Now or Later?: The Inter-temporal Decision-Making of Electoral Participation

Abstract

This study examines the dynamic nature of voting in modern elections with wide voting windows. Our stylized two-period model predicts that, if voters are not myopic, turnout in the current period tends to increase as the costs in the other period increase. The model also predicts that overall turnout does not always decrease even when the costs increase. We test these predictions using novel data from Japan’s General Election in 2017 with a weather disruption caused by a powerful typhoon. Our analyses show that the tremendous costs on Election Day shifted the timing of voting and did not decrease overall turnout in 2017, as compared to 2014. Our model and findings build a new benchmark to understand how voters decide their timing of voting. This study also has implications for the unprecedented popularity of early voting in the 2020 U.S. presidential election.

Introduction

Since the seminal work by Downs (1957), theoretical and empirical studies on the cost of voting have assumed that voters make a single decision of whether to turn out by considering the overall voting costs in the election. In other words, a turnout decision has been viewed as static—voters choose to vote now or never given the cost at the time of decision-making.

In reality, however, in modern elections with wide voting windows, voters can choose to vote now or later (or never) by comparing costs that may be higher or lower at particular periods compared with others. For example, voters may have to work on Election Day, but may have a more flexible schedule the day before. Amid a pandemic, voters may choose to vote early by mail with a fear of infection at a crowded polling place on Election Day. Alternatively, voters may anticipate that rainfall will be heavier in the morning than in the afternoon of Election Day. In these cases, voters can avoid higher costs by using early voting, mail voting, or by voting in the afternoon of Election Day, respectively. If voters are not myopic, they would choose the optimal timing of voting by considering variable costs during the election period. This means that the turnout decision can be viewed as an inter-temporal dynamic problem.

This study examines the dynamic nature of voting in modern elections for two reasons. First, the conventional model of turnout overlooks the possibility that voters can shift the timing of voting to avoid higher costs that they would otherwise face. As a result, overall turnout is always predicted to decrease as voting costs on Election Day increase. Yet this relationship may not hold in elections in which voters can choose the timing of voting during a wide voting window. If many voters anticipate that the cost on Election Day will be particularly large and choose to vote early, overall turnout may not decrease even when costs indeed increase.

Second, many regions and countries have widened voting windows and modes in the last few decades by introducing early voting and vote by mail,¹ and the number of individuals who use these modes is not negligible. Menger and Stein (2020) and Stewart (2021) examine the types of voters who use a particular mode of voting (e.g., in person vs. by mail), while Clinton et al. (2021) show that changing the location of Election Day polling places induces voters to vote early. Yet less is known about how voters decide when to vote and how this decision affects overall turnout.

Empirically, several studies have examined the effectiveness of widened voting opportunities for overall turnout, but their findings are mixed and inconclusive. Recent studies (e.g., Gerber et al., 2013; Kaplan & Yuan, 2020; Leighley & Nagler, 2014) show that wider voting windows increase turnout. By contrast, other studies (e.g., Gronke et al., 2007) find no such evidence. Notably, Burden et al. (2014) find that adoption of early voting even decreases turnout in U.S. presidential elections. We suspect that these mixed findings may originate from either the use of different empirical strategies, the focus on different electoral settings in which voters decide when and how to vote, or both. We claim that without a formal theory guiding us to predict how voters behave during the wide voting window, it is difficult to interpret what those mixed findings imply.

This study proposes a new theory to consider the inter-temporal decision-making of voting, in which voters decide when to vote or never by comparing anticipated costs across periods during the election. We develop a stylized dynamic model of turnout in which an election is divided into two voting periods (e.g., the morning and afternoon of Election Day, or before and during Election Day). In the first period, a voter either turns out or postpones the decision to the next period. In this decision, the voter compares the current net benefit with the expected future net benefit. The voter turns out now when it is sufficiently beneficial to do so now, and postpones the decision otherwise. If the voter postpones the decision, the next period offers only the options of voting or abstaining. The model assumes voting costs that vary over time.

The model generates two important predictions. First, if voters are not myopic and when the voting cost in the second period increases relative to that in the first period, turnout in the first period increases, whereas turnout in the second period decreases. That is, voters choose to vote in the first period to avoid the higher costs in the second period. We call this behavior “precautionary voting.” Second, notably, due to this shift in the timing of voting, overall turnout shows no decrease and even an increase if the difference in the costs between two periods is moderately large. None of these predictions can be derived from the conventional model of turnout, with static costs in a single voting window.

We test these model predictions using novel data from the 2017 Japanese General Election. On the day of the Japanese General Election in 2017, an exceptionally strong typhoon hit many parts of Japan, during which dozens of municipalities experienced record-breaking 24-h rainfall.² Our analysis uses voter turnout in this election with turnout in the previous General Election in 2014, which experienced no significant weather disruption.³

Using precipitation and turnout from municipalities in these two elections, we develop two sets of panel data. These data are unique because they include turnout in two different voting windows in each election. The first panel dataset uses hourly turnout on Election Day in 945 municipalities from 25 prefectures in the two elections. Several days before the 2017 election day, weather forecasts had already warned that heavy rain and strong wind would hit many regions in the late afternoon on that day. Given this situation, the model predicts that voters would turn out earlier on Election Day if they would seek to avoid the higher cost of voting later. Indeed, we show that turnout in the morning was higher in 2017 than in 2014 especially in municipalities with heavier afternoon rainfall in 2017 and a larger percentage of senior voters.

The second panel dataset uses turnout during the early voting period and on Election Day from approximately 1900 municipalities in 47 prefectures in the two elections. As mentioned earlier, several days before the 2017 Election Day, weather forecasts tracking the typhoon’s approach predicted that it would hit many parts of Japan on Election Day. Accordingly, the model predicts that voters who anticipate serious weather disruptions on Election Day are more likely to use early voting. Our analysis shows that turnout during the early voting period was higher in 2017 than in 2014 especially in municipalities for which stronger rainfall was predicted on Election Day and with more senior voters.

Finally, using the second panel data set, we also show that overall turnout in 2017 did not decrease in municipalities with extreme rainfall on Election Day. This indicates that overall turnout does not always decrease despite the increase in the voting cost.

Ultimately, this study offers a new benchmark model to understand dynamic turnout decisions in modern elections. Our model reveals under which conditions voters choose to vote early, which is vital to evaluate the effectiveness of election reforms. Moreover, this study explains why overall turnout does not necessarily decrease, even when the cost of voting increases.

Model

We consider a two-period model of voting, which divides a single election into two periods. A voter chooses to turn out in either period or to abstain. The two periods can be viewed as either the morning and afternoon of Election Day, or as an early voting day prior to Election Day and Election Day itself.

In each period, voter i compares the benefits of voting with the costs of voting. The benefits and costs of voting vary between these two periods. Let $e_{ti}$ be a random variable for voter i drawn from the distribution $G \sim U(0,1)$ in each period $t \in \{1,2\}$. This $e_{ti}$ includes, for example, the differential benefits a voter receives from the success of his or her preferred candidate over the less preferred candidate (which is weighted by the probability of being a pivotal voter), satisfaction from voting, and sense of civic duty. Thus, $e_{ti}$ denotes the overall benefits of voting.⁴ The costs of voting are deterministic and defined as $c_{ti}' + c_{i}' \in [0,1]$.⁵ To focus on a dynamic aspect of turnout decisions, we assume that the costs are common to all voters, i.e., $c_{ti}' + c_{i}' = c_t$ for all i and t.⁶ Such costs can be interpreted as a common weather shock. Taken together, voter i’s utility for period t is written as

$$\begin{aligned} \left\{ \begin{array}{ll} e_{ti} - c_t &{} \text{ if } \text{ vote, } \\ 0 &{} \text{ otherwise. } \end{array} \right. \end{aligned}$$

(1)

We solve the model backward. In Period 2, voter i votes if and only if

$$\begin{aligned} e_{2i} - c_2 \ge 0 \qquad \Longleftrightarrow \qquad e_{2i} \ge c_2. \end{aligned}$$

(2)

Thus, among those who did not vote in Period 1, only a fraction of voters in Period 2 turns out—the proportion for whom the benefits are greater than or equal to Period-2 costs, i.e., $1 - G(c_2)$, while the proportion for whom the benefits are less than the costs, i.e., $G(c_2)$, abstain.

In Period 1, the voter decides whether to vote in the current period or to wait until the next period. Voter i in Period 1 turns out if and only if

$$\begin{aligned} e_{1i} - c_1\ge & {} \beta [ 1 - G(c_2) ] \{ E[e_{2i} | e_{2i} \ge c_2] - c_2 \}, \end{aligned}$$

(3)

where $\beta \in [0,1]$ is a discount factor. Equation (3) means that she votes in Period 1 if and only if the benefit-cost difference in Period 1 is greater than or equal to her (discounted) anticipation of the benefit-cost difference in Period 2.

We rewrite Eq. (3) as

$$\begin{aligned} e_{1i}\ge & {} c_1 + \beta [ 1 - G(c_2) ] \{ E[e_{2i} | e_{2i} \ge c_2] - c_2 \}. \end{aligned}$$

(4)

For brevity, let us define $\epsilon _1 := c_1 + \beta [ 1 - G(c_2) ] \{E[e_{2i} | e_{2i} \ge c_2] - c_2 \}$ and $\epsilon _2 := c_2$, which are the threshold value for $e_{1i}$ and $e_{2i}$, respectively. Only a fraction $1 - G(\epsilon _1)$ of all voters votes in Period 1, while the remainder defer until Period 2. We already know that only a fraction of the latter group will actually vote in Period 2. Thus, overall turnout is written as

$$\begin{aligned} \underbrace{[ 1 - G(\epsilon _1) ]}_\text {fraction of those voting in Period 1} + \underbrace{G(\epsilon _1)[ 1 - G(\epsilon _2) ]}_\text {fraction of those not voting in Period 1 but voting in Period 2}, \end{aligned}$$

(5)

where the first and second terms indicate total turnout in Periods 1 and 2, respectively.

We now consider the extent to which the magnitude of voting costs, $c_t$, affects turnout decisions during each period. Assume that $\beta > 0$. This indicates that voters are not myopic; they do take into account the utility of voting during the second period, making a decision during the first period. This assumption is later tested using our data. When $\beta > 0$, the changing Period-2 costs affect turnout decisions in Period 1 because the threshold level for Period-1 turnout depends on $c_2$ (as in the Eq. (4)). We can show that $\epsilon _1$ (the threshold value for Period 1) is a decreasing function of $c_2$, with the larger Period-2 costs increasing Period-1 turnout and vice versa. By contrast, if $\beta = 0$ and voters are myopic, changing $c_2$ has no effect on Period-1 turnout. Formally, we can derive the following proposition:

Proposition 1

Let the cost in Period 1 be fixed and assume interior solutions.

• (1) Assume that $\beta > 0$. If costs increase during Period 2, then Period-1 turnout will increase and Period-2 turnout will decrease. If costs decrease during Period 2, they will have the opposite effect.

• (2) Assume that $\beta = 0$. If costs increase during Period 2, turnout will decrease during that period. The changing costs in Period 2 will have no effect on Period-1 turnout.

Proof

See the online appendix. $\square$

We refer to the first type of behavior, in which people turn out to vote early if they anticipate that voting later will be more costly, as precautionary voting.

We highlight the difference between the conventional turnout model and our model. The conventional model views an entire election as a single period, assuming that each voter makes a single decision about whether or not to vote. By contrast, our model splits the voting window into two periods, investigating how voters make decisions during both periods, sequentially. Importantly, our model assumes that the costs and benefits of voting may vary between the two periods. Voters consider the anticipated costs and benefits of voting during Period 2 while making their decisions during Period 1. This structure allows us to consider the possibility that voters decide both when to vote and whether to vote.⁷

Proposition 1 has important implications for overall turnout. Unlike the conventional turnout model, which suggests that overall turnout always decreases as costs increase, the proposition below suggests that overall turnout may not decrease as the costs of voting rise because higher Period-2 costs increase Period-1 turnout as long as voters are not myopic.

Proposition 2

Let the cost in Period 1 be fixed and assume interior solutions.

• (1) Assume $\beta > 0$ and $\epsilon _1 < \epsilon _2$. Even if Period-2 costs increase, overall turnout may not decrease. Under certain conditions, increasing Period-2 costs can increase overall turnout.

• (2) Assume (a) $\beta = 0$ or (b) $\beta > 0$ and $\epsilon _1 \ge \epsilon _2$. If Period-2 costs increase, overall turnout will decrease monotonically.

Proof

See the online appendix. $\square$

The first part of Proposition 2 is important. It argues that, if voters are not myopic (i.e., $\beta >0$) and Period-2 costs ($\epsilon _2$) exceed the sum of Period-1 costs and the anticipated benefit-cost difference in Period 2 ($\epsilon _1$), then the higher costs of voting (in Period 2) may not reduce overall turnout, even if it reduces Period-2 turnout, because the decrease in Period-2 turnout will be partially offset by the increase in Period-1 turnout.

To illustrate this mechanism, assume that the Period-2 costs ($c_2$) are moderately high. In this case, the Period-2 costs are likely to exceed the sum of the Period-1 costs and the anticipated net gain achieved by voting during Period 2, i.e., $\epsilon _1 < \epsilon _2$. This is because the threshold value in Period 1 ($\epsilon _{1}$) decreases as Period-2 costs increase (as in Proposition 1 (1)); the threshold value in Period 2 ($\epsilon _2$) is simply $c_2$. For example, if voters on the morning of Election Day anticipate moderately high costs later that day, they are likely to vote in the morning, rather than in the afternoon or evening. This shift in timing explains the prediction in Proposition 2 (1), namely, that the higher cost of voting (in Period 2) will not always reduce overall turnout. Interestingly, overall turnout can increase when $c_2$ increases if parameter values for $c_1$, $c_2$, and $\beta$ are within a certain range. Within this parameter range, the negative effect of Period-2 costs on turnout is dominated by its positive effect on Period-1 turnout.⁸ Finally, when $c_2$ becomes too high, it suppresses Period-2 turnout, causing overall turnout to decrease.

Figure 1 presents a graphic illustration of the discussion above. Based on Proposition 2, we set $\beta = 0.9$, indicating that voters place a relatively large weight on the future when making a decision.⁹ We fix the Period-1 costs at $c_1 = 0.1$, 0.5 or 0.9. When $c_1$ is smaller, $\epsilon _1$ decreases for a given $c_2$ (see Eq. (4)). Thus, $\epsilon _1 < \epsilon _2$ in Proposition 2 (1) is more likely to hold ceteris paribus. As the figure shows, when the Period-1 costs are low ($c_1 = 0.1$), overall turnout does not decrease, even when the cost of voting in Period 2 increases. This occurs, for example, when there is no weather disruption in Period 1 but voters anticipate moderate-to-severe weather disruption in Period 2. Moreover, overall turnout is shown to increase slightly when the Period-2 costs increase from 0.5 to 0.6. Even when the Period-1 costs are moderately large ($c_1 = 0.5$), overall turnout does not decrease rapidly, even when the cost of voting in Period 2 increases. Again, this phenomenon occurs because some voters change the timing of their voting, opting to turn out earlier.

Fig. 1

Overall turnout for different voting costs in Period-1 and Period-2. Notes We assume that $\beta = 0.9$

Weather Disruptions in the 2014 and 2017 Elections

An empirical test of the model requires an exogenous shock that significantly changes the cost of voting during the election. Building on previous research that uses rainfall as a measure of the voting cost (e.g., Gomez et al., 2007), this study uses a strong typhoon that hit Japan on the day of the General Election in 2017 as an exogenous shock to the cost. This typhoon generated two types of temporal variations in the cost during the voting window. First, the typhoon hit the country in the afternoon and evening of Election Day, meaning that the amount of rainfall on Election Day was significantly larger in the afternoon than in the morning. This feature leads to examining turnout in the morning versus the afternoon on Election Day in section ‘Turnout in the Morning vs. Afternoon of Election Day’. Second, no major weather disruption occurred prior to Election Day in 2017, so the early voting period was unaffected. This motivates us to examine early voting turnout versus Election Day turnout in section ‘Turnout Before vs. on Election Day’. These differences in rainfall between two periods indicate that the cost was considerably higher in the second period than in the first. In addition, as shown below, the typhoon in 2017 hit only a limited number of regions, which suggests that the differences in precipitation between two periods varied significantly among localities.

We create panel data on precipitation and turnout at the municipality level between the 2017 election and the 2014 General Election, which experienced no significant weather disruption.¹⁰ Thus, we use changes in precipitation and turnout in each voting window between the elections. For example, we compute the change in precipitation and turnout during the morning or on Election Day between 2017 and 2014. This differentiation allows us to control for time-invariant municipal characteristics. Importantly, the size of the changes in precipitation varies considerably across municipalities because the typhoon affected a limited set of regions. This means that we can exploit geographic variation in changes in precipitation to identify the causal effect. Thus, we do not merely compare the two elections. Our study can be viewed as a rare natural experiment, because the spatial and temporal variations of a serious natural disaster are beyond human control and therefore plausibly exogenous.¹¹

We briefly describe the main features of weather conditions in 2017 and 2014. The typhoon formed in the South Pacific Ocean on October 16, 2017, a week before the scheduled snap election, and subsequently moved toward Japan. As early as the morning of October 22, the day of the General Election, heavy rain and strong wind began to impact regions along Japan’s Pacific (East) coast. The center of the typhoon reached Omaezaki in Shizuoka Prefecture around 3 am on October 23. Figure 2 plots the forecasted and actual paths of the typhoon from October 16 to 22, using data from the Japan Meteorological Agency (hereafter JMA). The forecasted path indicates the predicted locations of the typhoon 48 h later. Figure 2 shows that the forecast was highly accurate because the forecasted and actual paths coincided very closely. Building on the forecast made by JMA and other weather services, four major national newspapers (i.e., Asahi, Mainichi, Nihon-Keizai, and Yomiuri) published a total of 109 articles between October 16 and 21 warning that Election Day might be disrupted by heavy rainfall and strong wind.¹² Therefore, it is reasonable to assume that most voters were aware of potential disruptions caused by the typhoon at least a few days prior to Election Day in 2017.

Fig. 2

The path of the typhoon in 2017. Notes Hours are in the 24-h clock

Figure 3 shows total precipitation by municipality during the voting window from 7:00 to 20:00 on Election Day in 2014 and 2017 using data from JMA.¹³ The amount of precipitation is measured every hour at approximately 1300 stations, which is then interpolated by JMA into 1 km $\times$ 1 km grid cells with JMA’s algorithm. Using this information, we calculate total precipitation in municipalities between 7:00 and 20:00 on the day of the General Election in 2014 and 2017 and later use these data to test our hypotheses. The left and center panels of Fig. 3 display total election day precipitation in 2014 and 2017, while the right panel displays differences in precipitation between 2017 and 2014. Municipalities colored orange or red had heavier rainfall or snow, while municipalities colored blue or green had smaller amounts. The left panel shows that in 2014, the number of municipalities with significant precipitation was limited. In other words, no major weather disruption occurred in most municipalities. By contrast, the center panel shows that many municipalities, especially in central Japan, were strongly affected by the typhoon in 2017. Finally, the right panel shows that the spatial differences in precipitation between the two elections were large.¹⁴

Fig. 3

Total precipitation on Election Day in 2014 (left) and 2017 (center), and the difference between them (right)

Turnout in the Morning vs. Afternoon of Election Day

Empirical Model

Our first set of analyses uses unique hourly panel precipitation and turnout data from 945 municipalities in 25 prefectures on the election days of 2014 and 2017. Hourly turnout data are from the election commissions of 25 prefectures.¹⁵ Our data cover approximately 50% of 1896 municipalities in the 47 prefectures of Japan. Our analysis treats wards in major cities as separate units.

On the day of the 2017 election, voters in several prefectures were warned that rainfall would be much heavier in the afternoon than in the morning. Figure 4 shows total precipitation from 7:00 to 11:00 (left), 11:00 to 15:00 (center), and 15:00 to 20:00 (right). Similar to Fig. 3, municipalities colored orange or red had heavier precipitation, while municipalities colored blue or green received smaller amounts. The typhoon hit the central part of Japan, especially in the afternoon and evening. By contrast, the eastern and western parts of Japan were only slightly affected by the typhoon throughout the day.

Fig. 4

Total precipitation between 7:00–11:00 (left), 11:00–15:00 (center), and 15:00–20:00 (right) on Election Day in 2017

Using these temporal and spatial variations in precipitation on election days, we test the hypothesis, derived from Proposition 1, that precautionary voting was more likely to occur in municipalities where it rained more heavily in the afternoon than in the morning. In other words, we expect that voters became more likely to vote during the morning hours in 2017 than in 2014, where they anticipated more severe weather disruptions later in the day.¹⁶

Note that our analysis uses actual weather disruptions on Election Day as a proxy for the expected costs of voting. This approach rests on the assumption that the expected timing and amount of precipitation were highly correlated with the realized timing and amount of voting. A supplementary analysis in the online appendix (Figs. A.3 and A.4 and Table A.1) offers evidence to support this assumption. First, the predicted probability of precipitation reported 1–7 days prior to Election Day is positively correlated with the actual amount of precipitation on Election Day; this relationship seems to become stronger as Election Day approaches. Taken together with news reports, warning that Election Day could be disrupted by the typhoon, voters in areas with a higher probability of rainfall were more likely to know that it could rain heavily on Election Day. Second, the predicted amount of precipitation reported for each region at 10 pm on October 21 is positively correlated with the actual amount of precipitation on Election Day, suggesting that areas with more predicted rainfall did receive a larger amount of rain on Election Day. Importantly, the JMA accurately reported on the morning of October 22 that a typhoon was approaching western and eastern Japan at night, leading to heavier rainfall on the afternoon of Election Day, rather than the morning. These results suggest that the weather forecast prior to Election Day conveyed accurate enough information about the actual amount and timing of precipitation on Election Day 2017 to allow the realized costs to be used as the expected costs.

We test the hypothesis using the following model specification:

$$\begin{aligned} \Delta T_{jt} = \beta _1 C_1 + \beta _2 C_2 + \beta _3 C_1\times \Delta D_j + \beta _4 C_2 \times \Delta D_j + \gamma \Delta P_{jt} + \Delta \epsilon _{jt}, \end{aligned}$$

(6)

where $\Delta T_{jt}$ and $\Delta P_{jt}$ denote the change in turnout in percentage and precipitation in millimeters between the 2017 and 2014 elections during time period $t \in \{1, 2\}$ in municipality j, respectively, and $\Delta \epsilon _{jt}$ is the error term. Voting hours on Election Day are split into two windows, from 7:00 to 10:59 and from 11:00 to 17:59, and dummy variables, $C_1$ and $C_2$, denote each of these windows. $\Delta D_j$ denotes the difference in precipitation between the afternoon and morning hours. We subtract morning precipitation (7:00–10:59) from midday and afternoon precipitation (11:00–17:59) for 2017 and 2014, and then compute the difference between the two election years. The values of $\Delta D_j$ are mostly positive because of the typhoon in 2017.

Two time windows, 7:00–10:59 and 11:00–17:59, are chosen due to the availability of hourly turnout data. Prefectural election commissions typically report turnout in municipalities every 2–3 h and the timing differs across prefectures. For example, Hyogo Prefecture reported turnout at 9:00, 11:00, 13:00, 15:00, 17:00, 18:00 and 19:00 in 2014 and 2017, while Gifu Prefecture did so at 10:00, 11:00, 14:00, 16:00, and 18:00. All 25 prefectures from which we could obtain data reported turnout at 11:00, while 23 prefectures reported it at 18:00 in 2014 and 2017.¹⁷ Using this information, we compute turnout between 7:00 and 10:59 and between 11:00 and 17:59.¹⁸ Percentage turnout is defined as the number of eligible voters who cast a ballot during each time window, divided by the total number of eligible voters in the municipality j. Summary statistics of all variables are reported in Table 1. The total number of observations is 1890.¹⁹

Table 1 Summary statistics of differences in hourly precipitation and turnout between 2017 and 2014 on Election Day

Recall that Proposition 1 from our model predicts that voters vote earlier if the cost in Period 2 is relatively larger than that in Period 1. Thus, we predict that $\beta _3$ is positive because voters, especially in municipalities with more severe weather disruptions in the afternoon of Election Day in 2017, were more likely to vote in the morning hours, compared to 2014. By contrast, $\beta _4$ is predicted to be negative because many voters tended to vote in the morning and be discouraged from doing so in heavy rain in the afternoon in 2017.

Note that these hypotheses rest on the assumption that most voters were aware of potential weather disruptions in the afternoon. If they were unaware of them, we would find no increase in turnout during the morning of Election Day in 2017, as compared to 2014. In addition, if voters were unable to make a plan for precautionary behavior, our hypotheses would receive no support. In these cases, neither $\beta _3$ nor $\beta _4$ would be statistically different from zero.

Our identification assumption is that $C_t * \Delta D_j$ was quasi-randomly assigned to the municipalities, and thus uncorrelated with the error term $\Delta \epsilon _{jt}$ in Eq. (6). This means that the typhoon shock should be uncorrelated with an omitted variable that could affect the timing of voting in the two elections. We argue that this assumption is justifiable for several reasons. First, the typhoon shock in 2017 is plausibly exogenous. Second, we control for the change in total rainfall, $\Delta P_{jt}$, allowing for the comparison of observations where the total amount of rainfall was similar but the timing of it within the day was different. Third, our estimation uses a cross-sectional variation in the change in rainfall between the elections as well as the morning and afternoon, thus controlling for time-invariant characteristics across municipalities.

Even so, one may be concerned with the possibility that the shock is accidentally correlated with other variables captured by $\Delta \epsilon _{jt}$. We alleviate this concern in two different ways. First, our regression model controls for prefecture fixed effects, leading to a comparison between the treatment and control groups within each prefecture.²⁰ The prefecture fixed effects capture common trends potentially correlated with the typhoon shock and the timing of voting across municipalities in each prefecture.²¹

Second, our regression model includes additional controls, such as the interactions between $C_t$ and municipality-level variables that we think might affect the timing of voting. For example, suppose that the typhoon shock was larger in municipalities where electoral competition became more intense between 2014 and 2017. If more intense competition increased turnout in the morning in 2017, omitting this variable would cause an upward bias. In other words, the more serious typhoon shock was by chance assigned to municipalities with higher competition, and both of these variables explain the increase in turnout during the morning hours in 2017. We check whether this is plausible by adding an interaction between the time window dummies and the vote margin as a measure of electoral competition. If the estimates on $\beta _3$ and $\beta _4$ are mostly unaffected by including this interaction, the typhoon shock is likely to be orthogonal to it. We also include interactions between the time window dummies and baseline socioeconomic characteristics that are potentially correlated with the timing of voting as additional robustness checks.

Results

Table 2 reports estimation results. We drop the intercept to include both time window variables in the regression model. Standard errors are clustered at the municipality level to account for autocorrelation and heteroskedasticity.²² The coefficients in column (1) suggest that turnout from 7:00 to 10:59 increased by 1.783 percentage point in 2017 compared to 2014, whereas turnout from 11:00 to 17:59 decreased by 4.580 percentage point. Coefficient sizes are different considerably between the two time windows, partly because the morning window includes only 4 h while the afternoon window includes 7 h. These results suggest that some portion of voters changed the timing of voting on Election Day in 2017 from that in 2014; they went to the polling station early in anticipation of afternoon weather disruptions.

Columns (3) and (4) of Table 2 are the main estimation results. They include the interactions of the time window dummies with the difference in precipitation between the afternoon and morning. Prefecture fixed effects are included in column (4).²³ The results indicate that the increase in turnout during the morning hours was larger in municipalities where rainfall was much heavier in the afternoon. For example, column (4) indicates that in municipalities where rainfall was more than 50 mm heavier in the afternoon, turnout in the morning increased additionally by 1.550 (= 0.031*50) percentage point. The results in columns (3) and (4) also indicate that the decrease in turnout during the afternoon was larger in municipalities with heavier rainfall.

Table 2 Differences in turnout between 2017 and 2014 during each time window on Election Day

Our estimation in Table 2 relies on the assumption that the difference in precipitation between the afternoon and morning hours in each election was uncorrelated with socioeconomic and political characteristics that could systematically change the turnout pattern in each window. This assumption seems plausible because the inclusion of prefecture fixed effects in column (4) does not change the signs and sizes of $\hat{\beta }_3$ and $\hat{\beta }_4$ between columns (3) and (4). This indicates that our results are not driven by different trends across prefectures. Moreover, we add to Eq. (6) the interactions between the time windows and local characteristics as additional controls. In particular, we consider the vote margin between the top candidates in the 2014 election, the log of population, and the shares of senior residents and college graduates.²⁴ The first variable is the proxy for electoral competitiveness at the district level. Estimation results in Table 3 indicate that adding these variables has a marginal influence on coefficient sizes and signs of the main interactions.

Table 3 Differences in turnout between 2017 and 2014 during each time window with additional controls

Next, we consider who was more likely to shift the timing of voting in response to the anticipated weather disruption in the afternoon in 2017. In particular, our analysis examines whether those with a higher propensity to vote tended to find a less costly timing to vote. Drawing on literature that seniors are more likely to vote than the young (e.g., Leighley & Nagler, 2014) and to do so earlier (Ashok et al., 2016), we split the sample into two groups below and above the median percentage of the voting-age population aged 65 and over in municipality j. Table 4 reports two estimation results, where column (1) is based on the sample below the median and column in (2) is based on the sample above the median. The prefecture fixed effects are included in the estimation. The coefficients of the interaction between the morning window dummy and the difference in precipitation between the afternoon and morning are statistically significant both in columns (1) and (2), but the coefficient in column (2) is much larger and statistically different from that in column (1).²⁵ Similarly, the coefficient associated with the interaction between the afternoon period and the difference in precipitation is much larger in column (2).²⁶ These results, together with the earlier results in Table 3 that the percent of senior residents per se does not alter our main estimates, might indicate that senior voters with a higher propensity to vote did not miss the less costly timing of voting and acted accordingly.

Table 4 Differences in turnout between 2017 and 2014 during each time window below and above the median of percentage 65 years and over

In summary, as predicted by our model, voter turnout in the first period increases when the cost of voting is much larger in the second period. This pattern for precautionary voting is stronger where voters anticipate a much larger cost in the second period, and where they are older.

We note that no other mechanisms can be a major explanation for the above findings. First, the typhoon was unlikely to have an immediate influence on other major determinants of voter turnout, such as participatory resources and psychological engagement (Verba et al., 1995). Second, the typhoon might induce political parties to change their mobilization strategy, but their focus was likely to encourage their supporters to vote early to avoid their abstention due to the higher cost during the afternoon. This possibility does not contradict with the prediction of our model.

Turnout Before vs. on Election Day

Empirical Model

Our second set of analyses uses panel data including information on precipitation and voter turnout during the early voting period as well as on Election Day in the 2014 and 2017 elections. The data include 1891 municipalities from all 47 prefectures, covering 99% of all municipalities in 2014 and 2017.²⁷ We treat 175 wards in 20 major cities as separate units.²⁸

Since 2005, voters in Japan have been allowed to vote early in person without an excuse at established early voting places during an 11-day period prior to the the General Election. Municipalities typically set up several early voting places that are open from about 8:30 to 20:00. Voters may cast a ballot at any early voting place within their municipalities. Early voting places are typically located at municipal offices and are therefore different from polling places used on Election Day. This means that transportation costs can be higher for early voting than for election-day voting. Those who do not use early voting can vote in their precincts on Election Day.

As discussed earlier, people in much of Japan were warned that the typhoon would affect their communities and that weather would be severe on Election Day in 2017. Accordingly, we hypothesize that precautionary voting was more likely to occur in municipalities where the anticipated precipitation on Election Day was extremely large.

We test the hypothesis using the same model as Eq. (6) with an alternative definition of two time windows. All variables are defined in similar fashion to Eq. (6), but for this analysis, $C_1$ means the early voting period, while $C_2$ means Election Day. Thus, $\Delta T_{j1}$ denotes early voting turnout and $\Delta T_{j2}$ denotes Election Day turnout in municipality j. $\Delta P_{jt}$ denotes total precipitation during the last four days of the early voting period and on Election Day. We focus on the last four days of the early voting period because the typhoon in 2017 was predicted to reach Japan only a few days prior to Election Day (Fig. 2). We interact $C_1$ and $C_2$ with $\Delta D_j$ that measures differences in rainfall between the early voting period and Election Day. We calculate $\Delta D_j$ by subtracting total precipitation during the 4-day early voting period from total precipitation on Election Day for 2017 and 2014, and then taking the difference between the two election years.

We expect that $\beta _3$ is positive because voters, especially in municipalities with more severe weather disruptions on Election Day in 2017, were more likely to vote during the early voting period, compared to 2014. By contrast, $\beta _4$ is expected to be negative because many voters were more likely to avoid voting in heavy rain on Election Day in 2017.

This analysis relies on a similar identification assumption, as discussed in section ‘Turnout in the Morning vs. Afternoon of Election Day’. We assume that $C_t * \Delta D_j$ was quasi-randomly assigned to the municipalities. To control for political and socioeconomic variables potentially correlated with $C_t * \Delta D_j$, we include prefecture fixed effects.²⁹ In addition, we also include interactions between the time windows and local political and socioeconomic characteristics as additional controls.

Data on turnout are obtained from the JED-M database (Mori, 2015, 2018) and the election commissions of 47 prefectures. Early voting turnout and Election Day turnout are computed by dividing the number of eligible voters who cast a ballot before or on Election Day, by the total number of eligible voters in municipality j in each election year. The total number of observations is 3782 because the data include two time windows for 1891 municipalities. Summary statistics for precipitation and turnout are reported in Table 5.³⁰

Table 5 Summary statistics of differencess in precipitation and turnout between 2017 and 2014 during the early voting period and on Election Day

Results

Table 6 presents estimated results. Standard errors are clustered at the municipality level.³¹ Column (1) indicates that turnout during the early voting period increased 8.736 percentage point in 2017, compared to 2014. On the other hand, turnout on Election Day decreased by 4.418 percentage point in 2017. These coefficients suggest that many voters decided to use early voting instead of voting on Election Day. Column (2) shows the similar results even after the prefecture fixed effects are included.

Table 6 Differences in turnout between 2017 and 2014 during the early voting period and on Election Day in 1891 municipalities of 47 prefectures

Columns (3) and (4) of Table 6 show the main results. As hypothesized, the change in turnout during the early voting period depends on the difference in precipitation between two periods. The coefficient associated with the interaction between the early voting period and the difference in precipitation is positive, whereas the coefficient associated with the interaction between Election Day and the difference in precipitation is negative. These results suggest that the increase in early voting turnout and the decrease in Election Day turnout were larger in municipalities with heavier precipitation on Election Day. The results hold even when prefecture fixed effects are included. Column (4) suggests that early voting turnout increased additionally by 0.65 (= 0.013*50) percentage point, where rainfall was more than 50 mm heavier on Election Day than during the early voting period.

Table 6 also indicates that turnout decreased by 0.2–0.3 percentage point as precipitation increased by 10 mm. This last result appears consistent with some previous studies (e.g., Fujiwara et al., 2016; Gomez et al., 2007) showing the negative effect of bad weather on Election Day turnout. The coefficient suggests that municipalities experienced a decrease in turnout by about 1.0–1.5 percentage point where they received 50 mm of precipitation.

Table 7 presents the results after including additional controls. As in Table 3, we consider the possibility that the difference in precipitation between the early voting period and Election Day might be correlated with local political and socioeconomic characteristics. We add the interactions between the voting window dummies and the vote margin, the log of population, and the percentages of seniors and college graduates. Table 7 shows that the main coefficients show only a minor change after the additional interactions are included. This again suggests that the typhoon shock is likely to be independent of municipal characteristics.

Table 7 Differences in turnout between 2017 and 2014 during the early voting period and on Election Day with additional controls

Table 8 examines the possibility that precautionary voting was more likely to occur among senior voters. As in Table 4, we split the sample into two groups, below and above the median percentage of the voting-age population aged 65 and over in municipality j. Column (1) of Table 8 indicates that the interaction terms between each period and the difference in precipitation show no statistically significant coefficient when we focus on the municipalities with the smaller size of senior population. By contrast, column (2) shows strong evidence for precautionary voting in municipalities with more senior residents.³² This result, together with the earlier result in Table 7, might indicate that senior voters with a higher propensity to vote tended to compare the costs over time and shift the timing of voting.

Table 8 Differences in Turnout between 2017 and 2014 during the early voting period and on Election Day below and above the median of percentage 65 years and over

In summary, the findings are consistent with our hypothesis. Turnout during the early voting period increased and turnout on Election Day decreased in 2017, compared to 2014. This pattern was stronger in municipalities where rainfall on Election Day was stronger and more senior residents resided.

Consequences for Overall Turnout

Our final analysis examines the consequences of the typhoon in 2017 on overall turnout. Proposition 2 derived from the model predicts that overall turnout changes little if the voting cost in the first period is small and the voting cost in the second period is moderately large, as shown by the red solid curve in Fig. 1. This happens because voters are more likely to engage in precautionary voting when the anticipated cost in the second period is large. Contrarily, overall turnout may decrease when the anticipated cost in the second period is not much larger, because voters wait to vote until the second period and then abstain. As a result, decreased turnout in the second period is not offset by increased turnout in the first period.

The dataset described in the previous section is ideal to test this prediction because precipitation during the early voting period was small in both the 2014 and 2017 elections, whereas the change in precipitation on Election Day between 2014 and 2017 was large particularly for dozens of municipalities. We examine how changes in Election Day precipitation between 2017 and 2014 as a measure of the cost in the second period were associated with the changes in overall turnout including both early voting and Election Day turnout. The changes are measured for each municipality. We expect that Election Day precipitation is negatively correlated with overall turnout in municipalities where Election Day precipitation modestly increased in 2017, as compared to 2014. We also expect that this negative relationship disappears in municipalities where Election Day precipitation considerably increased 2017 due to the typhoon.

Figure 5 plots changes in overall turnout against changes in Election Day precipitation between 2017 and 2014. We capture an overall relationship by adding a locally weighted regression curve in gray to the plot. Figure 5 shows two important patterns. First, the small to medium increases in Election Day precipitation (i.e., from 0 to 150 mm), as shown on the left side of the plot, were associated with a decline in overall turnout. However, the relationship between them was flat where the change in Election Day precipitation was much larger (i.e., from 150 to 300 mm), as shown on the right side of the plot. Municipalities where Election Day precipitation increased from 150 to 300 mm in 2017, as compared to 2014, exhibits no decline in overall turnout. Notably, the overall shape of the relationship is quite similar to the simulated red solid curve in Fig. 1 with a small cost in Period 1. In short, overall turnout does not necessarily decrease even as the voting cost increases, which is plausibly explained by precautionary voting.

Fig. 5

Changes in Election Day precipitation and overall turnout between 2017 and 2014. Notes Changes in overall turnout and Election Day precipitation between 2017 and 2014 are measured for each municipality

Conclusion

This study proposes a model to consider the inter-temporal decision-making of voting, in which voters decide when to vote, by comparing the varying benefits and costs during the time that the polls are open. We argue that the conventional Downsian model of turnout is not suitable to analyze the possibility that voters shift the timing of voting. Our stylized dynamic model of turnout predicts that turnout in each period changes as the relative costs between the two periods change. The model also predicts that, contrary to the conventional turnout model, overall turnout does not necessarily decrease even as the cost increases.

This prediction is tested using data for rainfall and turnout in the Japanese General Elections of 2014 and 2017. Using panel data from municipalities, we find evidence for our hypothesis that voters shift the timing to avoid the higher cost. This pattern was stronger in municipalities with more rainfall in the latter period and with more senior voters. These findings explain why voter turnout remained similar in the 2017 election with the greater costs of voting, compared to the 2014 election.

This study contributes to the literature in several ways. First, our model that considers turnout during the election as an inter-temporal dynamic problem can serve as a benchmark to understand the decision of when and whether voters turn out as costs vary temporally. Our model can apply to various types of costs that vary during the voting window. For example, the serious pandemic during the 2020 U.S. presidential election increased the cost of in-person voting on Election Day, which might explain why the historic number of voters chose to use early or mail voting. Alternatively, if elections are scheduled on weekday, a scheduling conflict may induce many voters to vote early. Most importantly, our theory is useful to understand the pattern of voter turnout when voters can predict temporal variations in the voting costs.

Second, we reveal that the relationship between the voting cost and voter turnout is not as simple as supposed in the literature. Turnout does not always decrease even as the cost increases because voters can shift the timing of voting.

Third, our findings imply what type of voters are more likely to engage in early (thus precautionary) voting, which might explain why the findings in the previous research are mixed. Early voting is expected to provide more voting opportunities for non-regular voters, but it does not necessarily encourage them to compare the voting costs during the election period. As Ashok et al. (2016) reported that older voters and party registrants are more likely to vote early than on Election Day in the U.S., early voting may only shift the timing of voting among those with the higher propensity to vote and retain their active participation. In combination with the findings about planning for voting (Nickerson & Rogers, 2009), we may stimulate participation among less active voters by encouraging them to compare costs during the voting period and to think about voting early if anticipated costs are high on Election Day. This is left for future research.

Revising the traditional view that voting is a static decision creates new opportunities for research. The literature in behavioral economics has developed theories on time preferences, such as present bias (O’Donoghue & Rabin, 1999). If voters have present-biased preferences, for example, they tend to procrastinate costs. Thus, if voting is costly, they tend not to go to the polling station until the very end of the election period, and most likely, they abstain. Although we cannot distinguish present-biased voters from other types of voters in our data, the magnitude of precautionary voting could be larger if there are fewer naive present-biased voters. Additionally, procrastination might explain why young voters and independents were more likely to vote on Election Day (Ashok et al., 2016). These groups with the low propensity tend to vote later or abstain not only because they may face the higher cost but also because they may be present-biased.

Finally, our findings relate to the literature on the relationship between turnout and election outcomes. Rainfall on Election Day tends to benefit the Republican Party in the U.S. presidential election because the negative effect of rainfall on turnout is larger on Democratic supporters (Gomez et al., 2007) and rainfall may change voters’ risk preferences and lead them to embracing more conservative views (Horiuchi & Kang, 2018). If convenience voting may only shift the timing of voting among voters with particular ideological views, their active participation may affect party vote shares (see Barber & Holbein, 2020; Thompson et al., 2020). Alternatively, severe weather disruptions like the typhoon in this study may also change voters’ political preferences. The relationship between weather disruptions, the timing of voting, and election outcomes is an important topic for future research.