Estimating the trade-off between higher turnout and a more representative election result

The relationship between voter turnout and election results is pivotal. If turnout is structurally lower among certain groups with distinct voting preferences, then election results are not representative of the entire electorate. Consequently, the policy preferences of groups with a relatively low turnout may not be adequately reflected in policies, which could be detrimental to their interests and alienate them from the state (Campbell 1960; Dahl 2015; Leininger & Heyne 2017; Wlezien & Soroka 2021). While increased turnout legitimizes elections and is therefore desirable in itself (Arnesen et al. 2024), it does not necessarily solve this problem of representativeness. Bias in election results may even be exacerbated when the turnout of groups with a higher propensity to vote increases (Berinsky 2005; Lutz and Marsh 2007; Blais et al. 2020; Damsbo-Svendsen and Hansen 2023; Dehdari et al. 2024). There could be a trade-off between voter turnout and the degree to which election results are representative of the entire electorate, which raises questions about the legitimacy of election results.

A key difficulty encountered when investigating the influence of voter turnout on election results concerns the endogeneity of this relationship. The variables determining whether citizens turn out to vote also influence their voting preferences. To circumvent this issue, many studies have used exogenous shocks in voter turnout to estimate causal relationships (Gentzkow 2006; Horiuchi and Saito, 2012; Funk 2010; Hansford and Gomez 2010; Campante et al. 2013; Finseraas and Verby, 2014; Artés, 2014; Persson et al. 2014; Lassen, 2005; Arnold and Freier, 2016; Bechtel et al., 2015; Stokes, 2015; Bratti et al. 2020; Damsbo-Svendsen and Hansen 2023). Studies that use exogenous turnout shocks combine a high level of internal and external validity. They offer insights into the voting behaviors of citizens who are sensitive to shocks and thus easiest to mobilize or de-mobilize and who, through their idiosyncratic behavior, shape public policy (Fowler 2015; Kurrild-Klitgaard 2013). For example, several studies have analyzed the effect of a turnout shock caused by rainfall variations on the result of the 2016 Brexit referendum. These studies found that low levels of rainfall increased voter turnout and that those who only voted when there was less rainfall were more likely to vote in favor of leaving the European Union (EU) (Leslie & Ari 2018; Rudolph 2020). However, these studies did not elucidate how this increased turnout affected the representativeness of the Brexit referendum. Therefore, their normative implications remain unclear.

To address this issue, we developed a three-step method for estimating the extent to which exogenous turnout shocks increase or decrease the representativeness of election results. First, regression analysis is used to decompose the election result into the choice of those voters who only voted because of the shock, called marginal voters, and the choice of those who voted regardless of the shock, called regular voters (Fowler 2015). Second, through a separate analysis that might require additional information, a counterfactual election result with 100% turnout is estimated, e.g., through a survey that is also held among those of the electorate that abstained from voting. In this paper we call this 100% turnout result the (fully) representative election result (Leininger and Heyne 2017). Finally, we estimate how varying degrees of exposure of marginal voters to the shock lead to an election result that either comes closer to the representative election result or moves away from it. To the best of our knowledge, this is the first study to estimate how marginal voters impact the representativeness of election results.

This method can be applied to a wide variety of elections, including U.S. presidential elections and the aforementioned Brexit referendum. Its use can inform public debates on whether or not exogenous turnout shocks make election results more or less representative. These public debates are important because they can impact the perceived legitimacy of election results. For example, following the Brexit referendum, a number of newspaper and opinion articles speculated on how the weather had impacted the result (see, e.g., The Guardian, 2016). The application of our method could also help to inform policy decisions involving a potential trade-off between turnout and the representativeness of election results. An example is deciding whether or not to schedule elections during a season in which there is a higher or lower probability of rainfall (see also Damsbo-Svendsen & Hansen 2023).

Our study is not the first to compare fully representative counterfactual election results with actual election results (see, e.g., Citrin et al. 2003; Leininger & Heyne 2017; Lutz & Marsh 2007). However, to the best of our knowledge, it is the first to conceptualize and measure the gap between an actual election result and a fully representative counterfactual election result by considering the percentage of marginal voters exposed to a shock. Conceptualizing this gap in terms of marginal voters is especially fruitful because they are relatively easy to (de)mobilize. By focusing on conceptualizing the gap in terms of marginal voters, we connect the literature that tries to estimate full-turnout election results (Citrin et al. 2003; Leininger & Heyne 2017; Lutz & Marsh 2007) to the literature that studies the effects of turnout shocks on election results (Funk 2010; Finseraas and Verby, 2014; Lassen, 2005; Stokes, 2015; Damsbo-Svendsen and Hansen 2023; Dehdari et al. 2024).

To demonstrate our method, we apply it to a national referendum held in the Netherlands in 2018 about the Intelligence and Security Services Act (ISSA). This Act could increase security at a cost to privacy. This case study adds to the literature in two ways. First, most studies on the effects of turnout shocks on election results have focused on legislative elections, with few focusing on referendums (Munley et al. 2023). Second, as the overview presented in Table 1 shows, previous studies have used instrumental variables such as precipitation or proximity to refugee centers. Our study adds to the literature by introducing a new, strong instrument, namely municipal amalgamation and, by extension, the concurrence of municipal council elections with a referendum.¹

We find that in municipalities with concurrent municipal council elections, voter turnout in the referendum was on average 23% points higher than in municipalities without concurrent elections. Our point estimates suggest that 92% of marginal voters were exposed to the shock, and such voters who would have stayed home in the absence of concurrent municipal council elections were estimated to be 34% more likely to vote in favor of security (i.e., “yes") in the referendum than those who would anyhow have voted in the referendum. Drawing on a large-scale survey that also included citizens who abstained from voting, we estimated the voting preferences of the entire Dutch electorate (Jacobs 2018b). Applying our method, we find that exposing voters who were sensitive to the shock increased both turnout and the representativeness of the referendum result until an exposure rate of approximately 68% was reached. However, when the exposure rate exceeded this point, voter turnout increased at the cost of the representativeness of the referendum result. Since point estimates indicate that 92% of marginal voters were exposed to the shock, we can conclude that a reduction in the share of marginal voters exposed to the shock to approximately 68% would have decreased turnout but increased the representativeness of the ISSA referendum result.

As previously stated, our method requires data to estimate the fully representative counterfactual election result. This may seem to be a stringent requirement, which could limit the method’s applicability. However, at least two of the six studies listed in Table 1, namely Rudolph (2020) and Schmid (2016) could have benefited from using our method. This is because following both the Brexit and Swiss referendums, surveys were held, which could have been used to estimate fully representative referendum results. Moreover, while estimates of fully representative election results are currently only rough approximations, methods for estimating or simulating fully representative election results are evolving (Citrin et al. 2003; Lutz and Marsh 2007; Leininger & Heyne 2017). Therefore, we foresee future opportunities for larger, more precise applications of our method.

We now introduce our method for investigating how an exogenous turnout shock affects the representativeness of an election result and explain when a trade-off occurs between higher turnout and representativeness. Assume that voters choose one of two alternatives, A or B. Examples of such alternatives include, for instance, Democrats or Republicans in the U.S. presidential elections or yes–no voting in a referendum. For the sake of convenience, we exclude blank votes. Also, assume that only a fraction of all eligible voters actually vote, with this fraction increasing when an exogenous shock occurs. This shock reduces the cost of voting for those it affects and neither discourages other citizens from voting nor influences voters’ preferences.

The electorate, \({N}_{tot}\), can be divided into three groups (Fowler 2015):

The presence of the non-voters group and the assumption that this group’s preferences could differ from those of the other groups means that an increase in turnout would not necessarily make the election outcome more representative.² In an electorate with only regular and marginal voters, an exogenous shock that boosts turnout but does not influence voters’ preferences will always make the outcome more representative.³ However, studies have reported that often a portion of the electorate simply does not care about politics and thus can be classified as non-voters.⁴ Therefore, the assumption of the existence of a group that would not vote even if it was subjected to a certain exogenous shock seems plausible.

Fowler (2015) demonstrated how to calculate \({V}_{rA}\) and \({V}_{mA,}\) and the difference between them, using regression results obtained by analyzing exogenous shocks in turnout (see also Rudolph 2020). We extend this framework by introducing a measure for evaluating to what extent exogenous shocks make elections more representative. We define a representative election result as the result of a free and fair election with total (100%) voter turnout. The support for alternative A in a hypothetical election with total voter turnout, \({V}_{totA}\), is calculated as the weighted average of the support in the three voter groups defined above, with \({s}_{m}\) equal to 1:

A turnout of 100% (\({N}_{n}\)= 0) almost never occurs in actual elections and cannot be directly observed. Therefore, the counterfactual \({V}_{totA}\) must be obtained through alternative means, such as surveys, simulation studies, or other techniques (Lutz & Marsh 2007; Leininger & Heyne 2017).

The actual observed election result is determined by regular voters and the share of marginal voters exposed to the shock:

The share of marginal voters that must be exposed to the turnout shock to achieve the fully representative election result, \({s}_{m}^{*}\), is calculated by equating the right-hand side of Eq. (1) with the right-hand side of Eq. (2), replacing \({s}_{m}\) with \({s}_{m}^{*}\).

Equation (3) is then rewritten and simplified to solve for \({s}_{m}^{*}\):

In our application we use \({V}_{totA}\) to calculate \({s}_{m}^{*}\) by rearranging the right-hand side of Eq. (4) as follows:

See Appendix A for the derivations.

If \({V}_{totA}\le {V}_{rA}<{V}_{mA}\) or if \({V}_{totA}\ge {V}_{rA}>{V}_{mA}\), then the exogenous shock will lead to a less representative election result. Representativeness is maximized (but not fully reached) if \({s}_{m}^{*}\) equals zero. In such cases, increasing turnout of marginal voters leads to a trade-off between higher turnout and representativeness. This is the case when, for example, an exogenous shock only increases turnout among groups that already vote relatively frequently. Similarly, if \({V}_{totA}\le {V}_{mA}<{V}_{rA}\) or \({V}_{totA}\ge {V}_{mA}>{V}_{rA}\), \({s}_{m}^{*}\) can never be sufficiently large to achieve the fully representative election result. Representativeness and voter turnout are maximized (but not fully reached) when \({s}_{m}^{*}\) equals 100%.

Thus, marginal voters are only able to close the gap between the voting preferences of regular voters and the fully representative counterfactual election result if one of the following conditions holds: \({V}_{rA}<{V}_{totA}<{V}_{mA}\) or \({V}_{rA}>{V}_{totA}>{V}_{mA}\). If either of these conditions holds, then \({s}_{m}^{*}<{s}_{m}\) indicates that fewer marginal voters should be exposed to the shock to obtain the representative counterfactual election result. The exposure of fewer marginal voters to the shock also leads to a lower turnout, thus giving rise to a trade-off between representativeness and higher turnout. If, however, \({s}_{m}^{*}>{s}_{m}\), then more marginal voters should be exposed to the shock to obtain the representative counterfactual election result with no trade-off arising. If \({s}_{m}^{*}={s}_{m}\), then the share of marginal voters exposed to the shock brings about the representative counterfactual election result.

In the next section, we apply this method in a case study of a Dutch referendum held in 2018. In our application, the counterfactual \({V}_{totA}\) (in Eq. 5) was estimated using data from a post-referendum survey. The values of \({V}_{rA},{V}_{mA} , {N}_{r}, {N}_{m},\) and \({s}_{m}\) were estimated using an instrumental variable regression based on data pertaining to the actual observed referendum result. As a final step, we derived \({s}_{m}^{*}\) using Eq. (5).

On March 21, 2018, the Dutch government held a national, non-binding referendum on the Intelligence and Security Services Act (ISSA; Wet op de inlichtingen- en veiligheidsdienst in Dutch).⁵ ISSA implied a substantial broadening of the surveillance powers of the Dutch Security Services. The policy trade-off between security and privacy was the focal topic of the referendum as well as public debates (Jacobs 2018a). A group of students initiated the referendum, and no group had a disproportionately large stake in its outcome apart from the Dutch Security Services (Van Klingeren 2018). For the referendum result to be deemed valid, a voter turnout of at least 30% was required.

Eligible voters could vote at a voting station within their municipalities of residence or in a different municipality after successfully applying for a voter card before election day. Only 0.38% of votes were cast from abroad, and these votes were excluded from our analysis. The turnout for the referendum was 51.5%, and the results, excluding blank votes, were 48.5% “yes” votes and 51.5% “no” votes.

Municipal council elections were held concurrently with the referendum, with an average turnout of 55%. The same voting stations were used for the referendum and the municipal elections. However, due to municipal amalgamations, concurrent municipal elections were held in only 335 of the 380 Dutch municipalities. For individuals voting in the municipal elections, the additional cost of voting in the referendum was lower than that for those who did not vote in the municipal elections, as they were already at the voting station. This situation provided the setting for a quasi-natural experiment in which the concurrence of municipal council elections represented shock exposure (“treatment”), as explained in more detail in the next section.

In the Netherlands, regular municipal council elections are held every four years on the same day in March across all municipalities. Municipalities that amalgamate (merge with other municipalities) hold special off-cycle municipal council elections. If these special elections are held close to (before or after) regular municipal council elections, then these newly formed municipalities are temporarily excluded from participating in the regular municipal council election cycle.

Municipal amalgamation has a long history in the Netherlands. Figure 1 shows that some municipalities have been amalgamated almost every year since 1950. Whereas countries like Denmark have applied a “big bang” approach, amalgamating many municipalities in a single year, the Dutch amalgamation approach has been gradual. Most amalgamations have involved two or three municipalities, although in some cases, multiple municipalities were merged into a single jurisdiction. Of the 45 municipalities that did not hold elections concurrently with the ISSA referendum, one had been amalgamated in 2016, another in 2017, and six more in 2018. The remaining 37 were scheduled for amalgamation into 12 new jurisdictions in 2019.

Bild vergrößern

Amalgamation may occur at the request of the involved municipalities, but it is usually initiated by a higher-level governmental tier. Municipal amalgamation is achieved through legislation, which can be pushed through by the central government against the wishes of the affected jurisdictions (Allers et al. 2021). The decision to amalgamate is, by and large, taken on the basis of perceived economies of scale opportunities, which are driven by municipal size (Allers and Geertsema 2016). The decisions to amalgamate were taken long before the referendum was on the political agenda, so there are no strategic considerations relating to the decision to amalgamate with an eye to influencing the referendum’s result.

To map our method from the previous section to this empirical application: regular voters are those who would anyhow have voted in the referendum notwithstanding concurrent municipal elections. Marginal voters are those who voted in the referendum only if it was held concurrently with municipal council elections. Non-voters are citizens who were eligible to vote but who abstained from voting regardless of whether the referendum was concurrent with local elections. We assume that there are no non-voters who did not vote in the referendum because it was held concurrently with municipal elections. This assumption is validated by the results of a survey (Jacobs 2018b), which revealed that none of the respondents listed concurrent elections as a reason not to vote in the ISSA referendum.

Figure 2 shows a scatterplot of voter turnout and yes votes, with an ordinary least squares (OLS) line overlayed. It indicates that voter turnout was higher in municipalities with concurrent elections (light-colored dots) and that both groups formed strikingly separate clouds.

Bild vergrößern

We used municipal-level data to estimate the impact of voter turnout on the referendum result. We included 380 Dutch municipalities in our dataset.⁶ The key dependent variable was the percentage of yes votes within a municipality in the ISSA referendum. We estimated the following 2-Stage Least Squares (2SLS) regression model:

To overcome potential endogeneity between voter turnout and the referendum result, we relied on instrumental variable estimations. The proposed instrument was the concurrence of municipal council elections with the referendum. In the first-stage regression, we estimated the effect of election concurrence (C) on turnout (T). Election concurrence was measured using a dummy variable with a value of 0 if there was no concurrent municipal council election on the day of the ISSA referendum and 1 if there was. In the second-stage regression, we used the predicted turnout \(\widehat{T}\) as our main explanatory variable for the actual share of yes votes in the referendum.⁷

Our identification of the causal effect thus relies on the assumption that municipal amalgamation that occurred circa 2018 was independent of the share of yes votes in the ISSA referendum held in a municipality except through its effect on turnout due to concurrent municipal council elections. Given the Dutch municipal amalgamation process (see Sect. 3), we expect this assumption to hold.

Nonetheless, the selection of municipalities for amalgamation circa 2018 was not random. To ensure that our estimates are unbiased, we also included a set of control variables (X) in our regressions. The number of eligible voters was included to capture the potentially distorting effect of municipality size. Following the literature, we included sociodemographic variables and variables capturing the local political landscape (e.g., Szczerbiak and Taggart 2004; Van der Brug et al. 2018; Goodwin & Heath 2016; Solvetti, 2020). Sociodemographic control variables were included because voters belonging to the same sociodemographic group tend to think alike on specific issues. The results of a large-scale survey held after the ISSA referendum revealed a correlation between how individuals voted in the ISSA referendum and their sex and age (Jacobs 2018a). Therefore, we included the share of the male population as well as the share of the population aged 45 + years as control variables. We also included the local unemployment rate and average per capita income. To capture local political preferences, we included a variable for measuring the vote share of political parties supporting ISSA in the 2017 parliamentary election.⁸ This was because voters may vote along party lines, either because they follow party cues or because political parties correctly represent the policy preferences of voters who support them. We also controlled for the number of voting locations per capita. This variable served as a proxy for the opportunity costs of voting (Allers & Kooreman 2009) and was also relevant because municipalities that did not participate in the municipal council elections could have fewer voting locations. Finally, we added a control variable for a single municipality that also held its own (local) referendum on this day.

We empirically scrutinized the assumption that amalgamation has no effect on the share of Yes votes in Appendix C. In Appendix C, we use the fact that almost every year some municipalities amalgamate. Accordingly, we were able to compare municipalities that were amalgamated circa 2018, and thus did not hold concurrent elections, with those that were amalgamated between 2010 and 2017, or between 2019 and 2022, which had concurrent elections. Confining the sample to only recently amalgamated municipalities did not change the results. We therefore concluded that our instrument is indeed exogenous. In other words, municipal council elections held concurrently with the ISSA referendum only influenced the results of the ISSA referendum through their effect on voter turnout.

We accounted for heteroscedasticity by using robust standard errors. Furthermore, as our units of observation were municipalities and numbers of eligible voters differed by municipality, we weighted the regressions by the number of eligible voters per municipality. The use of weights increased the representativeness of our regression results in relation to the entire population of the Netherlands. Table 2 shows descriptive statistics for all variables.

Table 3 presents the estimates of our 2SLS model. Columns 1 and 2 show the results of regressions that relied solely on our instrumental variable, while columns 3 and 4 also include control variables. We observed that our results hardly changed with the inclusion of control variables. Nevertheless, to minimize the risk of endogeneity, we only considered the results of the models that included control variables (columns 3 and 4) in our discussion and application of the model.

The first-stage regression results shown in column 3 reveal that turnout in the referendum was strongly related to the concurrence of municipal elections. It was, on average, 23% points higher in cases of concurrent municipal elections than in cases without concurrent elections. The referendum turnout coefficient in column 4 shows that a 1% point increase in turnout due to concurrent municipal elections increased the share of yes votes by 0.27% points. All control variables were of the expected sign and size, except the coefficient, aged ≥ 45 years in the first-stage regression.⁹ The value of the Kleibergen-Paap rk F-statistic in column 3 was well above the critical values of Stoko-Yogo for identifying weak instruments (this value was 16 for a worst-case 2SLS bias of 10%). It was also well above the critical value of 10 based on the widely used Stager and Stock rule of thumb (Andrews et al. 2019), thus confirming the strength of our instrument.

We applied these regression results in an analysis of the trade-off between turnout and the representativeness of the referendum result following our three-step approach.

Step 1: Decomposing regression results into the voting preferences of regular and marginal voters.

Using our regression estimates, we derived the equivalents of \({V}_{rA},{V}_{mA} , \frac{{N}_{r}}{{N}_{tot}}, \frac{{N}_{m}}{{N}_{tot}} ,\) and\({s}_{m}\), in which the “A” in the subscript indicated voting yes in the referendum. Most of these values could not be obtained directly from the regression output. Instead, the regression models were used to simulate the expected turnout or share of yes votes under different scenarios, such as no concurrent municipality elections. We used the Stata software’s postestimation command, Predict, for this simulation. In all of our calculations, we weighed the results for numbers of eligible voters. Below we briefly discuss how these values were obtained, with a more elaborate explanation provided in Appendix B.

To obtain \(\frac{{N_{r} }}{{N_{tot} }}\), we used the first-stage regression model to predict the turnout rate in the hypothetical scenario in which none of the municipalities held concurrent elections (i.e., the dummy for concurrent elections was set to zero for all municipalities). We then calculated the weighted average using the number of eligible voters. We found that \(\frac{{N_{r} }}{{N_{tot} }}\) \(=30.07\%\) (i.e., 30% of the electorate are regular voters). We calculated \(\frac{{N_{m} }}{{N_{tot} }}\) using the first-stage regression model to predict the turnout rate for a scenario in which all municipalities held concurrent elections, subtracting the previously calculated turnout of regular voters, and obtained a value of 23.49%.¹⁰ Therefore, 23% of the electorate are marginal voters.

To calculate \({s}_{m},\) we used the first-stage regression model to estimate voter turnout in the case that only those municipalities that actually had concurrent elections, also had concurrent elections according to the model.¹¹ We did so by setting the concurrent election dummy to one for the 334 municipalities that actually held concurrent elections, obtaining a predicted voter turnout of 51.58%. After subtracting turnout from regular voters, we found that marginal voters exposed to the shock comprised 21.52% of the electorate. Thus, the share of marginal voters that were exposed to the shock, \({s}_{m}\) was 0.92 or \(\left(\frac{21.5}{23.5}\right).\)

To obtain \({V}_{rA}\) we use the second-stage regression model to predict the percentage of yes votes in the hypothetical case in which none of the municipalities held concurrent elections. We first subtracted the predicted share of yes votes attributed to concurrent elections from the share of yes votes in municipalities that held concurrent elections. We then calculated the weighted average, obtaining a value of 42.27% for \({V}_{rA.}\) This was also the predicted referendum result when none of the marginal voters were exposed to the shock (i.e., when \({s}_{m}=0)\).

To obtain \({V}_{mA}\), we first calculated Fowler’s (2015) preference gap, \(\Delta V\), by multiplying the impact of the shock on turnout (i.e., \(\widehat{{\gamma }_{1}}\)=23.49) by the effect of turnout on the yes vote (i.e., \(\widehat{{\beta }_{1}}\)=0.27). This value was 6.36% points. To calculate \({V}_{mA}\), we used the following formula from Fowler (2015): \({V}_{mA}=\frac{\left(\left({P}_{r}+{P}_{m}\right) \left({V}_{rA}+\Delta V\right)\right)- {V}_{rA}{P}_{r}}{{P}_{m}}= \frac{\left(\left(0.30+0.23\right) \left(0.424+0.06\right)\right)- 0.42\times 0.30}{0.23}=0.57\) with \({P}_{r}=\frac{{N}_{r}}{{N}_{tot}}\) and \({P}_{m}=\frac{{N}_{m}}{{N}_{tot}}\).¹² Thus, 57% of marginal voters voted yes. It is noteworthy that marginal and regular voters voted differently, with marginal voters being 34% more likely to vote yes than regular voters.

Step 2: Obtaining an estimate of the counterfactual representative election result.

We now turn to the second step of our method, namely estimating the counterfactual representative election result. To do so, we drew on a survey carried out by the Netherlands Voter Research Foundation (Dutch acronym: SKON). The data were extracted from the Longitudinal Internet Studies for the Social Sciences (LISS) panel, a probability sample survey panel hosted by CenterData (University of Tilburg), which offers open access to their survey data (Jacobs 2018b). Participants in the LISS panel are paid and the panel is regularly updated to ensure that it is representative of the Dutch population (Jacobs 2018a). The survey was conducted in three waves with the first two completed before the referendum and the final one after it was held. After each wave, one-third of respondents were redrawn (Jacobs 2018a).

To estimate the counterfactual representative election result, we used data from the third wave conducted during the two weeks following the referendum. Because blank votes are not counted as valid votes under the Dutch referendum law, we focused on the percentage of yes and no votes. The survey queried, inter alia, whether people had voted, what they voted, and, in case of abstention, what they would have voted (Jacobs 2018b). Of the 2838 distributed survey forms, 2255 were completed. The turnout among survey respondents was higher than the actual voter turnout in the referendum. Moreover, in terms of demographics, those aged above 65 years were overrepresented in the survey, while youth with low education levels were underrepresented. To correct for this disparity, we used weighted survey results. Among those respondents who indicated that they had voted, we found that 48.5% voted yes and 51.5% voted no. These results matched the official referendum result. Considering the total number of eligible voters in the referendum and the response rate, the margin of error was 2% points (Jacobs 2018b).

Among those respondents who indicated that they did not vote, 45.4% indicated that they would have voted yes and 54.6% indicated that they would have voted no. Those who abstained were more likely to be female, less well-educated, and young. Using the weighted survey result for all respondents, we found that 47.3% of the electorate would have voted yes and 52.7% would have voted no.

Our estimation of the representative election result had important shortcomings. The fact that the survey was held after the referendum result became public may have influenced the responses. Another caveat is that voter turnout was higher among survey respondents. This is a well-known and persistent problem in survey research on voter turnout (Werner & Jacobs, 2022). It may be explained by the fact that those who did not vote may also have been more likely to have not completed the survey. Another reason could be that the survey was implemented in waves, with a majority of respondents having participated in previous waves. Consequently, survey respondents may have been more aware of the referendum, resulting in their increased turnout. We obtained a full turnout estimate only to illustrate our method and do not claim that this survey was a perfect estimation of the representative election result.

As we have pointed out in the second section of this paper, an increase in turnout could decrease the representativeness of the result only if there was a group of non-voters, who did not vote even when subjected to the exogenous shock. Before continuing our analysis, we checked whether such a group actually existed in this case using the survey data. In municipalities where the shock did not occur, non-voters were indistinguishable from marginal voters. Consequently, we focused on jurisdictions in which concurrent elections were held. Out of a total of 2037 respondents from those municipalities, 482 (24%) indicated that they did not vote, and were thus non-voters. Among these non-voters, persons with lower education levels (primary or pre-secondary vocational education) were significantly overrepresented, and those with higher education levels (college/university) were underrepresented. Older individuals (aged ≥ 65 years) were also underrepresented among non-voters (see Appendix D). Thus, there appeared to be a sizable group of non-voters with characteristics that set them apart from other voters. This indicated a possible trade-off between higher turnout and representativeness.

Step 3: Analyze how the exogenous shock affected the representativeness of the referendum result.

We were now able to analyze the trade-off between turnout and representativeness. Given that \({V}_{rA}=0.42\), \({V}_{totA}=0.47,\) and \({V}_{mA}=0.57\), the condition \({V}_{rA}<{V}_{totA}<{V}_{mA}\) held, and marginal voters were to some extent able to close the gap between the voting preferences of regular voters and the counterfactual fully representative election result. Inserting the various values in Eq. (5), we determined what share of marginal voters who were exposed to the turnout shock would have produced the counterfactual representative referendum result:

By varying the degree of exposure of marginal voters to the shock, we could quantify the trade-off between higher turnout due to concurrent municipal council elections and the representativeness of the referendum result. We did this by comparing four scenarios (see Table 4): (1) no marginal voters were exposed to the shock; (2) the share of marginal voters exposed to the shock was such that a representative referendum result was obtained; (3) the share of marginal voters exposed to the shock was equal to the actual share; and (4) all marginal voters were exposed to the shock.

Table 4 shows, for example, that if no marginal voters were exposed to the shock (\({s}_{m}=0\)), the estimated turnout would be 16% points lower, and the share of yes votes 5% points lower than would be the case under the fully representative referendum result scenario. It should be noted that we used point estimates in these calculations. In an application aimed at drawing conclusions (rather than providing an illustration, as intended here), it would be preferred to have a more accurate estimate of the counterfactual representative turnout result and to take into account confidence intervals.

From the results shown in Table 4 we can conclude that relative to a situation in which no municipal council elections occurred, the concurrence of the referendum with municipal council elections increased the turnout and representativeness of the referendum result. A representative referendum result would have been achieved if an estimated 68% of marginal voters had been exposed to the shock. However, as our results suggest that 92% of marginal voters were exposed, a trade-off occurred between the higher voter turnout and the degree to which the referendum result was representative of the entire electorate. Figure 3 visualizes this trade-off. In the ISSA referendum, exposure of up to 68% of marginal voters to the shock could have increased both turnout and the representativeness of the referendum result. When more than 68% of marginal voters were exposed to the shock, voter turnout still increased, but this came at the cost of the representativeness of the referendum result.

Bild vergrößern

Our identification of the causal effect of turnout on the referendum result was based on the assumption that amalgamation only affected turnout but had no other (indirect) effect on the share of yes votes in the referendum (see Sect. 4). To test this assumption empirically, we excluded our control variables (see columns 1 and 2 in Table 3) and restricted our sample to recently amalgamated municipalities (see Appendix C). These tests confirmed that our instrument was exogenous and that our results were robust. For example, when we restricted our sample to the 84 municipalities that were amalgamated between 2010 and 2022, our main variable of interest changed minimally from 0.27 to 0.28. Appendix E shows the results of the unweighted regression, which was performed as a final robustness check. They reveal that our results did not depend on the use of weights.

Studies that have investigated the effects of exogenous shocks on voter turnout have provided unique insights into how voters who are sensitive to turnout shocks and thus relatively easy to (de)mobilize influence election results. However, a shock that increases turnout does not necessarily increase the representativeness of election results. We introduced a method for quantifying the extent to which an exogenous shock in turnout makes an election result more or less representative by assessing the degree of exposure to the shock of marginal voters who are sensitive to it. A comparative analysis of how different degrees of exposure of marginal voters influence turnout and the election result yielded insight into the potential trade-off between turnout and the representativeness of election results. Our method can be applied to a wide variety of elections, including the U.S. presidential elections. It should be noted, however, that the identified trade-off will vary according to different elections and shocks, as every shock in voter turnout draws particular groups of marginal voters to the voting booth (Fowler 2015; Damsbo-Svendsen & Hansen 2023).

We would like to emphasize that a high voter turnout is important for the legitimacy of elections. This study should not be interpreted as an endorsement of policies that reduce voter turnout. However, we would caution policymakers to avoid the assumption that increasing turnout among marginal voters will automatically increase the representativeness of election results. Policies to increase turnout should not be targeted uncritically at groups that are relatively easy to mobilize, but should give due weight to groups that tend to be underrepresented. When organizing elections on tight budgets, governments have to make tough decisions that could involve trade-offs between higher turnout and the representativeness of election results, for example, when deciding whether or not to schedule elections during the rainy season (see also Damsbo-Svendsen & Hansen 2023). We aim to contribute to increasing the transparency of these trade-offs, which can benefit public discussions about the legitimacy of election results. This legitimacy issue is also an important reason why many politicians and newspaper articles frequently mention seemingly random events, such as the weather, and their effects on turnout when discussing election results (see, e.g., Arnesen et al. 2024; The Guardian, 2016).

We demonstrated our method using the ISSA referendum held in 2018 in the Netherlands as a case study. To examine how turnout influenced the result of the ISSA referendum, we treated the concurrence of municipal council elections following municipal amalgamation as an exogenous turnout shock. We found that compared with regular voters, marginal voters (those who only voted if there was a concurrent municipal council election) generally prioritized security above privacy. In the ISSA referendum, increasing exposure of marginal voters to the shock corresponded to increases in both their turnout and increases in the representativeness of the referendum result up to an exposure threshold of approximately 68%. Because our estimates suggest that in reality, 92% of marginal voters were exposed to the shock, a trade-off arose in which increased voter turnout among marginal voters reduced the representativeness of the referendum result.

Our results and method have important limitations. First, the results obtained using our method can only be as good as the estimates on which they are based. Estimating the counterfactual representative election result, in particular, is challenging. For example, the survey we used was conducted after the referendum result became public and this may have influenced the results of the survey. Another persistent problem in such surveys is the overestimation of voter turnout. Future studies should seek to estimate or simulate representative election results that address these issues. Second, the method is currently limited to elections with only two possible outcomes. It would be interesting to explore how it could be applied to elections that have more than two outcomes as is often the case in legislative elections with proportional representation.