016.

^a Note that until electoral reform in 2016, Italy employed vote transfers, which would have placed it in the mmm with partial-compensation category.

Among countries using pure mmm systems (no partial linkage), the electoral systems vary. In the nominal tier, Georgia, Guinea, Italy, Japan, Lithuania, Nepal, Niger, Pakistan, Panama, the Philippines, Russia, the Seychelles, Sudan, Taiwan, Tajikistan, Ukraine, and Zimbabwe use an FPTP-SSD system, with Georgia, Lithuania, and Tajikistan requiring runoffs if no candidate wins a majority in the first round. Libya, Mauritania, Senegal, and Venezuela use a combination of an FPTP-SSD system and other electoral systems in multi-seat districts.Footnote ³¹ Andorra’s nominal-tier districts are all two-seat districts for which it uses party bloc voting. In the list tier, Andorra, Georgia, Guinea, Italy, Japan, Libya, Mauritania, Monaco, Nepal, Niger, Pakistan, Panama, the Philippines, Russia, Senegal, the Seychelles, Sudan, Taiwan, Tajikistan, Ukraine, Venezuela, and Zimbabwe use closed-list PR.Footnote ³² Lithuania allows voters to cast preference votes for candidates on a party’s list. Niger reserves nominal-tier seats for underrepresented minorities, whereas Pakistan and Zimbabwe use list-tier seats for this purpose. In the Philippines, the number of seats parties can win in the list tier is limited, but approximately 80 percent of legislators are elected via an FPTP-SSD system in the nominal tier.Footnote ³³

The three countries that have mmm systems with partial compensation, Hungary, Korea, and Mexico, use an FPTP-SSD system in the nominal tier and closed-list pr in the list tier. Hungary adjusts the votes used to determine a party’s seat allocation in the list tier by the number of votes it wins in the nominal tier. Korea has allocated thirty of its forty-seven list-tier seats on a compensatory basis since 2019, but these seats are a small fraction of the three hundred–member legislature. Mexico places caps on the number of seats parties can win, which we describe below.

Chad and Cameroon, the two countries using an mmm system with majority-assuring provisions, use an FPTP-SSD system in the nominal tier and closed-list pr in the list tier, but grant parties capturing a majority of votes in any list-tier district all available seats in that district.

What distinguishes these systems from mmp systems is that votes in both tiers are valuable from the perspective of allocating seats. All countries in Table 1, with the exception of Andorra, Lithuania, and Monaco, use an FPTP-SSD system, not always exclusively, in the nominal tier, and closed-list pr in the list tier. To evaluate our theory, we turn to two of these countries, Japan, where the lower house has used a separate-vote mmm system since 1994, and Mexico, where the lower house has used its current version of a fused-vote mmm system since 1996.

IV. A Separate-Vote mmm System in Japan

Japan is a bicameral parliamentary system in which the lower house, the House of Representatives, is more powerful than the upper house, the House of Councillors. Representatives serve four-year terms, but prime ministers can dissolve the House of Representatives at any time. As noted above, the House of Representatives has used a separate-vote mmm system to elect its members since an electoral reform in 1994.Footnote ³⁴ Initially, three hundred members were chosen via an FPTP-SSD system and two hundred were chosen from party lists in eleven regional blocs according to closed-list PR. Over time, the number of members elected in both tiers has been reduced. As of 2017, 289 are chosen in ssds and 176 via PR, for a total of 465. The number of seats in each pr bloc has been adjusted over time for population changes and currently ranges from six to twenty-eight. Votes cast in each pr bloc are used to apportion seats in that bloc, which is done using the d’Hondt method (highest averages). In House of Representatives elections, voters receive two ballots. On one, they write the name of their preferred ssd candidate. On the other, they write the name or abbreviation of their preferred party.

Formed in 1955, Japan’s Liberal Democratic Party captured majorities in every House of Representatives election from 1958 to 1990, giving it uninterrupted control of government. In the 1993 election, it captured a plurality but lost control of government when other parties won enough seats among them to form a coalition government. In early 1994, this government introduced an mmm system. Midway through 1994, the ldp reentered government via a coalition of its own. Toward the end of 1999, the ldp convinced a small party, the Komeito, to join its coalition. The Komeito’s religious underpinnings made the parties unlikely bedfellows. Just three years earlier, ldp candidates made the slogan, “The Enemy is Komei,” the centerpiece of their campaigns.Footnote ³⁵ And for years, ldp politicians argued that the Komeito’s existence threatened the constitutional principle that religious organizations could not exercise political authority.Footnote ³⁶ Helpfully for the LDP, the Komeito had a history of preelectoral coordination.Footnote ³⁷ The LDP-Komeito coalition has proved durable. The two parties have governed together since 1999, with the exception of 2009-2012.Footnote ³⁸

The ldp and the Komeito began coordinating in 2000, the first election they faced as partners. Initially, leaders concentrated on how to divvy up ssds. The ldp reportedly floated the idea of standing down in as many as twenty-five ssds in favor of Komeito candidates.Footnote ³⁹ It ended up running in 271 ssds, and the Komeito ran in eighteen. In four of the eighteen, both parties ran candidates. By the 2003 election, they had stopped competing against each other in any ssds. In this and all subsequent House of Representatives elections, ldp candidates have run in approximately 90 percent of ssds and Komeito candidates have run in approximately 3 percent of them.Footnote ⁴⁰ Moreover, in the vast majority of ssds, the party standing down has given its supporters explicit recommendations to cast their ssd votes for the other party’s candidate. Whereas in 2000, the ldp recommended fourteen of the Komeito’s eighteen ssd candidates, since 2003 it has recommended all of them. In 2000, the Komeito recommended 156 (or 58 percent) of the ldp’s 271 ssd candidates. This percentage has risen since then, reaching 96 percent in 2017.Footnote ⁴¹

Newspaper articles from the 2000 election describe how the parties went about exhorting their supporters to split their votes. Around the country, local Komeito chapters held town halls, often attended by thousands, in which they explained to supporters that they needed to cast their ssd votes for the ldp candidate. The chapters invited prominent members of the ldp candidate’s camp to attend and had them publicly pledge to deliver pr votes to the Komeito in return for Komeito voters’ support of the ldp candidate.Footnote ⁴² As our theory predicts, ldp candidates in close races were especially solicitous of Komeito ssd votes and thus made more of an effort to deliver pr votes in return.Footnote ⁴³ In many cases, ldp candidates relied on ldp-affiliated local assembly members and organizations to deliver these pr votes to the Komeito. Local assembly members held small meetings in which they asked their supporters to vote Komeito in the list tier.Footnote ⁴⁴ Organizations like the Japan Trucking Association, prefectural hospitals, and agricultural cooperatives publicly pledged to deliver “every single one of [their] organization’s pr votes to the Komeito.”Footnote ⁴⁵ On occasion, ldp candidates shared their supporters’ names and addresses with the local Komeito chapter, whose members proceeded to visit supporters’ homes to solicit their votes.Footnote ⁴⁶ In other cases, ldp candidates attended a Komeito town hall with their supporters and had both sides publicly pledge to split their votes.Footnote ⁴⁷

In ldp ssds, then, the Komeito instructs its supporters to cast their ssd votes for the ldp’s candidate and their pr votes for the Komeito in exchange for the ldp candidate instructing its supporters to cast their pr votes for the Komeito and their ssd district votes for the ldp’s candidate.Footnote ⁴⁸ Less is known about Komeito ssds where ldp candidates stand down. We concentrate on explicating the benefits to a large party of having a small party stand down in nominal-tier districts in which its candidates need extra votes. As a result of differences in parties’ geographic distributions of support, however, it is possible that a small party’s candidate could be stronger than a large party’s candidate in certain ssds, such that the large party could decide to stand down in those ssds in exchange for pr votes from the small party. Our theory leads us to expect that in such ssds, ldp supporters will be instructed to cast their ssd votes for the Komeito’s candidate and their pr votes for the ldp in exchange for the Komeito instructing its supporters to cast their pr votes for the ldp and their ssd votes for their party’s candidate.

We expect that the LDP-Komeito coalition will try to elicit compliance by making the distribution of valued geographically targeted funding conditional upon it. In Japanese elections, votes are counted at the municipality level and almost every municipality is contained within one ssd.Footnote ⁴⁹ Being able to observe how many pr votes were cast for each party in each municipality gives the coalition the tools to verify whether their supporters complied. In ldp ssds, compliance can be verified by examining whether pr votes for the ldp declined as those for the Komeito increased in municipality m relative to the previous election. In Komeito ssds, compliance can be verified by examining whether pr votes for the Komeito declined as those for the ldp increased.

Our claim that members of the House of Representatives make the distribution of government resources to municipalities contingent upon their voting behavior has support in the Japanese politics literature.Footnote ⁵⁰ The literature credits a potent mix of conditions facilitating the tying of government resources to voting behavior: municipalities’ dependence on the central government for resources; the large pool of national treasury disbursements made available by the central government each year, which are allocated at the discretion of bureaucrats for funding projects in municipalities; and the ability of ldp incumbents to discern how municipalities vote and to lean on bureaucrats to allocate national treasury disbursements in ways that benefit certain municipalities more than others.Footnote ⁵¹ There is no question that national treasury disbursements are a valued resource. Approximately 16 percent of the average municipality’s revenue in 2015 came from this type of transfer.Footnote ⁵² We test the following hypotheses:

V. A Fused-Vote mmm System in Mexico

Mexico is a presidential federal republic with a bicameral legislature. Parties seek a majority of seats in the five hundred–member Chamber of Deputies, the lower house, to shape the legislative process and lead negotiations over the federal expenses budget, which is proposed by the president but requires approval of the lower house. The upper house, the Senate of the Republic, is smaller, comprising only 128 members. Senators do not have the same influence over the federal expenses budget as deputies. A mixed-member system has been used to select deputies since 1964. The current version is mmm with partial compensation, which has been in place since 1996.Footnote ⁵³ Its incorporation of a cap against overrepresentation disqualifies it from being pure mmm.Footnote ⁵⁴ In the chamber, three hundred deputies are elected via an FPTP - ssd system and two hundred are elected via closed-list pr in five regional constituencies. Each of these constituencies elects forty deputies. Deputies serve three-year terms. Following an electoral reform in 2014, deputies elected in and after 2018 are, for the first time since the 1930s, permitted to seek consecutive reelection.Footnote ⁵⁵ In elections, voters receive a single ballot on which appears a series of party-candidate combinations. They mark the combination for which they wish to vote. This translates into a vote for the candidate in the ssd race and a vote for the candidate’s party in the pr race.Footnote ⁵⁶

Formed in 1929, Mexico’s Institutional Revolutionary Party (pri) controlled an absolute majority in the chamber until the 1997 election, when economic crisis and social unrest prompted enough voters to cast their ballots for other parties.Footnote ⁵⁷ This proved the harbinger for the election in 2000 of Vicente Fox, the first president unaffiliated with the pri in more than seventy years. This result was widely credited as evidence of Mexico’s transition to democracy. The pri held onto a plurality in the chamber during Fox’s administration, only to lose it in 2006, when a presidential election held concurrently with legislative elections gave momentum to two opposition parties. The pri became the third-largest party, a position it held until 2009, when it regained a plurality. It controlled more than 40 percent of chamber seats until 2018, when another concurrently held election saw a coalition of parties excluding the pri regain the presidency and majorities in both houses.

At least since Mexico’s transition to democracy, coordination has been a staple among parties contesting elections at all levels.Footnote ⁵⁸ In 2003, the pri convinced the Ecological Green Party of Mexico (pvem), a small party, to ally with it in the chamber and to coordinate with it in elections. But in the 2000 election, the pvem (founded in 1993) had allied with the National Action, which helped to facilitate the alternation of power. Although the pvem leans further right than the pri, its choice of coordinating partner appears to be motivated mainly by the desire to survive.Footnote ⁵⁹ Since 2003, the pri - pvem coalition has coordinated in all elections.Footnote ⁶⁰

As noted above, under a fused-vote mmm system, coordinating parties can field joint ssd candidates. Since 2007, parties fielding joint ssd candidates have also been permitted to present separate party lists. Doing so means that in alliance ssds, voters are presented with a ballot on which the same candidate appears under the names of all coordinating parties. Voters voting for the joint candidate thus have the option of choosing which of the candidate-party combinations they prefer. They can choose all or a subset of these. When a voter chooses the joint candidate under more than one coordinating party, one vote is recorded for the joint candidate in the ssd race and one vote is divided up among the chosen coordinating parties for the purpose of allocating pr votes.Footnote ⁶¹

Our theory leads us to expect that in this setting, the pri will propose fielding joint candidates with the pvem in ssds where it anticipates tough races. In such cases, it can offer the candidacies of some of those alliance ssds to the pvem in exchange for the pvem instructing its supporters in those ssds to vote for the joint candidate exclusively under the PRl’s list. With this strategy, the pvem benefits from having all votes cast for both parties count as votes for its ssd candidate and the pri insures itself against the possibility that the pvem-affiliated joint candidate will lose. When all votes for this candidate are cast under the PRl’s list, then regardless of whether the candidate wins, the pri gets to keep these votes, which translate into pr seats.Footnote ⁶²

Studies of pri-pvem coordination have focused on coordinated entry into ssds.Footnote ⁶³ Evidence that pri politicians incorporated pr votes into trades forged with other parties in previous periods comes from Jeffrey Weldon. He cites interviewees in 1985, when the Chamber of Deputies used a version of a separate-vote mmm system, who told him that voters were instructed to cast one of their ballots for the pri and the other for its coordinating partner.Footnote ⁶⁴ More recently, local newspaper articles describe how the pri and the pvem exhort their supporters to comply. Their strategies include directly instructing supporters to cast their votes for the other party,Footnote ⁶⁵ forming brigades to promote voting for one party but not the other in ssds where the parties have fielded joint candidates,Footnote ⁶⁶ and distributing flyers encouraging supporters to vote for both parties.Footnote ⁶⁷

Further evidence, albeit indirect, comes from the affiliations of the two parties’ joint candidates. In the first two elections in which joint candidates were fielded, 2003 and 2006, the pri kept more than 92 percent of the joint candidacies. After the 2007 electoral reform permitting coordinating parties to present separate lists,Footnote ⁶⁸ we expect that the PRI would have begun to exchange ssd candidacies for pr votes. In every election since 2007, the number of joint candidacies that the pri has kept for itself has declined. Whereas it kept 90 percent in 2009, this share dropped to 78 percent in 2012 and to 77 percent in 2015.Footnote ⁶⁹

When the pri-pvem coalition controlled enough seats to dominate the Chamber of Deputies, our theory leads us to expect that it tried to elicit compliance with its vote-trading strategy by making the distribution of geographically targeted spending conditional upon it. Votes in Mexican elections are counted and reported at the polling station and easily aggregated to the municipality. As noted above, the great majority of municipalities are nested within ssds.Footnote ⁷⁰ Compliance can be verified by examining whether, in ssds with pvem-affiliated joint candidates, votes cast for the joint candidate under the pri label increased as votes cast for the joint candidate under the pvem label or under both parties’ labels decreased in municipality m relative to a previous election.

Beatriz Magaloni writes that for many years, government resources in the form of “patronage, pork and spoils” were the “glue” that bound voters to the pri’s “party-led hegemonic regime.”Footnote ⁷¹ Almost every study to date has focused on how presidents have wielded geographically targetable resources like allocations to municipalities under the poverty relief program Programa Nacional de Solidaridad (pronasol),Footnote ⁷² conditional cash transfers,Footnote ⁷³ and other federal transfers.Footnote ⁷⁴ Jonathan Hiskey provides evidence that these resources are distributed after elections, once vote shares have been verified.Footnote ⁷⁵ The fact that a president’s budget requires approval from the Chamber of Deputies, however, creates room for deputies to add amendments furthering their interests. Yann Kerevel finds that deputies alter the president’s budget to “a substantial degree” and documents a relationship between the number of amendments targeted at ssds added by deputies and the tier from which they are elected.Footnote ⁷⁶

We expect that the pri-pvem coalition used the Municipal and State Infrastructure Strengthening Fund (fortalece), which we are the first to study, to elicit compliance. Dubbed the “handouts fund” (fondo para moches) by the news media,Footnote ⁷⁷ it fell under the Economic and Salary Provisions section of the federal budget and consisted of annual allocations to municipalities that deputies added as amendments.Footnote ⁷⁸ Like national treasury disbursements in Japan, these allocations were awarded to fund specific projects that municipalities had to apply for.Footnote ⁷⁹ In 2015, a total of MX $10 billion (approximately US $500 million) was allocated to municipalities under this fund.Footnote ⁸⁰ Municipalities value fortalece allocations. In 2016, 70 percent of the average Mexican municipality’s income came from federal transfers.Footnote ⁸¹ Unlike Japan’s national treasury disbursements, which have been available for decades, fortalece funds appeared in the budget only in 2013-2017, which limits our analysis to this period.Footnote ⁸² We test the following:

VI. Data

We assembled original data on all municipalities in Japan (1996-2013) and Mexico (2011-2016). For Japan, election returns come from the JED-M data setFootnote ⁸³ and data on national treasury disbursements come from the Nikkei needs data set, supplemented where necessary with data from official government sources.Footnote ⁸⁴ We also used Nikkei needs for the standard control variables used in research on transfers:Footnote ⁸⁵ per capita income, population, fiscal strength, proportion of residents employed in agriculture, proportion of residents age fifteen and under, proportion of residents age sixty-five and over, and population density.Footnote ⁸⁶ Mexican election data are from the National Electoral Institute.Footnote ⁸⁷ For fortalece, we relied on the relevant section of the federal expenses budget for allocations in 2013Footnote ⁸⁸ and on data collected by the Ministry of Finance and Public Credit’s Budget Transparency Project for allocations from 2014 through 2017.Footnote ⁸⁹ We collected data on the following control variables: state of emergency declarations, population, poverty, area size, and designation as urban or rural.Footnote ⁹⁰

VII. Rewarding Vote Trading in Japan

To examine hypothesis 1, we restricted our analysis to Japanese municipalities located entirely within ldp ssds (those with ldp candidates and without Komeito candidates) in the 2003, 2005, and 2012 House of Representatives elections.Footnote ⁹¹ Table 2 presents the results of fixed-effect regressions using this sample of 4,497 municipalities. In all four models, the dependent variable is Log(Transfers_m,t;+1), the logarithm of per capita national treasury disbursement received by municipalities in the fiscal years following the 2003, 2005, and 2012 House of Representatives elections. We have three independent variables of interest. The first, ΔKomeito PR VS_m,t, is the change in share of municipality m’s voting population who cast their pr votes for the Komeito at time t (the current election) relative to the previous election, with higher scores indicating greater increases in share of voting population who voted Komeito in the list tier. The second, Negative (ΔLDP PR VS_m,t), is the change in share of municipality m’s voting population who cast their pr votes for the ldp at time t (the current election) relative to the previous election, multiplied by -1, with higher scores indicating greater decreases in share of the voting population who voted ldp in PR. The third variable, the interaction of ΔKomeito PR VS _t and Negative (ΔLDP PR VS_m,t), captures the effect of a simultaneous increase in the share of a municipality’s voting population who voted Komeito in pr and decrease in the share of its voting population who voted ldp in the list tier.Footnote ⁹²

Table 2

Rewarding Vote Trading in Japan: ldp ssds^a

***p < 0.01, **p < 0.05; robust standard errors clustered at the district level in parentheses

^a In ldp ssds, municipalities that increased pr votes for the Komeito while decreasing them for the ldp were rewarded with more money after the 2003, 2005, and 2012 House of Representatives elections. Municipalities that decreased pr votes for the ldp (without changes to Komeito pr vote share) were penalized with less money, while municipalities that increased pr votes for the Komeito (without changes to ldp pr vote share) were neither penalized nor rewarded.

In all four models, ssd-year fixed effects control for features of a municipality’s ssd in a given election that could influence the amount of transfers received by all municipalities in that ssd. These could include whether the coalition’s candidate was victorious or whether the ssd ended up with two representatives due to a candidate from one party winning and a candidate from another party losing but then entering parliament via the pr tier.Footnote ⁹³ Our inclusion of ssd-year fixed effects means that we are comparing the amounts of transfers received by municipalities in the same ssd-year. In models 2 and 4, we add municipality fixed effects, which controls for time-invariant features of a municipality that could influence the amount of transfers it receives, such as its ability to put together proposals for projects for which to seek funding and to build consensus around those projects. Municipality fixed effects enable us to leverage changes in the same municipality’s level of compliance with the coalition’s vote-trading strategy over time.

All models in Table 2 also include the following time-varying municipality-level controls: population (logged), per capita income (logged), proportion of residents employed in agriculture, proportion of residents who are dependent (ages fifteen and under or ages sixty-five and over), population density, and fiscal strength. All models also include the logarithm of per capita transfers received by the municipality the year of the election. The lagged dependent variable helps us to guard against the possibility that a municipality’s voting behavior has no independent effect on transfers once the transfers it received the year of the election are accounted for. If this was the case, it would suggest that another factor was causing municipalities to both exhibit greater compliance in elections and receive more transfers.Footnote ⁹⁴ Models 3 and 4 include an additional control, ΔLDP ssd VS_m,t, which captures the change in share of municipality m’s voting population who cast their ssd votes for the ldp candidate at time t relative to the previous election. This controls for the possibility that changes in electoral support for the ldp’s ssd candidate could be driving any observed effect of ΔKomeito PR VS_m * Negative (ΔLDP PR VS_m,t) on transfers. Because the nature of a municipality’s ssd determines how ldp and Komeito supporters are supposed to cast their pr votes, we cluster standard errors by ssd.

The positive, significant coefficients on ΔKomeito PR VS_m * Negative (ΔLDP PR VS_m,t) (all models) show that in ldp ssds, controlling for time-invariant and time-varying municipality-level features as well as features of the municipality’s ssd-year and changes in electoral strength of the ldp’s ssd candidate, municipalities that increased pr votes for the Komeito while decreasing them for the ldp in the 2003, 2005, and 2012 House of Representatives elections received more money after elections. Substantively, model 1 shows that a one percentage point increase in ΔKomeito PR VS_m,t in a municipality where the share of eligible voters casting pr votes for the ldp declined by 10 percent (Negative (ΔLDP PR VS_m,t) = 10) is predicted to increase the amount of national treasury disbursements received by ¥1,139 per person (approximately $10.50). In contrast, the same one percentage point increase in ΔKomeito PR VS_m,t in a municipality where the share of eligible voters casting pr votes for the ldp increased by 10 percent (Negative (ΔLDP PR VS_m) = -10) is predicted to decrease the amount of national treasury disbursements received by ¥1,695 per person (approximately $15.60). These average marginal effects, with their 95 percent confidence intervals, are displayed in Figure 1. Their substantive effects are summarized in Table 3.Footnote ⁹⁵ Jens Hainmueller, Jonathan Mummolo, and Yiqing Xu explain why valid inferences as to the effects of an interaction with at least one continuous variable can be drawn only after researchers have verified that the interaction effect is linear and that there is sufficient common support for the moderator.Footnote ⁹⁶ Section E of the supplementary material implements their diagnostics, which support both assumptions.Footnote ⁹⁷

Figure 1

Average Marginal Effects of ΔKomeito PR VS_m,t with 95 Percent Confidence Intervals in ldp ssds^a

^aAverage marginal effects of a one percentage point increase in ΔKomeito PR VS _m,t with 95 percent confidence intervals (shown with vertical lines) at different levels of Negative (ΔLDP PR VS_m,t) in ldp ssds (see Table 2, model 1).

We also examined whether the effect of ΔKomeito PR VS * Negative (ΔLDP PR VS_m,t) could be explained by other parties’ supporters switching their pr votes to the Komeito and the ldp ’s pr vote share declining for another reason. We created Negative (ΔNon-LDP/Komeito PR VS_m,t), which is the change in the share of municipality m’s voting population casting their pr votes for neither the ldp nor the Komeito at time t relative to the previous election, multiplied by -1, with higher scores indicating greater decreases in share of the voting population who voted for another party in pr. We reran the models in Table 2 with Negative (ΔNon-LDP/Komeito PR VS_m,t) instead of Negative (ΔLDP PR VS_m,t), keeping everything else about the specifications identical. The results are in section F of the supplementary material. None of the coefficients (on ΔKomeito PR VS_m,t, Negative (ΔNon-LDP/Komeito PR VS _t), or ΔKomeito PR VS _t * Negative (ΔNon-LDP/Komeito PR VS_m,t)) are significant in any specification. This suggests that our results are not attributable to other factors bringing about changes in the two parties’ vote shares. In sum, these results support hypothesis 1.

Next, we examined whether a similar reward regime, but in reverse, operates in the small number of ssds where the ldp stands down and a Komeito candidate runs (hypothesis 2). In these ssds, we expected municipalities that decreased pr votes for the Komeito while increasing them for the ldp to receive more money. Table 4 presents the results of a regression on the sixty-three municipalities in Komeito ssds in the 2003, 2005, and 2012 House of Representatives elections. The specification is identical to that in model 1 of Table 2.Footnote ⁹⁸ The negative, significant coefficient on ΔKomeito PR VS_m * Negative (ΔLDP PR VS_m,t) demonstrates that in Komeito ssds, controlling for time-varying municipality-level features and features of the municipality’s ssd-year, municipalities that increased pr votes for the Komeito while decreasing them for the ldp in the 2003, 2005, and 2012 House of Representatives elections received less money the year after the election. While this pattern of behavior is rewarded in ldp ssds, it is penalized in Komeito ssds.

Table 3

Substantive Effects on Transfers in Japan: ldp ssds^a

^a Substantive effects on transfers of the average marginal effect of a one percentage point increase in ΔKomeito PR VS_m,t at different values of Negative (ΔLDP PR VS_m,t) in ldp ssds (from Table 2, model 1). Marginal effects are calculated with continuous variables held constant at sample means.

^a Substantive effects on transfers of the average marginal effect of a one percentage point increase in ΔKomeito PR VS_m,t at different values of Negative (ΔLDP PR VS_m,t) in ldp ssds (from Table 2, model 1). Marginal effects are calculated with continuous variables held constant at sample means.

Substantively, we predict that in a Komeito ssd, a one percentage point increase in ΔKomeito PR VS_m,t in a municipality where the share of eligible voters casting pr votes for the ldp declined by 10 percent (Negative (ΔLDP PR VS _m,t) = 10) will decrease the amount of national treasury disbursements received by ¥10,525 per person (approximately $96.80). In contrast, we predict that the same one percentage point increase in ΔKomeito PR VS_m,t in a municipality where the share of eligible voters casting pr votes for the ldp increased by 10 percent (Negative (ΔLDP PR VS_m,t) = -10) will increase the amount of national treasury disbursements received by ¥9,651 per person (approximately $88.80). These average marginal effects, with their 95 percent confidence intervals, are displayed in Figure 2. Their substantive effects are summarized in Table 5.Footnote ⁹⁹ Like Table 2, section G of the supplementary material reveals that the assumptions of linearity and common support for the moderator are met. It is striking that we observe a statistically significant coefficient on ΔKomeito PR VS_m,t* Negative (ΔLDP PR VS_m,t) in the expected direction and in a specification controlling for prior transfers and ssd-year fixed effects on a sample of only sixty-three observations. In sum, these results support hypothesis 2.

Figure 2

Average Marginal Effects of ΔKomeito PR VS_m,t with 95 Percent Confidence Intervals in Komeito ssds^a

^aAverage marginal effects of a one percentage point increase in ΔKomeito PR VS _m,t with 95 percent confidence intervals (shown with vertical lines) at different levels of Negative (ΔLDP PR VS_m,t) in Komeito ssds (see Table 4).

What else can our results tell us about transfers? In ldp ssds, municipalities where pr votes increased for the Komeito as they decreased for the ldp received more money after elections. In Komeito ssds, the reverse was true; municipalities where pr votes increased for the Komeito as they decreased for the ldp received less money after elections. This supports our claim that in our period of study, the LDP-Komeito governing coalition used transfers to motivate ldp supporters to switch their pr votes to the Komeito in ldp ssds and Komeito supporters to switch their pr votes to the ldp in Komeito ssds. The coefficients on the uninteracted variables can tell us more about how the coalition used transfers.

Table 4

Rewarding Vote Trading in Japan: Komeito ssds^a

*** p < 0.01; robust standard errors clustered at the district level in parentheses a In Komeito ssds, municipalities that increased pr votes for the Komeito while decreasing them for the ldp were penalized with less money after the 2003, 2005, and 2012 House of Representatives elections. Municipalities that decreased pr votes for the ldp (without changes to Komeito pr vote share) were also penalized, while municipalities that increased pr votes for the Ko-meito (without changes to ldp pr vote share) were neither penalized nor rewarded.

To begin, we take a closer look at ldp ssds. In Table 2, the coefficients on ΔKomeito PR VS_m,t are negative and insignificant. In other words, municipalities where pr votes increased for the Komeito and stayed the same for the ldp were neither penalized with less money nor rewarded with more. This suggests that the coalition rewarded ldp supporters for switching their pr votes to the Komeito (the positive, significant coefficient on ΔKomeito PR VS_m,t* Negative (ΔLDP PR VS_m,t), but did not reward Komeito supporters for mobilizing more pr votes for their own party. This implies that Komeito supporters were unable to get more money for their communities by mobilizing more pr votes for their party in ldp ssds.

Table 5

Substantive Effects on Transfers in Japan: Komeito ssds^a

^a Substantive effects on transfers of the average marginal effect of a one percentage point increase in ΔKomeito PR VS_m,t at different values of Negative (ΔLDP PR VS_m,t) in Komeito ssds (from Table 4). Marginal effects are calculated with continuous variables held constant at sample means.

The coefficients on Negative (ΔLDP PR VS_m,t), by contrast, are negative and significant, except in model 4, where they are negative and insignificant. A negative, significant coefficient on Negative (ΔLDP PR VS_m,t) means that municipalities in ldp ssds where pr votes decreased for the ldp and stayed the same for the Komeito were penalized with less money after elections. This implies that transfers may also have been used to encourage ldp supporters to cast their pr votes for the ldp. In the model that leverages over-time variation in the same municipality’s voting behavior and also controls for changes in the share of eligible voters casting ssd votes for the ldp candidate (model 4), however, ΔKomeito PR VS_m,t* Negative (ΔLDP PR VS_m,t) remains positive and significant, whereas Negative (ΔLDP PR VS_m,t) loses its significance. This means that the coalition rewarded municipalities where ldp supporters switched their pr votes to the Komeito and not municipalities where they increased pr votes for the ldp.

Turning to Komeito ssds (Table 4), the coefficient on Negative (ΔLDP PR VS_m,t) is negative and significant, which means that municipalities where pr votes decreased for the ldp and stayed the same for the Komeito were penalized. In Komeito ssds, then, transfers are used to motivate ldp supporters to mobilize more pr votes for the ldp. The coefficient on ΔKomeito PR VS_m,t, by contrast, is negative and insignificant. This means that municipalities where pr votes increased for the Komeito and stayed the same for the ldp were neither penalized nor rewarded. In Komeito ssds, then, the coalition rewards municipalities in which Komeito supporters switch their pr votes to the ldp (as indicated by the negative, significant coefficient on ΔKomeito PR VS_m,t* Negative (ΔLDP PR VS_m,t)), but refrains from penalizing municipalities where pr votes for the Komeito increase. This implies that in Komeito ssds, Komeito supporters can gain more money for their community only by switching their pr votes to the ldp, not by casting them for the Komeito.

VIII. Rewarding Vote Trading in Mexico

We next examine hypothesis 3. Table 6 presents the results of fixed-effect regressions. The dependent variable is Log(Transfers_{m t+1}): the logarithm of per capita fortalece received by municipalities in the years following the Chamber of Deputies elections held in 2012 and 2015. Model 1 focuses on municipalities located exclusively within alliance ssds with pvem-affiliated joint candidates (that is, the type of municipalities hypothesis 3 addresses), model 2 focuses on municipalities located exclusively within alliance ssds with pri-affiliated joint candidates, and model 3 focuses on municipalities in nonalliance ssds, where each party fielded its own candidates.Footnote ¹⁰⁰

Table 6

Rewarding Vote Trading in Mexico^a

*** p < 0.01, ** p < 0.05, * p < 0.1; robust standard errors clustered at the district level in parentheses

^a In alliance ssds with pvem-affiliated joint candidates, municipalities that increased votes for these candidates under the PRI’s label exclusively while decreasing them for these candidates under the pvem label or both parties’ labels were rewarded with more money after the 2012 and 2015 elections (model 1). In alliance ssds with pri-affiliated joint candidates (model 2) and in non-alliance ssds (model 3), municipalities that increased votes for the PRI (exclusively, in the case of model 2) were rewarded with more money.

In models 1 and 2, there are three independent variables of interest. The first is ΔPRI VS_m,t, or change in share of municipality m’s voting population who selected the joint candidate under the pri label exclusively at time t (the current election) relative to the most recent similar election.^{Footnote 101} The second is Negative (ΔPVEM or pvem-PRI VS_m,t), or change in share of municipality m’s voting population who selected the joint candidate under either the pvem label or both parties’ labels at time t relative to the most recent similar election, multiplied by -1. The third is the interaction of the two previous variables, which captures the effect of a simultaneous increase in votes for the joint candidate under the pri label exclusively and decrease in votes for the joint candidate under the pvem label or both parties’ labels. In model 3 (nonalliance districts), our three independent variables of interest are ΔPRI VS_m,t, or change in share of municipality m’s voting population voting pri at time t relative to the most similar recent election; Negative (ΔPVEM VS_m,t), or change in share of municipality m’s voting population voting pvem at time t relative to the most similar recent election, multiplied by -1; and the interaction between the first and second variables.

In all models, ssd-year fixed effects control for features of a municipality’s ssd in a given election that could influence the amount of transfers received by all municipalities therein after the election. Our inclusion of ssd-year fixed effects means that we are comparing amounts of transfers received by municipalities in the same ssd-year. All models include the following time-varying municipality-level controls: population (logged), a dummy variable indicating whether the municipality is rural or urban, population density, surface area of the municipality in square kilometers, poverty index, and a dummy variable indicating whether the municipality is in a state of emergency. We cluster standard errors by ssd.

In model 1, the positive, significant coefficient on the interaction shows that controlling for features of a municipality’s ssd-year and other time-varying differences, municipalities in alliance ssds with pvem-affiliated candidates that increased votes for the joint candidate under the PRl’s label exclusively while decreasing them for this candidate under the pvem label or both parties’ labels received more money the year after elections. Substantively, model 1 shows that a one percentage point increase in Negative (ΔPVEM or pvem-PRI VS_m,t)– which corresponds to a one percentage point decrease in the share of voters choosing the joint candidate under the pvem label or under both parties’ labels–in a municipality where the share of voters choosing the joint candidate under the pri label exclusively increased by 10 percent, the amount of fortalece the municipality received was increased by MX $9.9 per person (approximately US $0.50). The same one percentage point increase in Negative (ΔPVEM or pvem-PRI VS_m,t) in a municipality where the share of voters choosing the joint candidate under the pri label exclusively decreased by 10 percent is predicted to increase the amount of fortalece received by MX $1.1 per person (approximately US $0.05). These average marginal effects, with their 95 percent confidence intervals, are displayed in Figure 3. Their substantive effects are summarized in Table 7.Footnote ¹⁰² Section H of the supplementary material shows that the assumptions of linearity and common support for the moderator hold.

Figure 3

Average Marginal Effects of Negative (ΔPVEM or pvem-PRI VS _m,t) with 95 Percent Confidence Intervals in Alliance ssds with pvem Candidates^a

^aAverage marginal effect of a one percentage point increase in Negative (ΔPVEM or pvem-PRI VS_m,t) with 95 percent confidence intervals (shown with vertical lines) at different levels of ΔPRI VS_m,t in ssds in which the PRI and pvem ran a joint candidate from the pvem (see Table 6, model 1).

Table 7

Substantive Effects on Transfers in Mexico^a

^a Substantive effects on transfers of the average marginal effect of a one percentage point increase in Negative (ΔPVEM or PVEM-PRI VS_m,t) at different values of ΔPRI VS_m,t in alliance ssds with pvem candidates. Marginal effects are calculated with continuous variables held constant at sample means.

The positive, significant coefficient on Negative (ΔPVEM or pvem-PRI VS_m,t), by contrast, shows that decreases in votes for the joint candidate under the pvem label or both parties’ labels are, when ΔPRI VS_m,t is zero, rewarded with more money after elections. Substantively, a one percentage point decrease in votes cast under the pvem label or both parties’ labels results in a per person gain of MX $5.44 (approximately US $0.30). The nonsignificant coefficient on ΔPRI VS_m,t means that increases in votes for the joint candidate under the pri label exclusively are neither penalized nor rewarded. Viewed together, these results show that in alliance ssds with pvem-affiliated candidates, the coalition uses fortalece to encourage supporters choosing the joint candidate under the pvem label or both parties’ labels to switch to casting them under the PRl’s label only.

In Table 6, models 2 and 3 serve as placebo tests. In alliance ssds with pri-affiliated candidates (model 2), neither the coefficient on the interaction nor the coefficient on Negative (ΔPVEM or pvem-PRI VS_m,t) is significant. In nonalliance ssds (model 3), neither the coefficient on the interaction nor the coefficient on Negative (ΔPVEM VS_m,t) is significant. This means that only in alliance ssds where the pri has forfeited the joint candidacy to the pvem (model 1) does the coalition use fortalece to encourage voters to switch their votes from the joint candidate under the pvem label or under both parties’ labels to the joint candidate under the pri label. These results support hypothesis 3.

What else can our results tell us about transfers? In ssds where the two parties fielded a joint candidate who was pri affiliated (model 2), the coefficient on ΔPRI VS_m,t is positive and significant, whereas the coefficient on Negative (ΔPVEM or pvem-PRI VS_m,t) is insignificant. This means that the coalition rewarded increases in votes cast for the pri-affiliated joint candidate under the PRI label alone, but neither rewarded nor penalized increases in votes cast for the pri-affiliated joint candidate under the pvem label or under both parties’ labels. Substantively, a one percentage point increase in votes for the pri-affiliated joint candidate under the pri label translated into an extra MX $2.65 per person (approximately US $0.15). In these ssds, the allied parties used transfers to encourage supporters to cast both components of their fused vote for the pri. Presumably because votes cast for the joint candidate under the pvem label or under both parties’ label in ssds where the joint candidate was pri increased the chance of the PRl’s candidate winning the ssd, the pri did not dissuade voters from casting their votes this way. But neither did it encourage them to do so.

In model 3, the coefficient on ΔPRI VS_m,t is positive and significant, revealing that the coalition rewarded increases in votes cast for the PRI. Substantively, a one percentage point increase in votes cast for the pri translated into an extra MX $4.41 per person (approximately US $0.25). Rewards for voting pri were largest in these nonalliance ssds. The coefficient on Negative (ΔPVEM VS_m,t) is insignificant. Thus, in nonalliance ssds, the coalition used transfers to encourage supporters to cast both components of their vote for the pri.

IX. Conclusion

Our theory is in two parts. First, we explained how an mmm system creates a distinct strategic environment in which a large party and a small party can form an alliance and trade votes in one tier for votes in the other in a way that increases the number of seats won by both parties. Second, we posited that governing parties dependent on such trades can use geographically targeted spending to cement them. We used original data on Japanese and Mexican municipalities to show that the LDP-Komeito and pri-pvem coalitions, respectively, did exactly this in the period under study.

For scholars of comparative politics, we have identified a new pathway through which governing parties can remain in power under an mmm electoral system. A large governing party is likely to prefer this pathway when its policies make it unpopular with the median voter. Under most other electoral systems, this party would be forced to refine its policy positions to make them more palatable to the median voter or to provide enough targeted goods to overcome any resistance by the median voter. Under an mmm system, however, it can form an alliance with a small party, have both parties’ supporters split their votes, and use targeted goods as a reward for doing so. With this strategy, the only constituencies the large party has to please are its own supporters and its ally’s supporters. This strategy is likely to have far-ranging consequences for governance and representation. It may mean that non supporters are cut out of the spoils and find government unresponsive to their concerns. Although these voters will be drawn to the opposition, they will not necessarily find a viable alternative there. A large opposition party aiming to establish itself as a party capable of unseating the governing coalition would gain from realizing a similar trade, but will have to face the fact that small parties are likely to form and function as mercenaries, vying for inclusion in the governing coalition. Non-supporters may end up having to bandwagon with the governing coalition.

The first step to investigating whether our theory’s more dire implications are borne out is to see whether parties in the twenty-six other countries with mmm electoral systems use vote trading and geographically targeted spending to win elections. Political science literature and news reports reveal evidence of coordination in all but one of these countries (Tajikistan). Electoral autocracies and recently transitioned democracies tend to seek coordination among opposition parties with the goal of unseating the dominant parties.Footnote ¹⁰³ Among established democracies, stand-down agreements in nominal-tier districts are common. The following four cases may be especially instructive to study: Italy, which since 2017 has used a fused-vote system similar to Mexico’s but without the cap on overrepresentation; Taiwan, which uses a system similar to Japan’s; Thailand, which used an mmm system until 2017, after which it introduced something closer to an mmp system;Footnote ¹⁰⁴ and Korea, which transitioned from a pure mmm system to an mmm system with partial compensation in 2019. In Korea, large parties had the audacity to create small parties with which they could ally after the passage of an electoral reform that ruled that some list seats would be awarded on a compensatory basis.Footnote ¹⁰⁵

After evaluating how common vote trading with geographically targeted spending is, future research should investigate how mmm systems stack up against alternative electoral systems in the ease with which governing parties are voted out of power, the alignment of government policies with the interests of the median voter, and the responsiveness of governments to crises and changes that influence the median voter. In addition, future work should flesh out how the distinct strategic environment created by mmm systems’ combination of electoral rules influences other outcomes.

For scholars of Japan and Mexico, our study shows that the longstanding governing coalitions of both countries contested elections by encouraging supporters to split their votes and by using government resources to facilitate this. Future research should focus on three questions. First, what role did this strategy play in perpetuating the dominance of the ldp-Komeito and pri- pvem coalitions? Central to this research would be investigating why the ldp-Komeito coalition lost the 2009 House of Representatives election, why the pri-pvem coalition lost the 2018 Chamber of Deputies election, and why, in the Japanese case, the parties that won in 2009 were unable to replicate the strategy to win again in 2012. Second, what, if any, relationship exists between the size of the payoffs supporters receive for splitting their votes and the policies implemented by the governing coalitions? Is Japan’s ldp neutralizing the Komeito’s opposition to its desired defense policies by increasing the size of the payoffs to Komeito supporters? Third, are the parties pursuing similar vote-trading strategies at other levels of government, such as for the upper houses, local governments, and, in the case of Mexico, the presidency? We urge scholars to tackle these questions.