We conducted 9 sessions in each treatment with a total number of 345 subjects (175 in NIA and 170 in IA). Around 61% of the subjects had past political experience and had voted in at least one election in the past. Of the 345 students, 172 (roughly half) identified as female. Three rounds from the main experiment and one of the post-experiment tests were randomly chosen for payment. Additionally, there was a show up fee of 6 euros. The experiment lasted 90 minutes and the average payoff was 22 euros. We now turn to the various hypotheses.
Selection versus retrospection
First we address the hypothesis on selection. A first result is that voters are more likely to vote for the incumbent when there is a selection incentive (in IA) than when there isn’t (in NIA), conditional on the transfers received. Figure 1 provides descriptive evidence. The four pairs of columns show the shares of voters who voted for the incumbent for each of the transfer amount received. Light grey bars represent the NIA treatment (left column) and the dark grey bars represent the IA treatment (right column). For all four possible levels of own receipts, voters are significantly more inclined to vote for the incumbent in IA than NIA (tests of equality of means done using Wilcoxon rank sum tests, \(p<0.001\)). The difference between the treatments are larger for own receipts of 0 and 30 taler and the gap closes down for own receipts of 40 and 60 taler.
Table 3 Effects of selection incentive, own receipts and level of accountability on voting for the incumbent Table 3 provides the regression analysis where the dependent variable, ‘vote for the incumbent’, is binary and takes value 1 if the vote is for the incumbent and 0 if it is for the challenger. Here, we report the results from an OLS regression for ease of interpretation but they are in line with the results from probit regression (marginal effects are reported in the online appendix). We use standard errors clustered at the individual level.Footnote 12 Column (1) indicates a significant treatment effect—voters are more likely to vote for the incumbent when there is an incumbency advantage, that is, voters have a selection incentive irrespective. This is true controlling for the transfers received by the voters. As predicted by the theory on the dominant role of selection incentives, even the quantitatively small selection incentive that is caused by the incumbency advantage has a clear treatment effect that has the predicted sign and is significant. We summarize this result as the selection result.
Selection result
For any given allocation choice of the incumbents, the voters are more likely to vote for the incumbent when there is an incumbency advantage.
Next we turn to the hypothesis on retrospective voting. Column (1) of Table 3 shows that a voter’s probability of voting for the incumbent rises with the transfer amount received by this voter. Column (2) repeats the same estimation with controls. Column (3) adds accountability levels to the regression. We define full accountability as when the incumbent does not keep any of the budget and distributes everything. Partial accountability is when the incumbent keeps a part of the budget for herself and transfers the rest to all or some of the voters. A case of no accountability is when the incumbent panders all of the budget for herself. From the Table 3, other things being equal, compared to no accountability, partial accountability of the incumbent increases the probability of voters voting for the incumbent by 13 percentage points and full accountability raises it by 16.8 percentage points. Voters who get 0 taler are more likely to vote for the challenger than the incumbent (Fig. 1). However, as the own receipts increase from 0 to 30 taler, voters are more likely to vote for the incumbent in both treatments. This holds for own transfers of 40 and 60 taler although the probability of voting for the incumbent is the highest when the transfers are 40 taler in both the treatments.
A closer look at the voters who receive 0 taler reveals that in addition to own receipts, the voters pay attention to the amount received by the other two voters and how accountable the incumbent was in stage 1 (Fig. 2, first three sets of bars). In the no accountability case of option 1 [120;(0,0,0)] the voters who receive 0 taler overwhelmingly vote for the challenger in both treatments (only 3.93% of the voters vote for the incumbent in NIA and 15.48% in IA). In the partial accountability case of option 4 [60;(30,30,0)] 5.48% of the voters who receive 0 taler vote for the incumbent in NIA and 19.64% in IA. In the full accountability case of option 3 [0;(60,60,0)] this increases to 19.52% in NIA and 30% in IA, indicating that more voters are willing to vote for the incumbent when the incumbent was fully accountable than when she was not, irrespective of their own receipt.
A similar pattern can be observed for voters who receive 30 taler (Fig. 2, last two sets of bars). In the partial accountability case of option 2 [30;(30,30,30)], 70.36% of the voters who receive 30 taler vote for the incumbent in NIA and that increases to 85.83% in IA. However, in the lower accountability situation of option 4 [60;(30,30,0)] the percentage of voters voting for the incumbent is lower in both treatments (39.88% in NIA and 51.43% in IA).
Retrospective voting result
In both treatments, voters are more likely to vote for the incumbents when incumbents behave more accountably.
So far the results can be seen as qualitatively in line with both a mild version of the selection hypothesis of Fearon (1999) and a mild version of the retrospective voting hypothesis of Ferejohn (1986). Both types of considerations are seemingly relevant for the voting decision and none of them dominates the other in a strict sense.
Pivotality
The theory analysis in Sect. 2 highlighted pivotality beliefs of voters and their potential key role for voting behavior. Beliefs about pivotality should be an element in voters’ decision making in the context of majority voting. The argument that the selection motive should dominate all other considerations becomes less compelling when voters’ pivotality is endogenous. Voting in line with the selection motive has a selection benefit only if the voter is pivotal. As seen by Proposition 1, this consideration opened up for a wealth of different voting behaviors that can be seen as equilibrium behavior, where some of these behaviors may be seen as more plausible than others from a theory perspective of equilibrium refinement.
These considerations led to the Pivotality hypothesis as well as the Favored majorities hypothesis. We now turn to the data analysis on these hypotheses.
Before we relate voters’ pivotality beliefs with their electoral choices, we consider these pivotality beliefs and their distribution. A voter needs to form beliefs about other voters’ electoral choices to evaluate their own pivotal probability in the election outcome. For a theory of this belief formation, one can draw on what psychologists call the theory of social projection (see, e.g., Marks and Miller 1987): a voter forms an own belief and projects this way of belief formation onto the other voters. Voters might believe that their own ways of how they form their beliefs is no different from how most of the other voters form their beliefs. A voter is pivotal in our context if exactly half of the remaining voters vote for incumbent and the other half vote for the challenger.
If a voter A is confronted with two other voters B and C who receive identical transfers this may induce the belief that it is more likely that they make the same decision; hence A is unlikely to be pivotal. If B and C are treated differently—say B receives transfers from the incumbent and not C, it appears less likely that they make identical electoral decisions; hence, A is more likely to be pivotal. For the budget allocations that attribute positive and identical amounts to two of the voters and zero to a third voter, in the equilibrium the voter who receives zero anticipates that he is not pivotal—and also observes that the two other voters receive identical amounts. Instead, each of the voters who receives a positive amount anticipates that he is pivotal—and also observes that the other two voters do not receive identical amounts.
This leads us to a prediction about voters’ pivotality beliefs as a function of the transfers \(x_{voter1},x_{voter2}\) and \(x_{voter3}\) which is expressed in the Table 4. The table also provides the overview of voters’ stated pivotality beliefs. It shows that the stated pivotality beliefs are, in fact, correlated with the predictions emerging from these considerations. The correlation between the stated pivotality beliefs and actual pivotality is also positive (Spearman’s correlation coefficient is 0.1338 with \(p <0.001\) from 8273 observations.Footnote 13)
Table 4 Overview of pivotality beliefs According to this line of thought, we would expect the likelihood that all voters vote identically is higher for symmetric allocations than for the asymmetric allocations. If all voters vote identically, we define the outcome to be a super-majority. A super-majority for the incumbent is when the incumbent receives all three votes and a super-majority for the challenger is when the challenger receives all three votes. The outcomes in symmetric allocations of option 1 [120;(0,0,0)], option 2 [30;(30,30,30)] and option 5 [0;(40,40,40)] would be super-majorities and the asymmetric allocations of option 3 [0;(60,60,0)] and option 4 [60;(30,30,0)] would not be super-majorities.
This can indeed be observed in the data. We can see that 75% of the cases option 1 [120;(0,0,0)] is chosen result in a super-majority for the challenger, while 52% of cases in option 2 [30;(30,30,30)] and 84% of cases in option 5 [0;(40,40,40)] result in a super-majority for the incumbent. Figure 3 graphically represents this.
Next we compare voting for the incumbent as a function of own pivotality beliefs, for the two treatments. We hypothesize that the effect of the incumbency advantage is stronger if the voter believes that he is pivotal. Table 5 looks at this analysis. Simply believing to be pivotal does not affect voting behavior. Being in the incumbency advantage treatment increases the decision to vote for the incumbent by 11.4 percentage points (Column (6)). However, the interaction between IA treatment and belief \(=\) pivotal is not significant as indicated in Column (8). This result does not change qualitatively if we control for the transfers received by the voters and use a slightly different specification (Table 6).
Table 5 Effects of pivotality beliefs on voting for the incumbent Table 6 Effects of pivotality beliefs on voting for the incumbent for each of the strategy cases
Pivotality result
Voters who believe they are pivotal are not more likely to vote for the incumbent when there is a selection incentive.
To look at why we do not find evidence for this hypothesis, we look at how the beliefs are formed. While voters’ pivotality beliefs and actual pivotality are correlated in the data, we also have a hypothesis on how beliefs depend on the allocation vector chosen by the incumbent and voters’ own share of the transfers received. The favored majorities hypothesis states that voters who belong to the favored majority expect to have a higher probability of being pivotal than voters in the less favored minority. We test this by looking at the effect of being the recipient of the non-zero amounts in option 3 [0;(60,60,0)] and option 4 [60;(30,30,0)] on the pivotality belief. The voters who receive 60 taler in option 3 and 30 taler in option 4 belong to the favored majority and the voters who receive 0 taler in these options are in the less favored minority.
Table 7 Effects of being in the favored majority on pivotality beliefs Table 7 reports these results. Pivotality beliefs are affected by whether the voter is in the favored majority or not (Column (1)). Being in the favored majority increases the probability of a voter believing to be pivotal by 43.7 percentage points.
Favored majorities result
Voters receiving a positive transfer and belonging to the favored majority are more likely to expect to be pivotal than voters who are in the less favored minority.
Pivotality beliefs are not affected by the treatment manipulation, i.e., whether there is an incumbency advantage or not (Column (2)). However, the interaction term between the favored majority and the treatment indicator (IA) has a coefficient of 0.117 and is significant at the 5% level. This indicates that voters in the favored majority in the IA treatment are 11.7 percentage points more likely to believe to be pivotal. This implies that beliefs are not entirely independent of the treatment manipulation. This could be a potential reason why we do not observe selection incentive being stronger on voters who believe to be pivotal. The selection incentive and pivotality beliefs interact in our data.
Incumbents and accountability
We now turn to the decisions made by incumbents. Given that voters react differently in the two treatments to the allocation choices made by the politician, one might expect that the incumbent behavior also differs in the two treatments.
Evidence for the decreasing accountability hypothesis is obtained by looking at the average transfers observed in the two treatments. The transfers chosen by the incumbents averaged 91 taler in NIA and 88 taler in IA. The transfers are statistically different in the two treatments (Wilcoxon rank-sum test: \(p<0.001\)).
Though the transfers in IA are lower than NIA, roughly three quarters of the budget is allocated to the voters by the incumbent in IA. The incumbents appear to take the retrospective voting into account even when there is a selection incentive.
There are also differences in the allocation vectors chosen by the incumbent as indicated by Fig. 4. Interestingly, both of the full accountability options see a drop in the IA treatment compared to the NIA treatment. There is a corresponding increase in the partial accountability options in the IA treatment compared to the NIA treatment. The fall in full accountability options is not seen to co-exist with a rise in the no accountability option of [120;(0,0,0)], but rather with a rise in the partial accountability options. This implies that even in the presence of a selection incentive, some accountability is retained.
It is also important to note that 45% of incumbents transfer the entire budget to the voters when there is no incumbency advantage in an attempt to win them over. In comparison only 28% of incumbents transfer the entire budget when there is an incumbency advantage. This indicates that the subjects in IA seem to understand that they have a large leeway to allocate a part of the budget to themselves.
Table 8 Expected payoff of incumbents Voters’ behavior is not deterministic, but the results revealed some patterns. Incumbents who observe these patterns might choose budget allocations that maximize their payoffs given these patterns. In fact, calculating the ex-post expected earnings from choosing each allocation vector using the voting probabilities indicates that incumbents are able to exploit this pattern. Table 8 displays the expected payoffs of the incumbents for each allocation vector calculated using the re-election probabilities from the data. It shows that incumbents choose the budget allocations that give them a higher expected payoff with a higher probability.
Decreasing accountability result
When there is an incumbency advantage the incumbent behaves less accountably compared to the case of no incumbency advantage. However, some degree of accountability is retained even when there is a selection incentive.
Figure 5 indicates the re-election probabilities of the incumbents for each allocation vector they choose. It differs for the two treatments. In NIA treatment, the highest probability of re-election is for the allocation vector [0;(40,40,40)]. Here the incumbent distributes the entire budget to the voters and hence is a case of full accountability. The second highest probability is for allocation vector [0;(60,60,0)], again an option of full accountability. The partial accountability options of [30;(30,30,30)] and [60;(30,30,0)] are preferred in this order after the former two.
In case of IA, the incumbents have the highest probability of getting re-elected when the allocation vector is [0;(40,40,40)]. Incumbents choosing the vector [30;(30,30,30)] has the next highest probability of re-election. This is followed by allocation vectors [0;(60,60,0)] and [60;(30,30,0)].
Incumbents deciding to appropriate the entire budget of 120 taler do not get re-elected even with the induced incumbency advantage. The difference between the two treatments is seen on the two partial accountability cases of [60;(30,30,0)] and [30;(30,30,30)]. When there is a selection incentive voters are more likely to re-elect the incumbents who are only partially accountable than in the baseline treatment. The re-election probability of an incumbent choosing [60;(30,30,0)] increases from 20 to 41% as a result of the treatment. For an incumbent choosing [30;(30,30,30)] this increases from 70% to nearly 97%. This indicates that voters do not press for full accountability when there is a selection incentive. On the other hand the selection incentive does not bite to the extent that they are willing to re-elect an incumbent who retains the entire budget. Accountability does not disappear entirely in the presence of a selection motive.