RELATED LITERATURE

Vagueness or ambiguity in political campaigning has spurred a number of theories that rationalize ambiguous platforms since Downs (Reference Downs1957a; Reference Downs1957b). Early contributions require risk-seeking preferences of voters to support ambiguous platforms (Aragones and Postlewaite Reference Aragones and Postlewaite2002; Glazer Reference Glazer1990; Page Reference Page1976; Shepsle Reference Shepsle1970; Reference Shepsle1972) or appeal to behavioral assumptions such as context-dependent preferences of voters (Callander and Wilson Reference Callander and Wilson2008). Compared with these papers, we show that ambiguity can arise even with rational and risk averse agents. In other words, behavioral biases or uncommon risk preferences are not necessary for explaining the ubiquity of ambiguous platforms. In our model, which shares the assumption regarding the correlation of preferences with Goeree and Grosser (Reference Goeree and Grosser2007), citizens can infer from their own preference type the probability of candidates being of the same type. Consequently, ambiguous candidates can simultaneously appeal to opposing risk-averse and rational voter groups by not being clear about their policy preferences.

In another strand of the theoretical literature, ambiguity arises as a response to different dynamic concerns. Generally, ambiguity either serves as a way for the candidate to hide her true preferences in the early rounds of the game or allows politicians to readjust policies to future information. Prominent examples of the first group of papers include Alesina and Cukierman (Reference Alesina and Cukierman1990), where politicians hold reelection concerns, and Alesina and Holden (Reference Alesina and Holden2008), who consider ambiguous platforms when there are campaign contributions that affect the position of the median voter. Examples of the second group of papers include Aragones and Neeman (Reference Aragones and Neeman2000), Meirowitz (Reference Meirowitz2005), and Kartik, Van Weelden, and Wolton (Reference Kartik, Van Weelden and Wolton2017). In the first paper ambiguity allows candidates to react to arriving information about the most expedient policy; in the second, primaries convey information about the preferences of the electorate and in the last one ambiguous platforms allow politicians to adjust policies to future policy-relevant information. Our model explains ambiguity in situations where there are no external forces such as reelection concerns or anticipated arrival of policy-relevant information that motivate ambiguity.

To the best of our knowledge, our paper is the first to use a laboratory experiment guided by a theoretical model to identify causal forces that can generate ambiguous platforms. In general, empirical evidence for any of the above theoretical explanations for ambiguous policies is scant and existing empirical studies are only loosely guided by theory. Our experiment is closely related to the survey experiment of Tomz and Van Houweling (Reference Tomz and Van Houweling2009), which studies voter responses to ambiguous policies conditional on different levels of self-reported partisanship. Compared with hypothetical survey responses, we test equilibrium predictions of candidate and voter behavior with financially incentivized choices. To identify causal effects, we need to consider both sides of the strategic interaction simultaneously. Otherwise we cannot tell whether an increase in the prevalence of ambiguous strategies is ultimately due to a change in candidate or voter behavior, as each will affect the other. Furthermore, our experiment uses neutral framing (labeling) of policies to isolate the strategic decision-making process from effects driven by political connotations or partisanship that potentially blur the strategic incentives underlying ambiguous platforms.Footnote ⁹

Somer-Topcu (Reference Somer-Topcu2015) and Rogowski and Tucker (Reference Rogowski and Tucker2018) investigate empirically how voters react to wide-appeal strategies of candidates and arrive at contradicting results regarding voter support (higher in the former and lower in the latter). Insights from our equilibrium model can explain these apparently contradicting findings. In particular, we show how the popularity of the wide-appeal strategy depends critically on the platform of the opposing candidate, the polarization of preferences, and the beliefs that voters hold about candidates. Milita, Ryan, and Simas (Reference Milita, Ryan and Simas2014) evaluate the clarity of US House candidates’ positions on the Iraq War and gay marriage and find, consistent with our model, that minority candidates are more likely to be ambiguous or silent on an issue compared with more popular candidates. Furthermore, they do not find support for their hypothesis that ambiguity should increase for minority candidates the more salient the issue becomes on average. This can be explained within our model because what we predict to matter is how much the minority voters dislike the centrist position. If the centrists in our model rank an issue very low on importance, the average salience can remain low while noncentrist candidates may still find it appealing to choose an ambiguous stance. Supporting this idea, Bräuninger and Giger (Reference Bräuninger and Giger2018) use electoral manifesto data from European parties to show that platforms become more ambiguous when preferences in the population diverge. Similarly, Han (Reference Han2020) provides empirical evidence for a number of European countries that candidates campaign more ambiguously if their own supporters are polarized on an issue, consistent with our theory. In summary, our model helps to organize many of the previous empirical findings on strategic ambiguity.

Finally, our study also contributes to the recently burgeoning behavioral literature on the effects of biased information processing on political behavior. Levy and Razin (Reference Levy and Razin2015a) demonstrate theoretically that the inability to understand the correlation between news sources can lead voters in elections to aggregate information better. In a related work, Levy and Razin (Reference Levy and Razin2015b) investigate conditions under which polarized opinions of voters lead to more extreme policies on the part of politicians. We show how neglecting correlations can influence elections not only through information aggregation (Levy and Razin Reference Levy and Razin2015a; Reference Levy and Razin2015b) but also through preference aggregation by potentially reducing the viability of ambiguous platforms.

AMBIGUOUS PLATFORMS: THEORY AND HYPOTHESES

In this section we first lay out the game-theoretic model that provides the foundation for our laboratory experiment. We then state the hypotheses we will test, which are based on our theoretical predictions as well as behavioral considerations.

Theory

Here we describe a model of electoral competition that allows for ambiguous platforms. It is based on Tolvanen (Reference Tolvanen2020), simplified to make it amenable for implementation in a laboratory experiment while maintaining the primary theoretical insights that the original paper demonstrates, with less restrictive assumptions. We first give a detailed verbal description of the model and its implications, then we provide a formal exposition.

We begin with a citizen-candidate setup (Besley and Coate Reference Besley and Coate1997; Osborne and Slivinski Reference Osborne and Slivinski1996) where two candidates drawn from the general population compete for votes in a one-dimensional policy space. Each candidate’s primary concern is implementing their preferred policy, outweighing the benefits of any perks of office. One of three possible policies can be implemented. For ease of exposition, we use the traditional political left–right spectrum and refer to these policies as “leftist,” “centrist,” and “rightist.” However, the model applies more generally to any election where preferences over an issue can be ordered in a single dimension.

Preferences over the policies vary across the population: Noncentrist voters (and thus candidates) like their “own” policy the most and the policy of the other end of the spectrum the least. Centrists are assumed to strictly prefer the centrist policy over either noncentrist policy, and they are indifferent between left and right policies. Candidates can run on four possible platforms. They can guarantee to implement one of the three policies, or they can run on an ambiguous platform whereby they promise to implement a noncentrist policy without specifying whether it will be leftist or rightist. For simplicity, we assume that candidates make good on their promise.

A novel feature of the model is that citizens (both voters and candidates) are uncertain over the distribution of preferences in society and these preferences are correlated with each other. All citizens understand that society is polarized, in the sense that noncentrists outnumber centrists, but do not know whether leftists outnumber rightists or vice-versa. It is also known that neither leftists nor rightists hold a majority on their own. Voters only know for certain their own political preferences. Note that in the model we speak of individual voters, but these individual agents could equally represent cohesive groups, such as communities or networks of friends, who share political views. The correlation between voter and candidate preferences in our model comes from the fact that voter and candidate preferences are drawn from the same (uncertain) distribution.

A first important remark is that a centrist policy is best for society as a whole in the sense that a majority of voters prefers this over either of the other policies. Furthermore, a candidate running on a centrist platform will always win against a nonambiguous noncentrist platform, as the centrists will unite with the opposing noncentrists to form a simple majority. However, an ambiguous platform can beat a centrist platform. The reason for this is that voters rationally update their beliefs about whether leftists or rightists are in the majority by using their own preferences as information about the true distribution: if they have leftist/rightist preferences, Bayes’ rule dictates that, given this information, it is more likely that leftists/rightists are in the majority. If all noncentrists believe that both leftist and rightist candidates run on ambiguous platforms, then they should believe that it is more likely that a candidate running on an ambiguous platform will share their own preferences and ultimately implement their preferred policy. Thus, the ambiguous platform gains support from both the left and the right.

If, as so far assumed, both candidates’ true preferences are unknown, the model permits other possible outcomes. For example, it may be the case that voters believe that only one type of noncentrist candidate uses ambiguous platforms but the other type guarantees to implement her genuinely preferred policy. The idea that voters believe only candidates of opposite political views use ambiguous platforms has a certain behavioral appeal if running on such a platform has negative connotations in the eyes of some voters. In this case, ambiguous platforms can still win on occasion but will be less common, less popular, and lose to a centrist platform. This motivates our treatment variation in the laboratory experiment. If one of the two candidates’ preferences are known in advance to be centrist, the only way a noncentrist can win is by using an ambiguous platform. Therefore, we predict that ambiguous platforms will be more common and more popular in the presence of a known centrist candidate.

The model shows clearly that the use of ambiguous platforms has a negative effect on aggregate voter welfare. Compared with a situation where all candidates commit to a particular policy, only noncentrists with the same preferences as the ambiguous candidate benefit. Because, by assumption, centrists and one noncentrist group together always form a majority, voters who benefit from ambiguous platforms are always in a minority. Ambiguous platforms can thus considerably weaken democratic decision making and its ability to implement majoritarian preference aggregation. Additionally, a minority group that supported the winning ambiguous campaign will always feel deceived because they will see their least-preferred policy realized instead of the ambiguously “promised” preferred one. Consequently, successful ambiguous policies also undermine trust in democratic voting procedures for a significant fraction of voters.

Formal Model: Players, preferences, and information. There is a population of N voters and two candidates, with N being an odd number. Candidates and voters can be of three different types $ \tau \hskip1.5pt \in \hskip1.5pt \left\{-\mathrm{1,0,1}\right\} $ . The type of a voter or candidate represents her most preferred policy.

We refer to preference type –1 as “leftist,” type 0 as “centrist,” type 1 as “rightist,” and sometimes call noncentrists simply “noncentrists.”

Preferences of noncentrists are given by

$$ u\left(a\hskip1.5pt =\hskip1.5pt -1,\tau \hskip1.5pt =\hskip1.5pt -1\right)\hskip1.5pt =\hskip1.5pt u\left(a\hskip1.5pt =\hskip1.5pt 1,\tau \hskip1.5pt =\hskip1.5pt 1\right)\hskip1.5pt =\hskip1.5pt 1, $$

$ \hskip3pc u\left(a\hskip1.5pt =\hskip1.5pt 1,\tau \hskip1.5pt =\hskip1.5pt -1\right)\hskip1.5pt =\hskip1.5pt u\left(a\hskip1.5pt =\hskip1.5pt -1,\tau \hskip1.5pt =\hskip1.5pt 1\right)\hskip1.5pt =\hskip1.5pt 0, $ and

$$ u\left(a\hskip1.5pt =\hskip1.5pt 0,\tau \hskip1.5pt =\hskip1.5pt -1\right)\hskip1.5pt =\hskip1.5pt u\left(a\hskip1.5pt =\hskip1.5pt 0,\tau \hskip1.5pt =\hskip1.5pt 1\right)\hskip1.5pt =\hskip1.5pt {u}_0, $$

where $ a\hskip1.5pt =\hskip1.5pt \left\{-\mathrm{1,0,1}\right\} $ is the implemented policy and $ {u}_0\hskip1.5pt \in \hskip1.5pt \left(0,1\right) $ captures how strongly the noncentrists, left or right, dislike the centrist policy as well as how risk-averse they are. For example, if $ {u}_0>1/2 $ , then both rightist and leftist agents prefer the centrist policy to a 50/50 gamble between the two noncentrist policies. Preferences of centrists are given by

$ \hskip5pc u\left(a\hskip1.5pt =\hskip1.5pt 0,\tau \hskip1.5pt =\hskip1.5pt 0\right)\hskip1.5pt =\hskip1.5pt {u}_1>0 $ and

$$ u\left(a\hskip1.5pt =\hskip1.5pt 1,\tau \hskip1.5pt =\hskip1.5pt 0\right)\hskip1.5pt =\hskip1.5pt u\left(a\hskip1.5pt =\hskip1.5pt -1,\tau \hskip1.5pt =\hskip1.5pt 0\right)\hskip1.5pt =\hskip1.5pt 0. $$

In state L (R) a fraction p of the voters are leftists (rightists), a fraction q of the voters are rightists (leftists), and the remaining 1 – p – q voters are centrists. Assume $ 0<q<p<\frac{1}{2} $ and $ p+q>\frac{1}{2} $ , which guarantees that none of the three preference types holds a majority alone. The latter inequality implies also that united, supporters of opposing ends of the spectrum hold a simple majority.

The type of each candidate $ c\hskip1.5pt \in \hskip1.5pt \left\{1,2\right\} $ is drawn from a distribution equivalent to the realized distribution of voters. To be precise, conditional on the state, candidate types are distributed independently according to

$$ \mathrm{\mathbb{P}}\left({\tau}_c\hskip1.5pt =\hskip1.5pt -1|L\right)\hskip1.5pt =\hskip1.5pt \mathrm{\mathbb{P}}\left({\tau}_c\hskip1.5pt =\hskip1.5pt 1|R\right)\hskip1.5pt =\hskip1.5pt p, $$

$$ \mathrm{\mathbb{P}}\left({\tau}_c\hskip1.5pt =\hskip1.5pt -1|R\right)\hskip1.5pt =\hskip1.5pt \mathrm{\mathbb{P}}\left({\tau}_c\hskip1.5pt =\hskip1.5pt 1|L\right)\hskip1.5pt =\hskip1.5pt q,\mathrm{and} $$

$$ \mathrm{\mathbb{P}}\left({\tau}_c\hskip1.5pt =\hskip1.5pt 0|R\right)\hskip1.5pt =\hskip1.5pt \mathrm{\mathbb{P}}\left({\tau}_c\hskip1.5pt =\hskip1.5pt 0|L\right)\hskip1.5pt =\hskip1.5pt 1-p-q. $$

Each candidate and voter learns her own type privately but does not know the realized state of world.

Timing and decisions in voting game. The timing of the game is given in Figure 2. First, nature chooses the state of the world and each citizen is assigned a preference type, which is private information. Then, both candidates simultaneously choose a platform from the set $ \mathcal{A}\hskip1.5pt =\hskip1.5pt \left\{\left\{-1\right\},\left\{0\right\},\left\{1\right\},\left\{-1,1\right\}\right\} $ . A singleton platform, $ A\hskip1.5pt \in \hskip1.5pt \left\{\left\{-1\right\},\left\{0\right\},\left\{1\right\}\right\} $ , represents a candidate’s commitment to a particular policy, whereas the ambiguous platform, $ A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ , is deliberately vague about which of the two noncentrist policies the candidate will implement if she wins the election. A candidate who runs on an ambiguous platform only commits not to implement the status quo centrist policy in case of winning. After observing the proposed platforms, voters decide which candidate wins the election by simple majority voting. If the winning candidate ran with a singleton platform, that policy is implemented and the type-dependent utilities for voters and candidates are realized. If the winning candidate ran on an ambiguous platform, she chooses which policy $ a\hskip1.5pt \in \hskip1.5pt A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ is implemented.

Results. We use perfect Bayesian equilibrium to derive the theoretical predictions of the model that underlie our main experimental hypotheses; all proofs are relegated to the Appendix. Notice first that the following version of the standard Median Voter Theorem holds in our setting.

Remark 1. If one candidate runs with platform $ {A}_1\hskip1.5pt =\hskip1.5pt \left\{0\right\} $ and the other runs with $ {A}_2\hskip1.5pt \in \hskip1.5pt \left\{\left\{-1\right\},\left\{0\right\},\left\{1\right\}\right\} $ , then the centrist policy is always implemented in any perfect Bayesian equilibrium.

In other words, a noncentrist candidate (leftist or rightist) has no hope of winning by committing to a noncentrist policy against a centrist in our setup. The result follows simply because the centrists together with the opposing noncentrists will vote for the centrist candidate and these two groups form a simple majority (cf. Downs Reference Downs1957b). In contrast, the main result from Tolvanen (Reference Tolvanen2020) shows that rational noncentrist voters of both ends can unite behind an ambiguous candidate to beat a centrist opponent as long as the benefit from the centrist policy is not too high compared with the correlation between candidates’ and voters’ preferences. Within our model, this insight can be stated as follows.

Proposition 1. If $ {u}_0<\frac{p^2+{q}^2}{{\left(p+q\right)}^2} $ , there exists a perfect Bayesian equilibrium where candidates of type $ \tau \hskip1.5pt \in \hskip1.5pt \left\{-1,1\right\} $ choose the ambiguous platform $ A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ and all centrists run on $ A\hskip1.5pt =\hskip1.5pt \left\{0\right\} $ . In this equilibrium, an ambiguous noncentrist candidate always wins against a centrist one.

If both types of noncentrist candidates are ex ante equally likely to play the ambiguous platform $ A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ , then, for example, a rational leftist voter (type $ \tau \hskip1.5pt =\hskip1.5pt -1 $ ) faced with the choice between $ A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ and $ A\hskip1.5pt =\hskip1.5pt \left\{0\right\} $ would understand that, conditional on her preference type, the state of the world is more likely L than R. Because candidates’ preferences are also correlated with the state, it follows that a leftist voter believes that an ambiguous candidate’s type is more likely to be $ \tau \hskip1.5pt =\hskip1.5pt -1 $ than $ \tau \hskip1.5pt =\hskip1.5pt 1 $ . Now, the probability that the ambiguous candidate is a leftist conditional on the voter’s type being $ \tau \hskip1.5pt =\hskip1.5pt -1 $ is $ \frac{p^2+{q}^2}{{\left(p+q\right)}^2} $ . Thus, her expected utility from the ambiguous noncentrist is $ \frac{p^2+{q}^2}{{\left(p+q\right)}^2} $ , and as long as this is more than the guaranteed outside option $ {u}_0 $ from the centrist policy, the leftist voter will vote for the ambiguous candidate. By symmetry, the same logic holds for rightist voters (type $ \tau \hskip1.5pt =\hskip1.5pt 1 $ ), and thus both types of noncentrist voters will vote for the ambiguous candidate in equilibrium. For the same values of $ {u}_0 $ , there exist also equilibria where all candidates play fully revealing strategies. This result is summarized in the following proposition.

Proposition 2. For each candidate $ c\hskip1.5pt \in \hskip1.5pt \left\{1,2\right\} $ , let $ {\tau}_c $ be the candidate’s type. Then, each candidate committing to a truthful platform, $ A\hskip1.5pt =\hskip1.5pt \left\{{\tau}_c\right\} $ , is part of a perfect Bayesian equilibrium if $ {u}_0\le \frac{p^2+{q}^2}{{\left(p+q\right)}^2} $ , and this condition is tight if centrist voters have a strict preference over the two noncentrist policies. If this equilibrium is played and a candidate proposes the centrist platform, the centrist policy will be implemented.

Similarly, all rightist (leftist) candidates playing $ A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ and all leftist (rightist) candidates playing $ A\hskip1.5pt =\hskip1.5pt \left\{-1\right\} $ ( $ A\hskip1.5pt =\hskip1.5pt \left\{1\right\} $ , respectively, while centrists play $ A\hskip1.5pt =\hskip1.5pt \left\{0\right\} $ , is consistent with a perfect Bayesian equilibrium under the same condition on $ {u}_0 $ . All of these equilibria are outcome equivalent and vary only in the equilibrium path beliefs that voters attach to ambiguous platforms. The voters do not believe the ambiguity in the two latter equilibria but attribute that platform always to a fixed type. This, in turn, will discourage the candidates of the opposing type from choosing that platform because based on the correlation between their and the voters’ type, they believe that it is more likely that a minority of the voters are of the opposing type who vote for the ambiguous platform.Footnote ¹⁰

We now turn our attention to the restriction of the model we implement in our experiment as a treatment variation. Here, one candidate is known to be a centrist who always runs on a centrist platform, whereas the other is drawn from the same distribution as before. We refer to this as the Known Centrist (KC) treatment, as opposed to our Baseline (BL) treatment described above. Remark 1 and Proposition 1 hold also in treatment KC, which leads to the following corollary.

Corollary 1. In case KC, in which the other candidate is known to be a truthful centrist—that is, $ \tau \hskip1.5pt =\hskip1.5pt A\hskip1.5pt =\hskip1.5pt \left\{0\right\} $ , the only way a noncentrist candidate can win is by committing to an ambiguous platform $ A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ . This is not true in case of BL, in which the preference type of the other candidate is unknown.

In KC, being ambiguous equilibrium-dominates any other platform in the sense that for all equilibrium beliefs associated with the ambiguous policy, and conditional on the voters best responding with undominated strategies, the noncentrist candidate does at least as well by choosing the ambiguous platform $ A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ as any other platform, and there exist equilibrium beliefs where $ A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ does strictly better than any other (singleton) platform. Put differently, if it is known that there is a centrist who truthfully plays her preferred policy, then the only equilibrium where no one plays equilibrium dominated strategies entails both noncentrist types choosing $ \left\{-1,1\right\} $ . In the case of BL, in contrast, it is not clear that a voter should vote for the ambiguous platform $ A\hskip1.5pt =\hskip1.5pt \left\{-1,1\right\} $ instead of $ A\hskip1.5pt =\hskip1.5pt \left\{0\right\} $ . There exists, for example, an equilibrium where leftist candidates choose $ \left\{-1\right\} $ , centrists choose {0}, and rightists choose the ambiguous platform $ \left\{-1,1\right\} $ . In this equilibrium, rational leftist voters vote for platform {0} over $ \left\{-1,1\right\} $ .

The model is robust to slightly different assumptions. In the Appendix, we discuss the robustness with respect to relaxing the model in three natural dimensions. Specifically, the equilibria identified here persist with minor changes to the parameter restrictions if centrists prefer one of the noncentrists over the other, if we allow for the whole power set as a possible set of platforms or if candidates are slightly office motivated.

EXPERIMENTAL DESIGN

Our experimental setup closely mimics the above theoretical voting model. In addition to the voting game, we implemented a number of tasks to explain individual-level variation in the attractiveness of ambiguous platforms. The details of the experimental parametrization of the model and the additional incentivized tasks performed by participants are as follows.

Preferences and information. A round in our experimental voting game consists of two candidates and N = 15 voters. At the beginning of each game, the state of the world $ \omega \hskip1.5pt \in \hskip1.5pt \left\{L,R\right\} $ , which determines the distribution of preferences over outcomes in the society, is drawn by nature randomly and with equal probability. In the experiment, the two possible states of the world are represented by urns containing a different number of colored balls as shown in Figure 1. Specifically, the urn for state L contains p = 7 white balls, q = 2 black balls, and 15 – p – q = 6 gray balls. The number of black and white balls (p and q) is reversed in the urn for state R. The color of a ball represents a subject’s preference type $ \tau \hskip1.5pt \in \hskip1.5pt \left\{-\mathrm{1,0,1}\right\} $ introduced in the theoretical model: white represents preferences of type $ \tau \hskip1.5pt =\hskip1.5pt -1 $ (leftist), gray stands for $ \tau \hskip1.5pt =\hskip1.5pt 0 $ (centrist), and black for $ \tau \hskip1.5pt =\hskip1.5pt 1 $ (rightist) preferences. Conditional on the realized state of the world, preferences are assigned to subjects (candidates and voters) randomly from the same urn (see Figure 1). Specifically, the two candidates’ balls are drawn with replacement, and then all 15 balls are distributed to voters without replacement. Drawing voter types without replacement implies that there will only be two possible realizations of voter-type distributions. This is intended to mirror the situation in large elections where the law of large numbers implies that, conditional on the state of the world in our model, the variance in type shares between separate random draws is negligible. It also implies that the relevant uncertainty players face pertains to these fundamentals. The urn composition and the probability with which each urn is randomly selected is common knowledge, but the selected urn is unknown to all players. A subject’s own preference type (color of ball) is private information.

Figure 1. State of World and Implied Preference Distribution

It is important to emphasize that we used colored balls to ensure a neutral framing for preferences, choices, and outcomes. Compared with field surveys, our experimental design increases the chance of isolating an important mechanism behind the attractiveness of ambiguous platforms because our setup is free from framing issues, ideological positions, or political partisanships that arise naturally in the field. The verbal and graphical instructions as well as screenshots of the decision interface are found in the Appendix. Regardless of our neutral framing, we will mostly relabel preference types here using the left–right spectrum for ease of exposition.

Choices and outcomes. The timing of decisions and information is depicted in Figure 2. After preference types have been assigned, each candidate simultaneously chooses one of the four possible platforms: commit to a singleton platform $ A\hskip1.5pt \in \hskip1.5pt \left\{\left\{ white\right\},\left\{ gray\right\},\left\{ black\right\}\right\} $ or run with an ambiguous platform A = {white, black}. Voters then vote simultaneously using the strategy method.Footnote ¹² After all votes had been made, the winning candidate was determined by simple majority. If the winning candidate proposed a singleton platform, the policy was implemented directly; in the case that a candidate won with an ambiguous platform, she would then choose which of the noncentrist policies contained in the ambiguous platform (white or black) to implement. Payoffs for each subject would then be determined and the game ended.

Figure 2. Timing of the Baseline Voting Game

Monetary payoffs attached to outcomes were decreasing in the distance to the subject’s own policy preferences. If a noncentrist policy was implemented, subjects of the same noncentrist preferences type received payoff $ {\pi}_H $ , those with the opposite noncentrist preferences received $ {\pi}_L $ , and centrists received $ {\pi}_M $ . We used the following values for point payoffs: $ {\pi}_H\hskip1.5pt =\hskip1.5pt 15>{\pi}_M\hskip1.5pt =\hskip1.5pt 8>{\pi}_L\hskip1.5pt =\hskip1.5pt 5 $ .Footnote ¹³ If the centrist policy (gray) was implemented, centrists received $ {\pi}_H $ and those with noncentrist preferences received $ {\pi}_M $ . Payoffs were the same for candidates and voters and depended only on the policy implemented by the winning candidate and the subject’s own preference type, not on their identity.

Treatments. We designed two between-subject treatments to address the behavioral differences related to ambiguous platforms and electoral competition predicted by Hypothesis 1.a and 2.a. Treatment BL entails competition between two candidates of unknown type. A candidate can be any of the three preferences types, $ \tau \hskip1.5pt \in \hskip1.5pt \left\{-\mathrm{1,0,1}\right\} $ and can choose either any of the singleton platforms or the ambiguous platform in the election as described in the model above. Treatment KC was identical to the BL with one exception: it was common knowledge that one of the candidates would always be a centrist, $ \tau \hskip1.5pt =\hskip1.5pt 0 $ , who plays the centrist platform A = {0} truthfully. Taken together, the only difference between the two treatments is that the type and action set is restricted to the centrist position for one of the candidates in treatment KC.Footnote ¹⁴

Measuring correlation awareness and strategic sophistication. After the voting game, subjects participated in additional tasks that were designed to test the validity of the theoretically posited mechanism behind ambiguous platforms for both candidates and voters (cf. Hypothesis 1.b and 2.b). From these tasks, we derive a participant’s degree of correlation awareness and her level of strategic reasoning. We use two simple urn tasks to measure correlation awareness. Both involved a pair of urns, one with 9 green balls and 1 purple ball, the other with 1 green ball and 9 purple balls. In each task, one of the urns was randomly selected, each with equal probability, and a ball drawn then replaced with the color of the drawn ball, which was revealed to the subject. The subject had to then guess how many of 20 additional balls, drawn with replacement, were the same color as the initially drawn ball. In the first task (Q1), the urn was randomly selected before each draw, whereas in the second task (Q2) all balls were drawn from the same urn as the initial ball. The tasks measure whether a subject understands the concept of independence (Q1) and positive statistical correlation (Q2) between random variables. For each task, subjects were paid €2 if their guess was correct; the expected-payoff maximizing answers are 10 in Q1 and 17 in Q2.

We measure subjects’ strategic reasoning using the standard beauty contest game (Nagel Reference Nagel1995), where subjects had to choose an integer between 0 and 100 and the person who guessed closest to 2/3 of the average guess in the session won €10. The game can be solved by iterative deletion of strictly dominated strategies and has only 1 and 0 as its equilibrium guesses. However, these guesses rarely win if parts of the population are expected to guess something else and ability to reason strategically about other players’ behavior and reasoning becomes critical. For example, if a person expects everyone else to make a random guess, the best response of the player would be to guess 33. In level-k models of strategic reasoning, such a player is commonly known as a level 1 player. Players best responding to a population of level-1 players (2/3 × 33 = 22) are level-2 players and so forth (cf. Nagel Reference Nagel1995).

Procedures. A total of 400 subjects participated in the experiments at the experimental economics laboratory of the Vienna Center for Experimental Economics (University of Vienna). We ran eight sessions for each of the two treatments (BL and KC), comprising 160 candidates and 240 voters. The experiment was fully computerized and programmed in z-tree (Fischbacher Reference Fischbacher2007). Before the experiment commenced, subjects were given written instructions and completed a set of comprehension questions that they had to answer correctly before continuing. Each session consisted of 25 participants of which 10 were assigned randomly to the role of candidate and the remaining 15 were assigned the role of voter; roles remained fixed for the duration of the experiment. Depending on the randomly assigned treatment, subjects played 20 rounds of either the BL or KC treatment of the voting game. A candidate and the voters in the KC treatment were informed that the other candidate would be playing the centrist platform. In each round, the outcome for each of the five candidate pairs was based on the election decisions of all 15 voters. This was possible because voters reported their full strategies and these reports could thus be used to determine the winner of each of the five candidate pairs. The candidate pairs were randomly rematched after each round. At the end of each round, all subjects received feedback about which urn was selected, the color of each of the candidates’ balls, and the payoffs of every player type in the game. Given that voter choices were used for five games within a round, voters received feedback from a single, randomly chosen game. The additional (incentivized) tasks as well as a short ex post questionnaire eliciting socioeconomic characteristics and self-reported risk preferences took place after the voting games.

The amount of money earned in the game and the additional tasks was revealed to each subject after all parts had been completed. To ensure incentive compatibility, all games had an equal probability of being selected for payment and all subjects involved in the game that was selected for payment were paid. This meant that candidates were paid based on a single game, whereas voters were paid for five games. To roughly equalize payments across the two player roles, the exchange rate from point earnings to euros was 1 point = €1 for candidates and 1 point = €0.2 for voters. Sessions lasted about 1.5 hours and participants earned an average of €20, ranging between €10 and €37.

CONCLUDING REMARKS

We have advanced and experimentally tested a novel explanation for the use and popularity of ambiguous platforms in electoral competitions. In particular, we have shown how a correlation between candidate and voter preferences can lead to ambiguous platforms and demonstrated that voters can be lured by these ambiguous messages into voting for a strategic candidate of even opposite policy preferences. This, in turn, can lead to negative consequences for the voter when such a candidate wins an election.

Our experimental results also indicate that a lack of awareness of the correlation of preferences in society and inability to reason strategically can shield voters to some extent from falling for ambiguous platforms.Footnote ¹⁷ Our results thus add to a recent debate on the relationship between voter rationality and political outcomes (see e.g., Ashworth and Bueno de Mesquita Reference Ashworth and de Mesquita2014; Ashworth, Bueno de Mesquita, and Friedenberg Reference Ashworth, de Mesquita and Friedenberg2018; Fowler and Hall Reference Fowler and Hall2018).

Nevertheless, we would like to caution against the naive conclusion that cognitive or behavioral biases would limit negative political consequences of ambiguity more generally. It is hard to know whether the observed level of strategic sophistication is likely to be higher or lower outside the laboratory. On the one hand, real-life voting takes place in a more familiar environment than our abstract setting and the strategies of real-life politicians may be more easily understood, potentially aided by media or discussion with friends and family. On the other hand, subjects in our experiment are faced with only a small number possible choices and have full information about their environment. However, having identified strategic sophistication as an important factor, we have provided a potential explanation for elections where an ambiguous challenger fails even when running against a known centrist.

Moreover, voter support for ambiguous platforms depends on perceived rather than actual correlation of preferences between voters and politicians. Understanding the correlation structure in our unframed experiment requires a degree of mathematical understanding that many of our subjects do not seem to possess. However, outside the lab there are forces that are likely to strengthen the perceived correlation for boundedly rational agents. Information bubbles in social networks are a prominent example of situations in which voters may mistakenly perceive a high correlation of preferences with others in general and with candidates who communicate in the same echo chamber in particular. Furthermore, influencing voter perception using personalized campaigning can increase the perceived correlation of preferences in society, which would make ambiguous platforms even more successful than is suggested by our model. This is especially apparent with so-called dog whistles, where elements of a politician’s messaging are understood differently by the general majority and a minority whom the politician is covertly targeting. Examples include hidden racist, sexist, or other antiminority messaging (see e.g., Haney-López Reference Haney-López2015; Rossing Reference Rossing2017) and coded religious signaling (Albertson Reference Albertson2015). Simply the ability to send a coded message can be seen as a signal of preference similarity by the targeted minority, so dog whistles can create strong perceptions of correlated preferences between a candidate and diverse voter groups.Footnote ¹⁸

In summary, we have introduced a theoretical model that clearly demonstrates how ambiguous platforms can be appealing to candidates and attractive to voters and yet have deleterious implications for election outcomes. Our laboratory experiments and discussion of the literature show how behavioral deviations from the assumptions of the model can diminish or augment these effects. Our research provides guidance for interpreting data on real-world elections, which can also be used in the future to test the external validity of our results.