Buying Votes across Borders? A List Experiment on Mexican Immigrants in the United States

Abstract As international migration has grown worldwide, the issue of how to assure the political rights of citizens living abroad has attracted much scholarly attention. One concern has been that if vote-buying is widespread in home countries, this practice could be exported to external elections. Although there have been numerous studies focused on electoral participation in external voting, there has been no systematic test of whether vote-buying is occurring across borders. This study aims to address this question by focusing on the 2018 federal elections in Mexico. Our list experiment shows that in our sample, approximately 32 per cent of Mexican immigrants in the United States experienced vote-buying during the electoral campaign. Furthermore, a multivariate analysis shows that the people most susceptible to vote-buying were living in areas where there was a high concentration of Mexican immigrants. The study results point to the importance of cross-border networks, which have been built between countries sending and receiving immigrants, in facilitating vote-buying across borders.


Introduction
Over the past several decades, increasing scholarly attention has been paid to the political participation of emigrant populations in their home countries, including the issue of external voting. Two forces, in particular, underlie a growing concern. First, the international migration population increased from approximately 83 million to 243 million between 1975(World Bank, 2020. This increase suggests that a growing number of people live in countries where they were not born but are still able to influence the politics of their home countries in places where external voting is stipulated. 1 Second, during this same time period, many developing countries have democratized, which has created opportunities for citizens living abroad to participate in the politics of their home countries through electoral and non-electoral channels (Burgess, 2014;Hartmann, 2015).
However, external voting is costly for both expatriates and political parties. On the one hand, citizens living abroad pay higher costs to obtain electoral information about party platforms, candidates and voter registration (Burgess and Tyburski, 2020). On the other hand, political parties must spend extra resources for overseas travel and access to expatriates and in situations where the electoral return is uncertain (Paarlberg, 2017)-which raises the question of why parties would bother to invest in such uncertain results. Recent work focused on incentives has helped to explain why and how parties support external voting and mobilize expatriates' votes (Burgess, 2018;Burgess and Tyburski, 2020;Paarlberg, 2017Paarlberg, , 2019. In many cases, expatriates maintain close contacts with their family and friends in their home country through remittances and frequent communication (Paarlberg, 2017). Using such cross-border networks, political parties pursue campaigns abroad not only to mobilize expatriates' votes but to influence, indirectly through the diaspora, the political behaviour of families and friends living in the home countries (Paarlberg 2017(Paarlberg , 2019. When parties, rather than states, take a leading role in outreach, the effect of mobilization is greater (Burgess, 2018). Parties also attempt to boost turnout by lowering the cost of voter registration (Burgess and Tyburski, 2020). Enfranchisement of expatriates is more likely to be supported by right-leaning parties (Østergaard-Nielsen et al., 2019).
These studies provide novel insights into the conditions under which political participation of a diaspora population is encouraged. However, one concern arises: the introduction of external voting does not automatically assure that expatriates can fully exercise their political rights. Especially in new democracies with recently reformed voting rights for expatriates, vote-buying in domestic voting is often reported, even when ballots are assured to be secret (Stokes, 2005). We assume that if vote-buying is a dominant form of electoral mobilization in home countries, political parties could apply the same strategy to external voting. We argue that cross-border networks, in particular, play a crucial role in facilitating the individualized transaction between particularistic goods and electoral support in overseas ballots. Parties may contact expatriates and monitor their behaviour through these networks, which closely tie together expatriates with their families and friends in home countries.
In this study, we test whether vote-buying occurs in external voting, focusing on Mexican immigrants in the United States. Approximately 10 per cent of Mexico's population lives abroad, and these immigrants tend to maintain close ties to their community of origin through family and region-based networks. 2 The right of voting abroad has been gradually expanded since the late 1990s. 3 In Mexico, external voting was introduced in 2005, which enables Mexicans living abroad to cast a ballot by postal voting. A 2014 electoral reform facilitated the procedures by enabling Mexican immigrants to obtain a voter registration card outside of the country. Following this reform, Mexico's political parties created sectors within the parties to cultivate the votes of migrants (Cárdenas, 2014;Ximénez de Sandoval, 2018). 4 The practice of vote-buying is widespread in Mexico (Cantú, 2019;Diaz-Cayeros et al., 2016), and some evidence has been presented that migrants were targeted for vote-buying in the country's recent local elections (Muñoz Pedraza, 2016); however, there has not been a systematic study done on whether vote-buying targeting migrants actually occurred.
Our study is an attempt to explore this unverified possibility. For this purpose, we conducted a list experiment using an online survey, which was performed between August 17 and September 15, 2018. The survey took place one and a half months after the federal election on July 1, 2018, which was the first federal election conducted after the 2014 reform. The list experiment is an appropriate method to assess politically sensitive questions, such as the accurate level of votebuying, by dealing with social desirability bias (Gonzalez-Ocantos et al., 2012). Our analyses found that in our sample, approximately 32 per cent of Mexican immigrants in the United States experienced vote-buying and that those most susceptible to vote-buying were living where there was a high concentration of Mexican immigrants.
The rest of the article is organized as follows. Section 2 provides a review of the burgeoning literature of external voting and presents the logic of buying votes across borders. Section 3 describes the context in which Mexican immigrants in the United States participate in external voting and then draws testable hypotheses. Section 4 presents the design of the list experiment, the multivariate regression analysis and the results. The final section discusses the contribution and limitations of this study and presents a future research agenda.

Why do parties promote external voting?
One puzzle of external voting is why political parties would support extending the right of voting to citizens living in other countries when the electoral return is expected to be low (Paarlberg, 2017). Recent work on external voting has focused explicitly on the role of political parties, looking at the conditions under which parties approve of reforms extending the right of voting abroad and of mobilizing diaspora voting (Burgess, 2018;Burgess and Tyburski, 2020;Østergaard-Nielsen et al., 2019;Paarlberg, 2017Paarlberg, , 2019. Building on this literature, we explore the possibility that vote-mobilization strategies, which are commonly employed in new democracies, may also be employed in overseas ballots. During a period of electoral reform, party ideology and competition determine political parties' attitude toward external voting (Østergaard-Nielsen et al., 2019). According to a study that looked at 13 European countries, emigration-related issues are less likely to gain salience than immigration-related issues, and while all political parties tend to support reforms of external voting, centre-right parties are the strongest supporters (Østergaard-Nielsen et al., 2019). This support is not based on nationalism but instead driven by pragmatic concerns, such as an increase in remittances and electoral turnout (Østergaard-Nielsen et al., 2019). On the same grounds, some African countries, such as South Africa and Ghana, promote reforms of external voting because they have "relatively institutionalized party systems," which allows parties to launch electoral campaigns abroad (Hartman, 2015: 921).
As part of the mobilization phase, political parties also attempt to encourage the electoral participation of expatriates by visiting their communities abroad, motivating interest in home-country politics, and co-ordinating election campaigns (Burgess and Tyburski, 2020). Cross-border networks may facilitate these actions, since expatriates use them to maintain close contacts with family and friends through remittances and frequent communication (Paarlberg, 2017). Focusing on Latin American cases such as Mexico and El Salvador, Paarlberg (2017) argues that through such cross-border networks, political parties campaign abroad not only to mobilize expatriate votes but also to influence the political behaviour of families and friends living in the home countries, albeit indirectly through the diaspora (Paarlberg, 2017(Paarlberg, , 2019. Some scholars have noted that there are cases in which states, rather than parties, engage in diaspora outreach. Burgess (2018) argues, however, that when parties, rather than states, take a leading role, the effect of mobilization is greater. For instance, emigrants from the Dominican Republic in the United States strengthened their engagement in the politics of home countries through two major political parties: the Dominican Revolutionary Party (Partido Revolucionario Dominicano, or PRD) and the Dominican Liberation Party (Partido de la Liberación Dominicana, or PLD). Consequently, the membership of these parties extended to large cities such as New York, and partisan conflict in domestic politics based on clientelist linkages was "exported" to destination countries through partydiaspora networks (Burgess, 2018: 377). Although the author did not provide a concrete account of how clientelist exchanges are undertaken, the finding suggests the possibility that the practice of vote-buying travels across borders. The following question still remains: Why are parties engaged in vote-buying in external voting in which the electoral turnout is supposed to be low? The incentives to buy votes across borders should be further scrutinized.

Why do parties attempt to buy expatriates' votes?
There are several reasons why external voting could provide parties and candidates with an incentive to buy votes in overseas ballots. First, in external voting, secret ballots cannot always be assumed, which may induce political parties to more blatantly engage in vote-buying. Doubts about secret ballots stem from the use of postal voting, which is typically used for those who are not in the country of residence or do not live in the country at the time of elections. After applying for postal voting to the electoral authorities, overseas voters receive "voting kits," fill in their preferences, and mail their ballots to electoral administrative bodies (Massicotte et al., 2004: 133). Compared to conventional voting conducted at a polling station, the secrecy of ballots in postal voting is difficult to evaluate because the electoral management bodies are unable to check how voters fill a ballot paper on site. 5 For instance, voters might fill in ballots in an open space while other people are watching.
Second, in external voting, the secret ballot can be undermined by lack of official oversight and lack of sanctions for inappropriate procedures. In national elections, polling workers and election observers can check whether voting is following a lawful procedure. Recent studies have shown that the presence of observers can suppress fraudulent and corrupt behaviour during the electoral process (Buzin et al., 2016). It is highly unlikely, however, that these mechanisms are applied to the process of external voting; there is no mechanism, for example, to ensure that a voter who marks a ballot at home has not been approached and pushed to vote for a specific candidate.
For instance, British elections introduced "postal voting on demand" in 2001, in which voters could request a postal ballot without specifying a reason (Hill et al., 2017). This new system undermines the secret ballot, and as Eleanor Hill and co-authors argue, it also makes immigrants from Bangladesh and Pakistan vulnerable to vote-buying through a hierarchical kinship network (biraderi) that serves as a political machine (Hill et al., 2017: 775-76). Through this network, elders exercise "undue influence" on young voters' choices by easily monitoring the process of postal voting (781). This example suggests that although postal voting can enhance the right of voting abroad, it also can make it more difficult to protect the secret ballot and to prevent fraud (Massicotte et al., 2004: 133, 135).
Third, the lower socio-economic status of immigrants may induce vote-buying in external voting. 6 Low-income voters become vote-buying targets because buying them off is less costly due to the diminishing marginal utility of income; if the income level of voters is low, they may attach a higher value to such benefits, compared to voters with higher incomes (Dixit and Londregan, 1996;Stokes, 2005). 7 The first generation of immigrants tends to occupy lower strata in the host society, although there are variations based on generations and countries of origin (Farley and Alba, 2002). The disadvantaged societal positions may make newcomers a target of vote-buying by politicians and parties of the country of origin.
Fourth, as discussed above, expatriates and their families and friends-and even political actors-may be closely connected through cross-border networks. Social networks not only encourage co-operation and transmission of information but also facilitate clientelist exchanges between political support and particularistic benefits (Cruz, 2019). When parties' machines penetrate these voters' social networks, they can develop an enhanced ability to ascertain voters' preferences and closely monitor their commitment (Cruz, 2019;Stokes, 2005: 315). The increasing flows of migration help to extend these social networks across borders, which facilitate parties' abilities to monitor migrant voting behaviour.
As Paarlberg (2017Paarlberg ( , 2019 has suggested, political parties and candidates use cross-border networks not to mobilize votes from expatriates but to influence the political behaviour of their families and friends in the home countries. Why do parties and candidates attempt to influence the expatriates' family and friends from abroad? Migration scholars have noted that there are many cases in which family members who emigrate maintain close communication ties with their families in their community of origin and exercise economic and political influence through remittances and other commitments (Andrews, 2018;Martínez Saldaña, 2003). Especially in new democracies, parties reach out and compete for expatriates' support as a way of anticipating their influence over families and friends and in order to win increasingly competitive electoral races (Martínez Saldaña, 2003). In this way, despite the low expected turnout, parties and candidates may find it beneficial to attempt to buy votes using cross-border networks.
Thus, we expect that if vote-buying is prevalent in domestic elections, extending the right to vote abroad may facilitate the export of this practice to diaspora voting. We also expect that there may be an enhanced possibility of diaspora vote-buying when (1) immigrants have lower expatriate socio-economic status, (2) there is the possibility of non-secret ballots and (3) there are cross-border networks.

External Voting and Mexican Immigrants in the United States
The federal elections conducted in Mexico on July 1, 2018, were the first after the most recent reform. We discuss below the possibility that the number and profiles of Mexican immigrants in the United States, the cross-border networks connecting these immigrants with their communities of origin, and the extension of voting rights to overseas voters might have provided fertile ground for vote-buying to proliferate in this pivotal election.

Mexican immigrants in the United States
Using data from the American Community Survey (ACS) conducted by the US Census Bureau, 8 the profiles of Mexican immigrants are characterized as follows: 87 per cent are of economically active age (16-64 years old), the immigrant populations are concentrated primarily in three states (37 per cent in California, 22 per cent in Texas, and 6 per cent in Illinois), 40 per cent did not complete a high school degree, 67 per cent do not speak English very well, 45 per cent work in manual labour industries, 9 and the average family income is lower than that of the native and overall immigrant population (US$60,684, US$68,680, US$87,537, respectively). 10 These statistics indicate that the living conditions of Mexican immigrants in the United States are neither favourable nor stable, 11 making this group a possible target of individualistic transactions between tangible benefits and votes. Further, many of these immigrants are engaged in manual labour, which is generally associated with lower incomes and with male workers 12 who are relatively young and work full-time. This leads us to expect that male, young, and full-time workers are subject to vote-buying.

The Cross-Border Networks across Mexico and the United States
Mexican immigrants in the United States are part of extended community networks, and they preserve family ties through remittances; the Hometown Associations (HTAs) play an essential role in building and consolidating these cross-border networks (Rivera-Salgado, 2006). Since the 1980s, the number of HTAs in the United States has increased, especially in Los Angeles and Chicago. The members of these groups have expanded their activities aimed at improving living standards of both immigrants in the United States and their communities of origin in Mexico (Rivera-Salgado, 2006: 5). Their activities also involve supporting regional development projects in the communities of origin by utilizing remittances (Ochoa O'Leary, 2014: 330).
While HTAs took the initiative to build networks both across the United States and across the border, Mexico's national and local governments joined the effort to strengthen ties with expatriates. During the administration of Vicente Fox (2000)(2001)(2002)(2003)(2004)(2005)(2006), who was a member of the National Action Party (Partido Acción Nacional, or PAN), a number of noteworthy public policies were undertaken. For instance, President Fox introduced the 3×1 program in 2002. This is a matching grant program: "For every dollar of immigrant remittance for community infrastructure projects, an additional three dollars is matched by combining the contributions for the projects provided from the three levels of the government: the state, federal, and municipal" (Ochoa O'Leary, 2014: 330-31). In 2003, the Institute of Mexicans Abroad (Instituto de los Mexicanos en el Exterior, or IME) was created to facilitate the immigrants' network building in the United States.
There is evidence that these cross-border networks were exploited to enhance the partisan interests of Mexico's elected officials. After the creation of the 3×1 program, the municipal authorities and residents governed by PAN became more involved in the creation of HTAs and the selection of specific projects within the program (Duquette-Rury and Bada, 2013: 68, 78; Simpser et al., 2016). Furthermore, evidence shows that the 3×1 program was manipulated to reward PAN municipalities with high-intensity migration (Meseguer and Aparicio, 2012), and the timing of expenditure followed the municipal electoral cycles (Simpser et al., 2016). Meseguer and Aparicio (2012: 413) emphasize that HTA leaders are "mostly pragmatic and nonpartisan" and that the political bias in the 3×1 program came from local government officials, not from the HTAs.
Political bias was also observed in external voting in Mexico's local elections. In a survey of 114 migrants from Chiapas, District Federal and Michoacán living in California, Muños Pedraza (2016: 172-79) found that a portion of respondents from Michoacán experienced vote-buying during the local electoral process. Five respondents from Michoacán were offered various benefits in exchange for votes; for three of them, the offer was the promise of support for their families living in Mexico (Muños Pedraza, 2016: 176). Although the analysis is confined to the case of a specific local election and the sample size is small, it provides important evidence that political parties sought to buy expatriates' votes by exploiting cross-border networks.
The survey also found that these respondents belonged to migrant organizations (Muños Pedraza, 2016: 178). This would lead us to assume that HTAs served as a broker, mediating between migrants and political parties from Mexico. Nevertheless, given Mexico's "state-led outreach" (Burgess, 2018) and since political parties, the state and HTAs are autonomous to each other, it is highly unlikely that HTAs served as a catalyst for vote-buying. It would be more reasonable to suppose that political parties mobilized migrants' votes where the density of migrant population was high and thus HTAs were concentrated. In short, we expect that cross-border networks centred on HTAs may be used to spread the practice of vote-buying to the United States, facilitating Mexico's politicians and/or parties in offering benefits to their expatriates in the United States and monitoring the outcome of vote-buying.

Overseas voting in Mexico
Since the late 1990s, a series of reforms have been implemented in Mexico to assure the right of external voting (see Tables A1 and A2 in the online appendix), 13 which has been a long-cherished desire of Mexican immigrants in the United States (Ochoa O'Leary, 2014: 331). As discussed above, the first PAN government deliberately strengthened the institutional ties between Mexico and the migrants living abroad with the creation of the 3×1 program in 2002 and the IME in 2003. In 2005, a law introducing external voting was approved in Mexico.
Although the right to vote had been attained, turnout was low in the subsequent elections in 2006 and 2012, due to technical and institutional barriers (INE, 2016b). Electoral authorities in Mexico were responsible for issuing voter identification cards, which meant that Mexican expatriates who had left the country without a card had to go back to Mexico to obtain one. Registration and voting procedures were also costly and time-consuming. Before the elections were conducted, expatriates were supposed to have registered for the Nominal List of Electors Residents Abroad (Lista Nominal de Electores Residentes en el Extranjero, or LNERE). To apply for registration and ballot papers, they needed to send a request to the Federal Electoral Institute (Instituto Federal Electoral, or IFE) by registered mail. In addition, political parties and candidates were banned from running electoral campaigns outside of Mexico, so expatriates had limited opportunities to become informed about elections.
To increase the electoral participation of expatriates, the government and civil society in Mexico, in co-ordination with migrant leaders and organizations in the United States, made an effort to reform aspects of external voting. After intense debates, the legislatures, supported by all major political parties, approved the reform proposal, and on May 23, 2014, and the General Law of Electoral Institutions and Procedures (Ley General de Institutiones y Procedimientos Electorales, or LEGIPE) was promulgated. Under the current law, Mexican citizens living abroad can mail a registration application to Mexico, apply via the internet, or apply at embassies and consulates in their country of residence. Voter ID cards can also be issued at embassies and consulates in the country of residence, and ballots can be either mailed to Mexico or submitted to Mexican embassies and consulates in the country of residence (INE, 2016a(INE, , 2016b. According to various informants, the secret ballots in this postal voting are well protected. 14 However, the validity of this statement should be verified by a systematic analysis. Because the electoral law prohibits political parties and candidates from running electoral campaigns outside of Mexico, 15 it was primarily the Instituto Nacional Electoral (INE) and the HTAs that disseminated electoral information among migrant communities. 16 Prior to the 2018 elections, the major political parties also articulated a number of strategies to mobilize migrants' votes. For instance, in the case of Yucatán, PAN planned to use contact lists of migrants in the United States provided by mayors, as well as to utilize communication channels with migrants established through the 3×1 program (Cárdenas, 2014). The National Regeneration Movement (Movimiento Regeneración Nacional, or MORENA) has the most extensive party committees (comités) in the United States, and these are strongly linked with activist-based movements. The main strategy of MORENA committees consisted of recruiting members to launch get-out-the-vote campaigns, including calling their families and friends in Mexico by phone (Ximénez de Sandoval, 2018).
This mobilization effort by the INE, the HTAs and the political parties might have contributed to the increased participation, which included a tripling of voter registration for the 2018 elections. 17 More precisely, there were 40,000 registered voters in 2006, 59,000 in 2012, and 180,000 in 2018, whereas the number of participants was 32,000 in 2006, 40,000 in 2012, and 98,000 in 2018. 18 Calculating the precise turnout of external voting is technically difficult because the exact number of documented and undocumented expatriates is unknown. As a rough estimate, the turnout of external voting in the 2018 presidential elections was about 0.8 per cent, which was calculated by dividing this figure by the number of Mexicans living abroad that were 18 years old or over. 19 Given this low registration and turnout, buying votes of the family and friends in Mexico indirectly through the diaspora and cross-border networks becomes more likely. 20 Based on the above discussion, we postulate the following hypotheses to be tested in this study: Hypothesis 1: Mexican immigrants in the United States are subject to vote-buying.
Hypothesis 2: Mexican immigrants in the United States are more likely to experience vote-buying if they are surrounded by a dense network of HTAs.

Empirical Analysis
To assess whether vote-buying occurred during the 2018 federal elections, we conducted a list experiment using an online survey with a sample of Mexican immigrants in the United States. The challenge is how to accurately estimate respondents' experiences for a sensitive question such as vote-buying.
Respondents might underreport what they truly experienced, when asked whether they were offered gifts or favours in exchange for votes. A social desirability bias might cause the problem of measurement error. A list experiment is a method that can be used to reduce a social desirability bias from survey responses; thus, it enabled us to accurately estimate the extent to which vote-buying occurred (Imai, 2011;Gonzalez-Ocantos et al., 2012). In the following analysis, after describing the data, we present the design and results of the list experiment to estimate what proportion of respondents experienced vote-buying. Then we implement a multivariate analysis to identify who experienced vote-buying, with a special focus on the effect of cross-border networks. How we operationalized the cross-border networks is discussed below.

Data from the online survey
We conducted an online survey between August 17 and September 5 in 2018, about a month and a half after the federal elections were conducted in Mexico on July 1. The sample comprised 1,114 Mexican immigrants, drawn from a panel of people who registered with Survey Sampling International (SSI). 21 The respondents were first asked two screening questions about their eligibility for voting: whether they held Mexican citizenship and whether they were 18 years old or over. If they responded in the affirmative to both, they could proceed to answer the survey questions, selecting English or Spanish as language. The exact wording of the questions is given in Text A1 in the online appendix.
Ensuring a representative sample is methodologically challenging when targeting a hard-to-reach population such as immigrants, who are not fully registered within official statistics. One problem is that researchers can't obtain sampling frames (Reichel and Morales, 2017). Although our online sample tends to overrepresent some categories, such as highly educated groups, it has the merit of partially overcoming some shortcomings. Among Mexican immigrants, 78 per cent have smartphones and 77 have internet access; thus, they can participate in the online survey, 22 which increases the geographical representativeness of the sample, which extends across the United States. Given the lack of a sampling frame, we do not know the population parameters; nevertheless, we can assume overlaps of covariates between the population and sample (Gelman and Hill, 2007).
In addition to asking questions about vote-buying experiences (Hypothesis 1), we asked questions about demographic and socio-economic attributes (age, education, gender, income, job status, length of residency in the United States, and so forth), partisanship, political attitude, information environment, and vote choice in past presidential elections. 23 The responses were used to run a multivariate analysis to examine what kinds of respondents experienced vote-buying. The multivariate analysis included the responses to questions on age, dual citizenship, education, marital status, income, employment status, and length of residency in the United States, as they are generally used as variables of interest in migration studies.
We also used geographic information on the locations of HTAs to test Hypothesis 2. We hypothesized that the density of HTAs can be used to examine the effect of networks on vote-buying, because the closer that HTAs are to where immigrants are living, the more easily politicians could monitor voters and assure compliance with the transaction thorough HTAs. 24 Ideally, to test the effect of cross-border networks on vote-buying directly, one would measure the distance between the living location of each respondent and the HTAs representing specific communities of origin. Although a list of representatives' names, addresses, contact information, states, and municipalities in Mexico represented by HTAs (N = 2,241) is available on the official website of the IME, 25 the information on the HTAs' connection to regions in Mexico is incomplete. Thus, instead, we used the number of HTAs close to the immigrants' living locations-the density of HTAs-to test the effect of cross-border networks on vote-buying. 26 We measured the density as follows. First, we extracted information on the latitude and longitude of both the respondents' living locations (based on internet survey) and HTAs (based on address) and computed the distance between them. Afterward, we calculated the number of HTAs within 10 miles of the respondents' locations for which the information was available (N = 2,107). 27

The list experiment: Proportion of respondents who experienced vote-buying
We conducted the list experiment as follows. First, the respondents were randomly assigned to three groups: a control group, a treatment group and a direct question group. 28 The control and treatment groups were asked how many activities they performed during the election campaign; the respondents did not have to specify which activities. This indirect assessment provided respondents with "a high degree of anonymity," which induced them to honestly report their experience of votebuying, thus reducing the social desirability bias in the survey responses (Gonzalez-Ocantos et al., 2012: 205). The respondents in the control group had to report how many activities they performed out of a list of four items. 29 They were shown the following statements: Now we are going to show you four activities that some people may experience during the electoral campaign. After you read all four, just answer HOW MANY activities you experienced during the last electoral campaign. (We do NOT want to know which ones, just how many.) • I saw public debates between candidates for presidential elections on TV.
• I saw official websites/blogs of politicians and candidates.
• My family/friends told me about the election.
• Candidates or political activists threatened me to vote for a candidate.
The respondents in the treatment group were asked the same question, but the list of items also included the following sensitive vote-buying item: • Campaign activists gave any monetary benefits or did a favour to me or my family in Mexico.
Although this item may be interpreted as concerning vote-buying directed to immigrants' relatives in Mexico, there is a convincing reason to consider it an appropriate way of assessing immigrants' own experience of vote-buying involving their relatives in Mexico "in" an overseas ballot. Evidence suggests that political parties from El Salvador, the Dominican Republic and Mexico tailor electoral campaigns to the diaspora communities in the United States, aiming at indirectly influencing the political behaviour of their relatives in home countries (Paarlberg, 2017;emphasis added). According to Paarlberg (2017), this is the reason why political parties travel to diaspora communities, even if their electoral participation is very low in overseas ballots and the cost of campaigning is disproportionately high. More directly, the survey conducted by Muños Pedraza found that migrants from the state of Michoacán were offered support (apoyo) for their families in their hometown in Mexico in exchange for their votes (Muños Pedraza, 2016: 178). Nevertheless, there is a caveat in using this question item: a positive response to the question does not distinguish between the following four possible scenarios of vote-buying. 30 Table 1 classifies these scenarios in terms of benefits to the receiver (the person who received monetary offers or a favour) and the target of vote-buying (who was offered monetary benefits or a favour?): • Scenario A: A migrant in the United States was offered monetary benefits or a favour, and she or he received them. In line with Paarlberg (2017) and Muños Pedraza (2016), we assume that the positive response to the list experiment means scenarios A or B. While scenario C is highly unlikely, the wording does not allow us to preclude the possibility of scenario D. We acknowledge this limitation. However, since the survey asks about the respondent's experience, we expect that she or he interprets the question as depicted in the cases of A or B. We will come back to this issue in the discussion section.
The respondents in the direct question group were provided the same list of five items as the treatment group but were asked to indicate which activities, rather than how many, they experienced during the election campaign, as described below:

Results
The difference in the means of the number of chosen items is calculated to estimate the proportion of respondents who experienced vote-buying. Before that, we examined whether two conditions were met-that is, the absence of a design effect, as well as balance between control, treatment and direct question groups. For the former, we conducted a statistical test with the null hypothesis that there was no design effect in our list experiment. The validity of a list experiment depends on the assumption that the responses to a treatment item and control items are independent of each other (Blair and Imai, 2012). The p value from the statistical test proposed in Blair and Imai (2012) is about 1.0 in our list experiment, which leads to the non-rejection of the null hypothesis. Thus, we confirm that the list experiment is free from a design effect. 31 As for the latter, we compare the descriptive statistics of the direct question group, the control group and the treatment group (Table A4 in the online appendix). All the mean values of covariates are numerically similar among these groups with p > .05, which indicates that the respondents were randomly assigned to each group. Table 2 shows the difference in means estimates and estimated proportion of vote-buying between the list experiment and the direct question group. The difference in means estimators reflects whether the respondents in the treatment group responded to the sensitive item honestly. The mean of the number of chosen items in the treatment group is 1.930, which is 0.324 points higher than the control group, with p < .001. 32 This indicates that 32.4 per cent of respondents in our sample responded to the sensitive item, or about one-third of respondents or their family members received monetary benefits or favours. This supports Hypothesis 1 that Mexican immigrants in the United States are subject to vote-buying. Moreover, the estimated proportion of respondents who experienced vote-buying (32.4 per cent) is much higher than the proportion of those who reported vote-buying in the direct question group (19.8 per cent). 33 This suggests that a social desirability bias affects whether the respondents report any vote-buying experience and that the list experiment provides a more accurate estimate of the proportion of Mexican immigrants who experienced vote-buying.  Table 3 presents the coefficients and standard errors from the regression models proposed by Imai (2011). We conducted multivariate analyses to examine what specific respondents' attributes influenced the probability of responding positively to the question concerning vote-buying. The response variables of the two models were whether the respondents checked the sensitive item and item counts, respectively. We estimated the coefficients using logistic regression analysis for the direct items group and robust maximum-likelihood method proposed by Blair and Imai (2012) for the treatment group. Although it is difficult to compare the estimates between these two models directly, the tendency is mostly consistent.

Results
The results for the treatment group indicate that statistically significant covariates include employment status ("full-time"), length of residency in the United States, and number of HTAs within 10 miles of the respondents' locations. Specifically, respondents who were full-time workers and residing in a neighbourhood with a high density of HTAs showed a higher probability of experiencing vote-buying. In contrast, respondents who had lived longer in the United States were less likely to experience vote-buying. However, the findings do not necessarily mean that these covariates significantly influence vote-buying. For example, the results suggest that approximately 26.8 per cent of respondents at the age of 18 experienced vote-buying (90 per cent confidence interval: 0.6 to 53.1 per cent), whereas approximately 53.7 per cent of respondents at the age of 68 did (90 per cent confidence interval: 12.2 to 95.2 per cent). Both estimates were statistically significant. It should be mentioned that to examine the effect of age on the probability of vote-buying, we need to see the difference in those estimates: if the difference is 0 percentage points, it suggests that regardless of age, the respondents experienced vote-buying, resulting in no effect of age on vote-buying.
To address this issue, we calculated the effect size of all covariates (Figure 1). Each panel presents the estimated proportions of respondents by individual  Blair and Imai (2012). Italicized cells represent statistical significance with α = 0.1.
characteristics that take the minimum and maximum values. The left and middle points in each panel are the estimated proportions of respondents who experienced vote-buying when the respondents' characteristics take the minimum and maximum values, respectively. Only when the estimate is statistically significant, the point is shown with the 90 per cent confidence intervals (a solid line). For example, the left and middle points on the "length of US residency" are the estimated proportions of the respondents who have lived in the United States for 20 years or more (length of US residency = 2) and the respondents who have lived there for less than one year (length of US residency = -3). The right points are the difference between the two estimated proportions, which is the effect size of the respondents' characteristics. The circle dots represent the estimated proportions from Table 3. The results are averaged over the sample distribution of covariates. If the solid lines do not cross the value of zero, the effect is statistically significant. Using these definitions, we find that the covariates with a statistically significant effect are employment status, length of residency in the United States, and the number of HTAs within 10 miles of the respondents' living locations.
In light of our hypotheses, Figure 1 shows the following main findings. First, the number of HTAs within 10 miles from the respondents' locations has a statistically significant effect. Its estimated effect size of 0.507 indicates that the respondents who live in an area with the highest concentration of HTAs (the maximum number is 221) within 10 miles of their location are 50.7 per cent points more likely to experience vote-buying than those with the minimum value (0) of HTAs, which supports Hypothesis 2. Second, among the control variables, employment status and length of time living in the United States are noteworthy. More specifically, the Figure 1. The Effect Size of All Covariates effect size of 0.261 of employment status means that the respondents with full-time status are more likely to experience vote-buying than those with other types of status such as part-time, unemployed, students, and retired. As for the length of US residency, the effect size of −0.665 suggests that the longer respondents have lived in the United States, the less likely they are to be subject to vote-buying. Other covariates do not have significant effects on the probability of being a target of vote-buying.

Discussion and Conclusions
The results of our empirical analysis show that cross-border networks can induce vote-buying across borders. The most important finding from the list experiment is that in our sample, approximately 32 per cent of expatriate voters were exposed to vote-buying during the last Mexican presidential election (Hypothesis 1). This finding also suggests the possibility that a traditional observational survey includes 12 per cent points of measurement error, implying that a list experiment might be an appropriate method to deal with the social desirability bias and estimate the level of vote-buying more accurately.
We also found that well-developed cross-border networks interconnecting immigrants, their communities of origin, and HTAs increased the chance of those immigrants being targeted for vote-buying in overseas elections. For respondents who lived near a dense network of HTAs, the chances of experiencing vote-buying were approximately 50.7 per cent points higher than they were for respondents who did not. The results indicate that full-time workers-who generally earn a higher income than workers with other types of employment status-are susceptible to vote-buying, which also merits special attention, whereas level of income is not a predictor of vote-buying. Previous studies have argued that due to the diminished marginal utility of income, low-income voters tend to be attracted to inexpensive benefits. The evidence presented here suggests that when looking at vote-buying abroad, the diminishing marginal utility of income, which is typically assumed in the literature of vote-buying, does not apply under these conditions. Why income has no effect on vote-buying in overseas election requires further investigation. Finally, we found that the longer expatriates live in the United States, the less likely they are to be subject to vote-buying. As the period of absence from a home country increases, expatriates may become increasingly disconnected from the community of origin, and, accordingly, the influence of cross-border networks may be weakened.
Despite these novel findings, several caveats should be mentioned. First, the primary purpose of our study was to examine whether vote-buying occurred in overseas ballots. However, it did not delve deeply into the question of how it happened. Second, we did not assess vote-buying performance; that is, we did not address how many votes were actually acquired by each party through vote-buying. Third, as discussed earlier, the wording of the sensitive question does not preclude the possibility that the positive response was based on what respondents heard about, rather than on their own experiences. Furthermore, it does not allow us to distinguish between who received monetary benefits or a favour (the respondents or their family in Mexico) and the ratio of each type of vote-buying across borders.
In addition to the empirical shortcomings, the methodological concern remains. It has been argued that while the method of list experiments has been increasingly used for political science research, the issues deriving from measurement errors such as misreporting, lying, and ceiling and floor effects have been properly addressed (Aronow et al., 2015;Blair et al., 2019;Kuhn and Vivyan, 2021). Recent studies have proposed a variety of statistical tests and estimation to deal with them (Arrow et al., 2015;Blair et al., 2019;Kuhn and Vivyan, 2021). 34 The newer methods mostly propose the use of parallel design, by which all the respondents are simultaneously asked a direct question and randomly assigned to experimental groups. However, we were unable to follow this novel method because we designed the experiment assigning respondents to three groups: a direct question group and two list experimental groups. Although the current design allowed us to partially deal with the issue of measurement errors, improving the design of the list experiment is an important future research goal.
However, these shortcomings do not reduce the importance of this work as the first systematic study on vote-buying in external ballots. Internet voting was introduced in external voting in 2021, which may change the logic of "buying votes across borders." Future studies with updated methods and empirical approaches will help clarify this understudied issue.
24 The idea that the geographic proximity and the likelihood of vote-buying are associated, as assumed in Hypothesis 2, is derived from Cantú (2019). To estimate the effect of distributed gift cards on the probability of vote-buying, Cantú used the distance between supermarkets and voters' living locations. He assumed that the geographic proximity facilitated voters' shopping at the store using the distributed gift cards, thus affecting "the net valuation of consuming the card" regardless of voters' party identification and political behaviour (Cantú, 2019: 791). To examine the exogeneity of this variable, we calculated a correlation with other covariates. We found a small value of Spearman's rank correlation coefficient between them ( Figure A1 in the online appendix). Thus, we can safely assume that the density of HTAs is uncorrelated with other covariates that may affect the probability of being a target of votebuying. We appreciate the comments of an anonymous reviewer who indicated the importance of testing this assumption. 25 The data are available at https://asociaciones.sre.gob.mx/ (September 15, 2019). 26 The assumption underlies this individual-level measurement that HTAs are connected to the immigrants in the United States regardless of their places of origin in Mexico. 27 The information about the latitude and longitude of the respondents' living locations is an approximate measure of where they live but does not pinpoint the exact address. We confirmed that there was a significant overlap between the location of respondents and HTAs. The geographic distributions of respondents and HTAs are visualized in Figures A2 and A3 in the online appendix. 28 Whereas Gonzalez-Ocantos et al. (2012) split the respondents into treatment and control groups and asked both groups the direct question, we randomly assigned them to treatment, control and direct question groups in order to avoid the possibility that the list experiment and direct questioning affect each other. 29 The question items for our list experiment are created based on Gonzalez-Ocantos et al. (2012) and modified in a way that better applies to the context of Mexican immigrants in the United States. 30 We appreciate an anonymous reviewer's suggestion of this point. The argument here follows the recommendation made by the reviewer. 31 Following Blair and Imai (2012) and Blair et al. (2019), we additionally tested the "no design effect" assumption, which did not detect a design effect (for the results, see Table A5 in the online appendix). Furthermore, for multivariate analysis, we estimated models using top-biased measurement error and uniform measurement error as a robustness check. However, the results did not significantly differ between these models, which held the validity of our argument. Only the variable "full-time" lost the statistical significance in the models correcting measurement errors. For the comparison of the estimates between the models, see Table A6 and Figures A4 and A5 in the online appendix). 32 This estimate refers to the coefficients obtained by using the difference-in-means estimator. The estimates computed using other methods are presented in Table A6 and Figures A4 and A5 in the online appendix. 33 The 19.8 per cent seems large. However, this proportion includes not only the respondents but also their families who received monetary benefits or favours. Gonzalez-Ocantos et al. (2012) reported that the proportion of respondents' neighbourhoods that had received gifts or favours was approximately 17.84 per cent. 34 We appreciate the comments of an anonymous reviewer who pointed this out.