1 Introduction " [. . . ] information that increases perceptions of the reality of climate change may feel so frightening that it leads to denial and thus a reduction in concern and support for action." Clayton, Manning, Krygsman, and Speiser (2017) "Yes, There Has Been Progress on Climate. No, It's Not Nearly Enough." The New York Times, 25 Oct 2021 Climate change is one of the most pressing issues of our time, threatening the livelihoods of millions of people around the globe. Information about climate change and global warming has been available for more than a century, dating back at least to Svante Arrhenius' (1896) famous paper "On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground." However, despite an ever-growing scientific consensus that increasing atmospheric CO2 concentrations will severely impact our planet, little to no action was taken to stop this process for most of the last few decades. Many reasons have been put forward to explain the inaction of political decision-makers, ranging from lobbying interests to widespread misinformation campaigns like those of ExxonMobil. In this paper, I discuss a different, simpler channel: the electoral incentives of politicians when voters may choose to hold motivated beliefs. The looming dire consequences of climate change may, if taken seriously, create stress and anxiety. In an effort to avoid these negative emotions, people may choose to hold motivated beliefs, ignoring information that suggests climate change is severe, while overreacting to information suggesting there is nothing to worry about. Psychologists and economists alike have long been aware of such information processing biases, as exemplified by Kunda's (1990) seminal paper or the recent survey by Amelio and Zimmermann (2023), and multiple studies have provided evidence for their empirical relevance (for example, Lewandowsky, Gignac, and Oberauer, 2013, Thaler, 2021, 2024, and Lois, Tsakas, Yuen, and Riedl, 2024). To study the potential consequences of such behavior for the implementation of policies targeted at climate change, I construct a game-theoretic model in which two politicians compete in an election by proposing policies. There are two possible states of the world: severe climate change and moderate (or no) climate change. The state determines which policy is optimal and establishes a baseline welfare level. If climate change is severe, the baseline welfare is lower than in the mild state, regardless of the chosen policy. Voters and politicians receive signals about the state of the world, and society is best served when the policy that matches the state is implemented. As discussed by authors like Bénabou and Tirole (2016) or Spiegler (2016), voters have anticipatory utility, meaning they feel anxiety or stress when the future looks grim. To cope with these negative emotions, they may choose to hold motivated beliefs, interpreting information about the future in a non-Bayesian way to increase anticipatory utility. How voters react to information is an important determinant of how politicians compete to win an election. The model highlights the importance of the portrayed severity of climate change for the efficiency of policy-making. In particular, if severe climate change has only moderate consequences for baseline welfare levels, then there always exists an efficient equilibrium in which politicians choose the optimal policies for each state. However, this equilibrium only exists if voters have sufficient trust in government, i.e., if they belief that elected politicians will enact the right policies with a sufficiently high probability. Otherwise, with low trust in government, there always exists an equilibrium in which politicians ignore their information and choose policies for mild or no climate change. The analysis suggests two important determinants for the efficiency of policy-making. First, trust in government is important, because it determines in which way voters interpret information when severe climate change only has moderate effects on baseline welfare. With sufficient trust in government, there always exists an efficient equilibrium in which politicians strictly choose the optimal policies. To the contrary, if trust in government is low, then politicians will ignore their information and policy choice will be inefficient. Second, the analysis suggests that political rhetoric could be an important determinant of the quality of policy choice as well. In particular, if the consequences of severe climate change are portrayed as catastrophical, then the efficient equilibrium ceases to exist. Voters will ignore any information that climate change is severe, inducing office motivated politicians to ignore their information as well, and in the unique equilibrium politicians always choose policies for mild or no climate change. However, if the consequences of severe climate change are portrayed as moderate or mild, then the efficient equilibrium survives. Literature: The paper contributes to several areas of literature. Firstly, it adds to the literature that examines the incentives of political candidates to select efficient policy platforms when the true state of the world is unknown. Important contributions to this litera-ture include Heidhues and Lagerlof (2003), Laslier and van der Straeten (2004), and Kartik, Squintani, and Tinn (2015). Unlike Heidhues and Lagerlof (2003) and Kartik, Squintani, and Tinn (2015), I assume that voters also receive information, which creates the main tension of whether to ignore it or not. In Laslier and van der Straeten (2004), voters receive a single public signal as well, whereas in the current paper, each voter receives an independent signal. The two most closely related papers in this literature are Gratton (2014) and Crutzen, Sisak, and Swank (2024). Gratton (2014) assumes that candidates observe the state perfectly while voters receive imperfect but informative signals about the state, and the focus of the analysis is to identify conditions that lead equilibria such that candidates choose efficient policies. Crutzen, Sisak, and Swank (2024) study a game like Gratton (2014), but there are two groups of voters, elites and commoners, who stochastically differ in their policy preferences and who always differ in quality of the information they receive. The analysis focusses on deriving conditions such that candidates cater to the elites or engage in populism.
Unlike in those papers, the focus in the current paper is on misinterpreting information, and how this influences candidates' incentives to provide efficient policies. A cornerstone of the model is that voters have anticipatory utility, "meaning that the individual experiences pleasant or aversive emotions from thinking about future welfare" (Bénabou and Tirole, 2016). As in Akerlof and Dickens (1982), Caplin and Leahy (2001), Bénabou and Tirole (2002), Spiegler (2016), Eliaz and Spiegler (2020), and other papers, this means that voters have preferences not only about states and policies but also about their own beliefs. A consequence of this is that voters may engage in motivated reasoning; see, for example, Kunda (1990), Bénabou andTirole (2016), Zimmermann (2020), Oprea andYuksel (2021), or Thaler (2024). The most closely related papers in this area are Levy (2014) and Le Yaouanq (2023), which also examine electoral contexts. Levy (2014) presents a model featuring a policymaker trying to signal quality/congruency to voters. Voters have imperfect memory and can suppress certain news by purposefully conflating positive and negative signals. In contrast, there is no signaling in the current paper. Furthermore, voters have perfect memory but may choose to interpret some signals as more or less informative than they really are. Finally, it is not just voters' beliefs about the state that matter, but also their expectations regarding policy outcomes. This difference introduces a novel self-fulfilling aspect that becomes critical for equilibrium. Le Yaouanq (2023) suggests that voters may interpret signals in a contrary manner at a cost. In the current paper, I assume that voters can modulate the perceived informativeness of a signal, but they cannot alter its direction. Moreover, unlike in Le Yaouanq (2023), a key component of my model is that the state influences baseline welfare levels, which has important consequences for equilibrium. The paper also contributes to a recently revived literature on environmental policymaking. Delfgaauw and Swank (2024) show that there can be locked-in effects that prevent the adoption of environmentally friendly policies. Blumenthal (2024) shows that efficient environmental policies may not be adopted if voters' preferences are expected to change over time. Van der Straten, Perotti, and Van der Ploeg (2024) study the relationship between climate change adoption policies and inequality in society. Besley and Persson (2023) examine the conditions for green transitions to occur, depending on voters' ideological preferences and the extent to which the production sector remains reliant on brown energy sources. Gullberg (2008), Shapiro (2016), and Balles, Matter, and Stutzer (2024) show that special interest groups may prevent climate change policies from being adopted. Denter (2024) shows that the wrong kind of climate activism may decrease support for climate policies. In contrast to these papers, the current paper provides an explanation based purely on the electoral incentives of office-motivated politicians in the presence of a common information processing bias among voters. The paper is organized as follows. In Section 2, I describe the baseline model, which is then solved in Section 3. Section 4 extends the baseline model along several dimensions. In Section 5, I derive testable predictions of the model and have a first quick look at the data. Section 6 concludes. All proofs are relegated to the appendix. In this section I introduce the main building blocks of the model. There is an unknown state of the world, ω ∈ {0, 1}, indicating whether climate change is mild, ω = 0, or severe, ω = 1. The prior probability that ω = 1 is q ∈ (0, 1). There are two different kinds of actors. On the one hand, there are two kinds of purely office motivated politicians, indexed by i = 1, 2. On the other hand, there is a continuum of voters of mass 1. Candidates vie for voters' support by proposing policies, p i ∈ {0, 1}, to which they commit. Denote the vector of policies by

Voters policy preferences depend on the state of the world ω. Given a winning policy p and given a state realization ω, voters' realized policy utility is

Hence, for each state realization ω, the optimal policy is p = ω. But the state ω determines not only optimal policy, but the baseline welfare level in society. In particular, if ω = 1, i.e., when climate change is severe, then baseline welfare decreases by ∆ > 0, independent of the chosen policy, while it remains constant if climate change is mild, ω = 0. The parameter β > 0 measures the importance of choosing the right policy when climate change is severe:

the greater is β, the more important is taking the right action. Note that the worst outcome is choosing policy incorrectly in state 1, yielding -∆ -β, while the best outcome is choosing correctly in state 0, yielding a utility of zero. I make the following assumption to capture the idea that at the outset, voters believe the optimal policy choice is p = 0:1 Assumption 1. Throughout I assume that q < 1 1+β . At the beginning of the game, both types of players receive a signal that is informative about ω. In particular, as in Gratton (2014), before announcing policy platforms every politician i receives a signal s P i that perfectly reveals ω . Hence, after receiving s P i , each politician perfectly knows wether climate change is severe or not. Voters receive two kinds of signals. On the one hand, the policy platforms p may function as signals about ω, depending on the strategies chosen by the candidates. On the other hand, they receive information from news or from direct experience about ω. I model this by assuming that each voter receives a signal s ∈ R. When the state is ω, the c.d.f. of s is Φ s+(2ω-1)µ σ , where Φ is the c.d.f. of the standard Gaussian distribution and µ > 0 and σ > 0 are parameters.
Therefore, the typical monotone likelihood ratio property (MLRP) is satisfied, meaning that any s > 0 is evidence for ω = 1 and increases the belief compared to the prior, while any s < 0 is evidence for ω = 0 and decreases the belief. Following Callander (2011) and others, I interpret µ as a measure of the complexity of the issue climate change. If µ is small, the issue is very complex, and thus voters tend to hold imprecise beliefs about ω. To the contrary, if µ is large, climate change is not a very complex issue and beliefs tend to be precise. We assume that the complexity of the issue climate change is such that, absent motivated beliefs and any signaling about the state ω through platform choices p, the election aggregates information whenever p 1 ̸ = p 2 . In other words: if both policies are offered, a majority chooses to vote for the welfare-maximizing policy. The following assumption guarantees that this is true:

I assume that voters have anticipatory utility. In particular, a voter has expectations about her future utility, which is derived from a belief bout the true state and a second belief about the enacted policy. This causes anticipatory utility, "meaning that the individual experiences pleasant or aversive emotions from thinking about future welfare" (Bénabou and Tirole, 2016). To increases anticipatory utility (to be defined precisely below), a voters may use motivated reasoning, which means that she may update beliefs using a distorted complexity parameter μ. Clearly, processing information using such a distorted complexity parameter comes at a cost, because higher anticipatory utility may imply lower utility because of imperfect decision making. As Bénabou and Tirole (2016) write, "one can react to bad news objectively, which leads to better decisions but having to live with grim prospects for some time [. . . ], or adopt a more "defensive" cognitive response that makes life easier until the day of reckoning, when mistakes will have to be paid for." I do not model these costs in the baseline model to be able to identify the pure effect of motivated reasoning, but in Section 4.4 two models of distortions are discussed. If a voter is indifferent between having μ = µ and some other μ ̸ = µ, I assume without loss of generality that she chooses μ * = µ. Choosing μ > µ implies the voter interprets the signal as more informative than it really is, and hence beliefs will change excessively, while choosing μ < µ implies a more conservative stance and that beliefs move less than they should. Based on s and p, and after choosing μ, each voter forms beliefs π(s, p, μ) and κ. π(s, p, μ)

is the posterior belief about ω, whereas κ is the probability assigned to the event that policy 1 will be implemented after the election. Because candidates commit to policy platforms,

Equipped with these beliefs, we can now calculate a voter's anticipatory utility:

Thus, anticipatory utility equals the utility the voter expects to receive once policies are determined. Note that a voter is never pivotal, because there is a continuum of voters. I thus assume that voters vote sincerely as defined by Austen- Smith and Banks (1996). In words, each voter forms beliefs based on s, p, and μ and then votes to maximize (1). We are now in a position to define equilibrium of our game. (i) each voter maximizes AU (s, p, μ) given a belief about the probability that policy 1 will be enacted κ; (ii) each voter votes sincerely given s and μ; (iii) κ is correct given s, μ, and given the strategies of all other voters; (iv) politicians choose policy platforms that maximize the probability to be elected, given their expectations about voters' behavior. As typical in signaling games, there are multiple equilibria. I focus attention on symmetric equilibria, that is, equilibria in which candidates, holding the same information and trying to achieve the same, choose identical strategies. Further, if on the equilibrium path both candidates choose the same pure strategy, then we must have p 1 = p 2 . If, off the equilibrium path, voters observe p 1 ̸ = p 2 , I assume that they do not learn anything from this about ω. That is, if off the equilibrium path p 1 ̸ = p 2 , then observing p does not change voters' belief about ω.2

In this section, I solve the baseline game. I begin by analyzing equilibrium play in the voting subgame. In Section 3.2, I analyze candidates' incentives and equilibrium behavior, and in Section 3.3 I study the equilibrium of the whole game. First I turn to the optimal motivated beliefs of voters. The focus is on situations in which p 1 ̸ = p 2 , because otherwise voters choose a winner, but not a winning policy. If p 1 ̸ = p 2 off the equilibrium path, p is not informative about ω. However, it may be so on the equilibrium path. In a symmetric equilibrium, p 1 ̸ = p 2 is only possible in mixed strategies. Because both candidates hold the same information, assume that, when the state is ω, each chooses p = 1 when with probability ρ ω and p = 0 with probability 1 -ρ ω . Therefore, if ρ 1 = 1 and ρ 0 = 0, then both choose the policy that matches the state with probability 1. If ρ 0 = ρ 1 = 0, then candidates never choose p = 1, irrespective of ω. If p 1 ̸ = p 2 off-equilibrium, p is not informative by assumption, and p 1 ̸ = p 2 in a symmetric pure strategy equilibrium is not possible. Hence, the belief about ω of a voter who receives signal s and who chooses μ, is

.
(3)

To see how a voter optimally chooses her motivated belief μ, take the derivative of AU (s, p, μ)

with respect to μ:

, then this is equal to zero, independent of s. If ∆ > 1, then κ > 1, and because κ is a belief, it must be true that κ < κ, implying that the sign of (4) is independent of κ. In particular, if this is the case, then AU (s, p, μ) decreases in μ if s > 0, and it increases in μ if s < 0. Otherwise, that is, if ∆ ≤ 1, then whether or not AU (s, p, μ) increases in μ depends on both s and the belief κ. Note that for each voter κ can be interpreted as a measure of trust in government. κ is the distribution of beliefs about the policies that will be enacted. If a voter believes that the government will always enact the policy that matches the true state, then κ = π(s, p, μ). If, however, there is little trust in government regarding policy choices, then κ ̸ = π(s, p, μ), and if trust is very low, we have κ ∈ {0, 1}. We can now derive the optimally distorted complexity of the issue climate change:

κ < κ, or s > 0 and κ > κ, and (ii) μ * = 0, if either s < 0 and κ > κ, or s > 0 and κ < κ. The lemma provides us with an important intermediate result, the optimal distortions of µ for different voters. We see that beliefs about policy only matter if severe climate change causes only moderate baseline welfare losses. Otherwise, if severe climate change leads to catastrophical welfare losses, then any signal indicating that ω = 1 will be interpreted as pure noise and hence completely ignored. To the contrary, any signal indicating ω = 0 will be accepted as a perfect indication that climate change is indeed mild, independent of the signal's strength. Finally, a voter with a signal s = 0 or a voter with κ = κ has no incentive to distort her signal's precision and hence updates her belief about ω like a perfect Bayesian. What does this imply for the beliefs about ω the voters hold? Clearly, if μ = 0, then beliefs do not change at all, and π(s, p, 0) = q. The same is true for a voter receiving a signal s = 0, which is not informative about ω. Moreover, if μ = ∞, then any signal that contains only the slightest bit of information will completely move beliefs to the extremes, and hence π(s, p, ∞) ∈ {0, 1}. Only if s ̸ = 0 and κ = κ will the belief be a non-constant continuous function of s and it equals π(s, p, µ):

We now know the beliefs of all voters as functions of their signals and of their policy belief κ. Corollary 1 shows that if ∆ > 1, and hence severe climate change has catastrophic consequences, then the equilibrium has a simple structure, and κ actually plays no roll. Voters have two different beliefs, π(s, p, μ) = 0 and π(s, p, μ) = π. What does this imply for voters' decisions at the ballot? Recall that voters vote sincerely for the alternative that they believe maximizes (1). The expected utility from policy 1 is u(p = 1) = -π(s, p, μ)∆ -(1π(s, p, μ)), while from policy 0 she gets u(p = 0) = -π(s, p, μ)(∆ + β). Hence, the voter cast her ballot for policy 1 iff

If the reverse is true, then policy 0 is strictly preferred, and if π(s, p, μ) = π, then a voter is indifferent. Clearly, 1 > π > 0. Note that by Assumption 1 we have π > q. If ∆ > 1, then voters hold two different beliefs, either π(s, p, μ) = 0 or π(s, p, μ) = π. A voter with the former belief always votes for policy 0, while the decision at the ballot of the other voter depends on q, β, as well as on the politicians' strategies ρ 0 and ρ 1 . If π > π, then these voters vote for policy 1, and as a consequence all voters vote informatively, i.e., they vote according to their signals. This means that in each state ω the policy that matches this state is chosen. If, however, π ≤ π, then a majority of voters always supports policy 0, implying it wins independent of the state. Things are slightly different when ∆ ≤ 1. On the one hand, the equilibrium just described continues to exist also when severe climate change decreases baseline welfare only moderately. In particular, this is the case if π ≤ π and κ < κ for sufficiently many s. To the contrary, if π ≥ π and κ > κ for sufficiently many s, then policy 1 wins independent of the state. Hence, when severe climate change is not catastrophic, then there might exist an equilibrium in which politicians always campaign on the policy tailored for severe climate change, independent of the true state. It follows that we cannot yet exclude that, when ∆ ≤ 1, a second inefficient equilibrium may exist. What about the efficient equilibrium, in which candidates choose the optimal policies given ω? Assume each voters wants to believe her signal and thus has κ < κ when s < 0 and κ > κ when s > 0. Then every voter votes informatively, and therefore the policy matching the state wins for all π ∈ (0, 1). Hence, if even severe climate change decreases baseline welfare only moderately, then there always may exist an equilibrium in which voters vote informatively, and hence the correct policy is chosen with probability 1. We summarize the results of this section in our next proposition:

1.
If ∆ > 1, then there is a unique subgame equilibrium. (a) If π ≤ π, then κ * (s, p, μ) = 0 for all s and a majority of voters always votes for policy 1. (b) If π > π, then κ * (s, p, μ) = 0 if s < 0 and κ * (s, p, μ) = 1 if s ≥ 0, and a majority always votes for the policy p i that matches the true state ω. 2. If ∆ ≤ 1, then there exist multiple subgame equilibria. (a) For any π ∈ (0, 1), there exists a subgame equilibrium with κ * (s, p, μ) = 0 if s < 0 and κ * (s, p, μ) = 1 if s ≥ 0, and a majority of voters always votes for the policy p i that matches the true state ω. (b) For π ≥ π, there exists a subgame equilibrium with κ(s, p, μ * ) = 1 and policy 1 always wins. (c) For π ≤ π, there exists a subgame equilibrium with κ(s, p, μ * ) = 0 and policy 0 always wins. (d) There is no subgame equilibrium in which the policy p i , that does not match the state ω, always wins. On the positive side, there always exists a subgame equilibrium in which information aggregates, if severe climate change decreases baseline welfare not too much, i.e., if ∆ is small. However, this equilibrium depends on the expectations about the efficiency of political process. If voter believe that the policy suggested by their signal is chosen, then the election leads to efficient results. However, if voters are pessimistic, and believe policy 0 will be chosen no matter what is the true state ω, then this becomes a self-fulfilling prophecy if π is low. When ∆ becomes larger, and hence severe climate change leads to more dire welfare losses, then the efficient equilibrium disappears when π is small. We now study the platform choices of the candidates as a function of their signals. Of course, when they decide which policies to offer they think ahead which policies are likely to lead to electoral success, and therefore voters' reactions, in particular the one's formalized in Proposition 1, matter for candidates' incentives. From the perspective of an office motivated candidate, the optimal platform is the one that maximizes the chance to win the election. In a symmetric equilibrium, if both candidates choose identical platforms, voters may learn from the platforms' congruence something about the true state ω, but they cannot choose policies anymore, since all candidates offer the same. Because voters only care about policies, both candidates win with an equal probability of 50 percent if p 1 = p 2 . If some candidate deviates and chooses off-equilibrium a platform different from his opponent, voters learn nothing about ω from this deviation. However, if equilibrium play permits p 1 ̸ = p 2 , then platforms may indeed be partially informative and change voters' beliefs, as discussed before. First consider potential mixed-strategy equilibria. Focussing on symmetric equilibria, the probability that each candidate choose policy 1 in state ω is ρ ω as before. Note that if ρ 1 ̸ = ρ 2 , voters learn from platform choices even if p 1 ̸ = p 2 . Choosing such a mixed strategy can only be an equilibrium if it leads to a chance of winning of 50%, because candidates need to be indifferent. The probability to win is 50%, if either both receive exactly half the votes, or if the probability that a majority chooses either candidate is 50%. But note that candidates know the state ω, and thus they can infer the exact distribution of signals voters receive. Therefore, in a mixed-strategy equilibrium we need to have that both receive exactly half the votes. This implies policy 1 is implemented with probability of 50%, independent of the state ω. Hence, we need to have κ = 1 2 for all s. If κ < 1 2 , any voter with s > 0 will hold belief π(s, p, μ) = 1 and thus they all vote for 1. But this means that in state ω = 1, the candidate offering p = 1 wins with certainty, and thus this cannot be equilibrium. If κ > 1 2 , any voter with s < 0 will hold belief π(s, p, μ) = 0 and thus they all vote for policy 0. But this means that in state ω = 0 the candidate offering p = 0 wins with certainty, and thus this cannot be equilibrium, either. Finally, if κ = 1 2 , any voter will choose μ * (s) = µ. But then information aggregates by Assumption 2, and thus this cannot be an equilibrium belief, either. Hence, we can conclude that no mixed strategy equilibrium can exist. What about pure strategy equilibria? In a symmetric equilibrium, we must have p 1 = p 2 , because candidates hold the same information. Suppose voters observe off-equilibrium that p 1 ̸ = p 2 and both candidates expect voters to vote informatively. Hence, they vote for policy 1 if s > 0, for policy 0 if s < 0, and they randomize when s = 0. Then, in each state ω, the candidate offering the policy that matches the state wins the election. Hence, when choosing which policy platform to offer, candidate i knows that p i = ω wins the election if p -i ̸ = ω and otherwise both win with a probability of 50%. To the contrary, choosing p i ̸ = ω wins the election with 50% if also p -i ̸ = ω and otherwise loses the election for sure. Hence, p i = s i is the unique optimal strategy. It follows that if sufficiently many voters vote informative, candidates will choose informative policy platforms.
To the contrary, if candidates expect a sufficiently large number of voters to not vote informatively when p 1 ̸ = p 2 , then there exists a policy p ∈ {0, 1} that wins the election with certainty, independent of the state ω. Candidates then know they win the election by choosing p i = p if p -i ̸ = p, and they win with a probability of 50% if p -i = p. Choosing p i ̸ = p will lose the election for sure if p -i = p, and hence both candidates are best served by offering p.

Proposition 2. There is a unique symmetric equilibrium in the platform choice stage, which is in pure strategies. Candidates choose p * i = ω, if they expect a majority of voters to vote for the policy that matches the state, when p 1 ̸ = p 2 . Otherwise, there exists a policy p that is expected to win independent of the realization of ω if p 1 ̸ = p 2 , and both candidates choose

We can now determine equilibrium platform choices as functions of the parameters of the game. If severe climate change leads to catastrophic baseline welfare level losses, ∆ > 1, then voters ignore any signal indicating that ω = 1. Our analysis so far reveals that then a majority always votes for policy 0, whenever p 1 ̸ = p 2 . Proposition 2 tells us that in this case candidates never campaign on policy p = 1, independent of the information they hold. Hence, if severe climate change is catastrophic, then candidates will ignore any information and always choose the optimal policy for mild climate change, p * = (0, 0). When ∆ ≤ 1, the set of equilibria becomes larger. The reason is that now voters' beliefs about the enacted policy become self-fulfilling. If voters trust the government in the sense that they believe the policy that is optimal given ω wins, then voters always vote informatively, implying that p * = (ω, ω) can indeed be equilibrium. However, there always coexists another equilibrium, in which candidates again ignore their information. If voters are convinced that p = 0 is chosen, then any voter with s < 0 will choose μ = ∞, while a voter with s > 0 chooses μ = 0. Therefore, as in the case of ∆ > 1, a majority always votes for policy 0, and candidates choose p * = (0, 0). The next proposition is the paper's main result and formalizes the above intuitions:

Proposition 3. If ∆ > 1, then there exists a unique pure strategy equilibrium in which κ * (s, p, μ * ) = 0 and candidates choose p * = (0, 0). If instead ∆ ≤ 1, then there are multiple equilibria:

1. If ∆ ≤ 1 and voters have trust in the government, then there exists a pure strategy equilibrium in which κ * (s, p, μ * ) = π(s, p, μ * ) and candidates choose p * = (ω, ω). 2. If ∆ ≤ 1 and voters have no trust in the government, then there exists a pure strategy equilibrium in which κ * (s, p, μ * ) = 0 and candidates choose p * = (0, 0). In this section I informally discuss further extensions that seem relevant. For the sake of brevity and clarity, throughout this section I assume that ∆ > 1. In Section 4.1 I discuss how conclusions change if candidates are not only office motivated, but care also about welfare. In Section 4.2 I discuss the implications of differences in candidate valence. In Section 4.3, I discuss the implication of misinformation campaigns. Finally, in Section 4.4 I study the implication of costly deviations from Bayesian rationality. Suppose candidates not only care about being elected but also value welfare, as captured by

(1). Knowing which state has materialized, candidates are aware of which policy maximizes welfare. Thus, one might hypothesize that adding a policy motivation would improve the situation. However, this is only partially correct. On the one hand, if policy motivation is sufficiently important compared to simply being elected to office, there is indeed an equilibrium in which candidates always choose p * = (ω, ω). To see this, assume the spoils of office have value V and that each candidate receives V + u(p, ω) if elected and u(p, ω) otherwise. Now, suppose candidate 1 expects candidate 2 to choose p 2 = ω = 1. Choosing p 1 = 0 would win the election but result in a welfare loss due to the wrong policy being chosen. Alternatively, choosing p 1 = 1 reduces the chance of winning the election to 50%, but it ensures that the optimal policy is selected with certainty. Candidate 1 has a strict incentive to also propose

If, however, β < V 2 , there remains a unique pure strategy equilibrium with p * = (0, 0). Thus, if policy motivation is sufficiently strong, the previously identified problems may not occur. However, there is always another equilibrium in pure strategies where candidates continue to ignore their information despite policy motivation. Assume candidate 1 expects candidate 2 to choose p 2 = 0. In this case, the unique best response is to also choose p 1 = 0, because policy 0 now wins with certainty. Although candidate 1 cannot influence the policy, she can increase her chances of winning. Therefore, despite policy motivations, and even in the absence of any office motivation, there always exists an equilibrium with p * = (0, 0). Next, consider valence differences as in Ansolabehere and Snyder (2000), Groseclose (2001), Aragones and Palfrey (2002), and more recently Denter (2021).
Specifically, assume that voters evaluate candidates not only by the policies they offer but by v i + u(p i , ω), where v i ∈ R is the valence utility the voter gets from candidate i in the office and u(p, ω) is policy utility and defined as before in (1). Let v 1 > v 2 , implying that candidate 1 has a valence advantage. How does introducing valence alter the model's conclusions? On the one hand, it has no effect on μ * (s), which remains as described in Lemma 1, because valence is independent of the state ω. However, valence does affect a voter's choice at the ballot box for a given belief π(s, p, μ). If both candidates choose the same policy, candidate 1 always wins because v 1 > v 2 . Equilibrium in the extended game resembles equilibrium in Ansolabehere and Snyder (2000). If the valence advantage is not too large, candidate 1 will always choose p 1 = 0, while candidate 2 may choose any p 2 ∈ {0, 1} without having a chance to win. If the valence advantage is large enough, candidate 1 may choose any p 1 ∈ {0, 1} and still win with certainty. Thus, it is possible that a candidate with a large valence advantage might use this advantage to propose an optimal policy. In fact, if we combine a large valence advantage with policy motivation as described in Section 4.1, then it is a dominant strategy for candidate 1 to choose p 1 = ω, and this policy indeed wins the election. The analysis so far has revealed a robust mechanism through which the electoral incentives of candidates are sufficient to prevent the implementation of adequate policies against climate change. However, climate change is also one of the topics where organized misinformation is most prevalent (see, for example, Lewandowsky, 2021). Perhaps the most famous example of such campaigns is that of ExxonMobil, which, despite having very precise knowledge about the causes and consequences of climate change (see Supran, Rahmstorf, and Oreskes, 2023), chose to downplay the phenomenon in their public communications and editorial-style advertisements in The New York Times (see Supran and Oreskes, 2017). I follow Papanastasiou (2020), Sisak and Denter (2024) and Denter and Ginzburg (2024) to incorporate misinformation into the model. In particular, I assume that each voter receives a fake signal with a probability of α, while with the complementary probability of 1 -α the signal comes from a proper source and is informative. An informative signal is drawn from the distribution F ω with corresponding density f ω . I assume that f 1 (s)/f 0 (s) is an strictly increasing function of s, which is the standard MLRP assumption. Note that in the model described in Section 2 with normally distributed signals this is automatically satisfied. Moreover, without loss of generality let f 1 (0) = f 0 (0), implying that s = 0 is an uninformative signal as before. Unlike proper signals, a fake signal is not informative. In particular, I assume that the distribution of fake signals is G(s) which is independent of ω. For simplicity, further assume that F θ and G have full support on R.

Because the literature has shown that in the presence of fake news motivated reasoning is often regarding the reliability of an information source, voters cannot change the precision of a signal anymore, but have motivated beliefs about the probability that a given signal is fake or proper. In particular, they can choose α

For a given signal s and a given choice α, the belief about the state ω is

. Choosing α = 0 means ignoring the chance that the signal could be fake, and hence the belief equals the perfect Bayesian belief when no fake signals exist. To the contrary, setting α = 1 means ignoring the signal completely because it originates from a fake source. Lemma 2. The optimal motivated belief about α is

Hence, any bad news about climate change will be interpreted as fake, while any good news will be interpreted as proper and hence credible. This is in line with recent empirical evidence (Thaler, 2024). What are the consequences for political decision making? The political equilibrium is the same as in Section 3. The reason is that any signal indicating climate change is severe will be ignored, and hence a majority of the electorate will prefer policy 0 in each state. Proposition 4. Suppose ∆ > 1. There exists a unique pure strategy equilibrium in which voters hold pessimistic beliefs about the enacted policy, κ * (s, p * , α * (s)) = 0, where α * (s)

follows from Lemma 2, and in which candidates ignore their information about ω and choose p * = (0, 0). their beliefs, and all voters interpret information as perfect Bayesians. It follows from Assumption 2 that in this case, information aggregates correctly in an election with p 1 ̸ = p 2 , and therefore the conditions for efficient policy platforms in equilibrium are satisfied. If γ < min {γ -, γ + }, there will be both voters who received good news (s < 0) and those who received bad news (s > 0) who choose μ * ̸ = µ, while others will interpret signals correctly. Proposition 5. Suppose ∆ > 1. There exists γ > 0 such that iff γ < γ, then there exists a unique pure strategy equilibrium in which voters hold pessimistic beliefs about the enacted policy, κ * (s, p * , μ * ) = 0, where μ * follows from Lemma 3, and in which candidates ignore their information about ω and choose p * = (0, 0). The proposition shows that our earlier analysis is robust to the introduction of a fixed cost that needs to be paid if a voter chooses μ ̸ = µ.
The result is of course not very surprising given Proposition 3. However, one thing to note is that the incentives to distort µ of voters with s < 0 do not matter for the result. In fact, those voters vote more often informatively with motivated beliefs than without, which is beneficial for choosing the optimal policy. Next consider the case of a smooth cost of distortion function. We demand a number of properties our cost function should satisfy. It should be convex increasing when we move away from µ and zero when there is no distortion. Moreover, it should not be symmetric in the sense that μ = µ + ϵ and μ = µ -ϵ should not lead to the same cost. To see why assume µ = 1. A symmetric cost function would imply that C(μ, µ)| μ=0 = C(μ, µ)| μ=2 . But note that μ = 0 implies that the issue is perceived as infinitely incomplex, and any signal s ̸ = 0 will lead to updating to either 0 or 1. At the same time, μ = 2 represents only a gradual increase in complexity. If both have the same cost, then downward distortions are generally "cheaper" than upward distortions. We therefore demand that the cost of equal relative distortions upwards and downwards are the same. This implies the cost function is compressed for downwards distortions. More formally, C(μ, µ)| μ=λ•µ = C(μ, µ)| μ=µ/λ for all λ > 0 and all µ > 0. In particular, we assume the following cost function:

With this cost function we have C(μ, µ)| μ=λ•µ = C(μ, µ)| μ=µ/λ = c 2 µ 2 (λ -1) 2 for all λ > 1 as desired. In the left panel of Figure 1, the cost function is plotted for µ = 1 and c = 2. One property of it is that lim μ→∞ C(μ, µ) = lim μ→0 C(μ, µ) = ∞, and therefore we have μ ∈ (0, ∞) for any s.

When deciding how to optimally distort µ, each voter aims to maximize

As before, focus on p 1 ̸ = p 2 . When the signal is uninformative, s = 0, any distortion only causes cost, but does not change AU (s, p, μ). Hence, in this case, μ * = µ. But what happens when signals are very informative? Suppose s → ∞. Then any distortion except μ = 0 will move the belief about ω to π = 1. But the cost of choosing μ = 0 is infinite, and hence this cannot be optimal. Therefore, it is optimal to not distort at all. The same is true for s → -∞. For any other signal realization, s ∈ (-∞, 0) ∪ (0, ∞), the direction of the optimal distortion is the same as in Lemma 1. Moreover, W (s, p, μ) is a continuous and smooth function of both s and μ, and hence also μ is a continuous and smooth function of s.

To get a better intuition of how μ * changes with s, I plotted it for µ = 1 and different values of c in the right panel of Figure 1. The next lemma states the above intuitions formally:

Otherwise, and if s > 0, then μ(s) < µ, and there exists s > 0 such that μ(s) decreases in s if s ∈ [0, s + ), and it increases in s if s > s + . If s < 0, then μ(s) > µ, and there exists s -< 0 such that μ(s)

decreases in s if s ∈ (s -, 0], and it increases in s if s < s -. Moreover, for every s, the absolute distortion |µ -μ| decreases in c Now let us discuss the implications of the lemma for voters' decisions at the ballot, and by extension, for candidates' incentives to offer the optimal policy. First, just as in the case of fixed costs, if s < 0, voters tend to amplify the signals, leading more voters to vote informatively compared to the absence of motivated beliefs. This improves the ability to select the right policy through an election. Therefore, to understand the conditions under which candidates ignore information and choose policy 0 regardless of ω, we need to focus on voters receiving s > 0. These voters interpret signals as less informative than they truly are, resulting in fewer voters casting informative votes compared to the absence of motivated beliefs. Because q < π, if either the distortion of µ is significant or the signal is too weak, such a voter may cast a ballot for policy 0 despite s > 0. Intuitively, as c increases, voters choose to distort µ less and less. Consequently, lim c→∞ μ * (s) = µ. In this case, by Assumption 2, a majority will always cast a ballot for p = ω, giving candidates an incentive to heed their information. However, if c is small, we revert to the result from Proposition 3. By continuity, there exists a ĉ > 0 such that if c ∈ [0, ĉ], motivated beliefs will lead to distortions and voting behavior that prevent candidates from following their information. Proposition 6. Suppose ∆ > 1. There exists ĉ > 0 such that iff c < ĉ, then there exists a unique pure strategy equilibrium in which voters hold pessimistic beliefs about the enacted policy, κ * (s, p * , μ * ) = 0, where μ * follows from Lemma 4, in which candidates ignore their information about ω and choose p * = (0, 0). The analysis in this section has given us more nuanced results for the optimal distortion of beliefs. Moreover, in both extensions discussed so far, the inactive equilibrium prevails as the unique equilibrium if the cost of distorting informativeness of signals is low enough.
However, the two models discussed differ significantly in how voters choose to distort information and hence beliefs, see Figure 2, allowing to derive testable predictions. With fixed costs, only the worst signals are distorted, both in the case of good news (s < 0) and bad news (s > 0). When news are bad, the worst signals are the ones suggesting ω = 1 the strongest. This leads to low anticipatory utility and thus the signal is interpreted as not informative. However, if bad news is weak, then the belief does not change a lot anyway, and hence choosing μ ̸ = µ at a cost is not attractive. When news is good, the worst signals are the ones suggesting ω = 0 the least. Weak good news leads to little updating of beliefs, and overreacting to information is better for anticipatory utility, even if it is somewhat costly. However, if good news is strong enough, then overreacting to the signal does not change beliefs that much anymore, and hence distorting beliefs is not in a voters interest. If, instead, we consider a continuous and convex cost function, the results are to some degree reversed. In fact, when s is very large, implying a voter receives strong bad news, then interpreting the signal as not informative is very costly, and hence a voters will be better served simply interpreting the signal in an (almost) Bayesian fashion. The same is true when s is close to zero. However, bad news of intermediate strength will be downplayed significantly. When a voter receives good news we find similar results. If s is very low, the voter's belief about ω is close to zero even if μ = µ, and hence distorting µ is not very attractive. The same is true if good news is very weak. However, if good news is of intermediate strength, then distorting µ upwards is attractive. The formal analysis highlights at least two important determinants of the efficiency of policymaking in the face of climate change, rhetoric and trust in government. The Importance of Rhetoric: When ∆ > 1, there is no equilibrium in which officemotivated candidates campaign with the policies needed for severe climate change, even if they know for sure that ω = 1. Of course, in real life, we do not discuss the issue of climate change in terms of baseline welfare losses, but rather using verbal descriptions. In recent years, an increasing number of people have stopped using the relatively neutral terms "global warming" or "climate change" and have instead adopted more extreme and loaded language such as "climate crisis" or "climate emergency." Indeed, a comparison of Google search trends in the U.S. from January 2014 to July 2024 shows that, starting around 2019, the relative frequency with which these terms are used has been increasing, see Figure 3. One reason for this change is that many activist groups started to use a more aggressive rhetoric in an effort to emphasize the importance of swift climate policy changes. For example, the activist group Extinction Rebellion writes on their homepage:3 "This is an Emergency. Life on Earth is in crisis. Our climate is changing faster than scientists predicted and the stakes are high. Biodiversity loss. Crop failure. Social and ecological collapse. Mass extinction. We are running out of time, and our governments have failed to act." The model suggests that such a shift in language may have undesired consequences, because it may lead voters to ignore information suggesting that climate change is a problem, whereas information stating the opposite is trusted more than it should. And in fact, the fraction of U.S. Americans who stated in PEW polls that they "personally care a great deal about the issue of climate change" increased between 2016 and 2018 from 36% to 44%, but then dropped to 37% in 2023. At the same time, the fraction of people who stated to either not care too much or to not care at all about the issue first decreased from 26% in 2016 to 22% in 2018, but then increased again to 27% in 2023. 4 These changes can be explained by the model, and they create stronger incentives for politicians to ignore their information about the true state of the world when designing policies. That framing and language may have an important effect on wether people learn or not is well established in psychology. For example, Smith and Mackie (2007) mention the importance of not creating too much anxiety in receivers when the intent is to change their attitudes:

"To be successful, fear appeals must arouse just the right amount of anxiety by showing the negative consequences [. . . ] that will follow if behavior doesn't change. showing how the negative consequences can be avoided." Smith and Mackie (2007), page 257 Excessively negative rhetoric may create too much anxiety and may hence prevent attitude changes and learning, see also McDonald, Chai, and Newell (2015). The risk to trigger such excessive emotional responses is particularly large when people's general livelihood seems threatened, which is true in the case of climate change. Writing explicitly about the issue climate change, Clayton, Manning, Krygsman, and Speiser (2017) state that "[t]he ability to process information and make decisions without being disabled by extreme emotional responses is threatened by climate change. Some emotional response is normal, and even negative emotions are a necessary part of a fulfilling life. In the extreme case, however, they can interfere with our ability to think rationally, plan our behavior, and consider alternative actions." Clayton, Manning, Krygsman, and Speiser (2017), page 16

Other papers that highlight the importance of framing for the efficacy to learn about climate change include Spence and Pidgeon (2010), Jones andPeterson (2017), andNgo, Poortvliet, andKlerkx (2022). Hence, language or rhetoric may indeed be important factors in explaining voters' attitudes towards climate change, and therefore may as well be determinants of political inactivity in the face of climate change.
The Importance of Trust in Government: On the other hand, Trust in the Government to choose appropriate policies for the problems at hand matters. In the model this is captured by κ(s, p, μ). If voters belief the correct policy will be chosen, then κ(s, p, μ) = π(s, p, μ), and in this case an efficient equilibrium exists if ∆ < 1. However, if voters are pessimistic about politician's ability or incentives to implement the right policies-κ(s, p, μ) is then independent of the signal s-then this becomes self-confirming, leading politicians to ignore their information, and the optimal policy may not be chosen. Hence, the model suggests that there is a positive relationship between efforts against climate change and trust in government. Note that in a model with no motivated beliefs, such a prediction could not emerge, because the belief about climate change is independent of trust in government, and hence so is the implemented policy. It is the interaction of trust in government κ and motivated beliefs μ that causes this result. Of course, trust in government is not the only determinant of progress against climate change. Different countries face different costs of adopting new policies. In the model, this is captured by β. When β is large, inaction may be very costly, while if β is small, inaction has little consequences. Empirically, β could be interpreted as economic cost of (not) dealing with climate change in an appropriate way. Often, anti-climate change policies aim at reducing CO2 emissions. This may be quite costly for countries rich in oil and gas, while it is less costly for other countries. Hence, countries rich in fossil energy sources are less likely to make progress against climate change than countries with little or no such resources. We can test the hypotheses using cross-sectional data. As the dependant variable, I use the Climate Change Performance Index (CCPI ) published jointly by Germanwatch, the NewClimate Institute, and the Climate Action Network International. 5 The CCPI takes values between 0 and 100, where higher values indicate that a country performs better in enacting appropriate policies against climate change. The considered policies include reductions in greenhouse gas emissions (40%), expansion of renewable energy sources (20%), general energy use (20%), and other climate policies (20%). As controls for trust in government I use the OECD's Trust in Government Indicator (TGI ). 6 The TGI also takes values between 0 and 100 and equals the share of people reporting to have confidence in the national government. As additional control variables, I use countries' confirmed oil reserves in billion barrels (Oil ), which can be interpreted as a measure of the cost of climate change policies, and the Global Climate Risk Index (Risk ), published by Germanwatch, which can be interpreted as a measure of the benefits of climate change policies. 7 In Table 1 I summarize the included variables. Unfortunately, the number of countries for which all of these variables are available is small (N = 19), and hence power is limited. Nevertheless, let us now take a first look at the data. Figure 4 shows a scatter plot of CCPI and TGI for the different countries including

The estimate of β captures the relationship we are interested in. Table 2 below shows the regression results. Despite the low power, β is positive and statistically significant in all specifications. Moreover, a one standard deviation increase of TGI leads to an increase of CCPI between 0.463 and 0.495 standard deviations, depending on the chosen specification. Therefore, the relation appears to be of relevance. Checking for potential heteroscedasticity, the p-values of the Breusch-Pagan test are larger than 0.4 for all specifications, suggesting that heteroscedasticity is no problem. Inspecting the Q-Q plots of the different specifications (see Figure 5 in Appendix B), further supports this conclusion. Hence, there indeed seems to be a significant and positive correlation between CCPI and TGI, as suggested by the model. This paper illustrates the negative impact that voter beliefs and expectations can have on political decision-making, particularly in the context of climate change policy. The model demonstrates that when voters are inclined to dismiss the severity of climate change, this skews the equilibrium toward suboptimal policy choices by incentivizing office-motivated politicians to act in ways that contradict their own information. The analysis reveals thatin the presence of motivated reasoning-trust in the functioning of government plays a critical role for the efficiency of policy-making. A first look at the data confirms this result. Moreover, the paper suggests that political rhetoric plays an important role as well: if politicians, scientists, journalists, and activists aim to contribute to better climate change policy, they must navigate a delicate balance between conveying information truthfully and avoiding the risk of pushing voters into denial. The proof follows from (4):

Here we have s and the expression in brackets that jointly determine the derivative's sign. Consider next the term in parentheses: Finally, if ∆ = 1, then we cannot have κ(s, p, μ) > κ. Thus, AU (s, p, μ) is either flat in μ if κ(s, p, μ) = 1, implying any μ yields the same anticipatory utility, and we have μ * = σ, or the situation resembles the case with ∆ > 1 discussed above. Follows from the discussion in the text and Lemma 1. We prove the different cases successively. ∆ > 1: We know from Corollary 1 that all voters with s > 0 have belief π(s) = π, while those with s < 0 have belief π(s) = 0. Hence, the latter always vote for policy 0. Wether a voter with s > 0 votes for policy 1 or policy 0 depends on the comparison of π and π. In particular, we know from (5) that a voter votes for policy 1 if π(s) > π, for policy 0 if π(s) < π, and they choose each with a probability of 50% if π(s) = π.
Hence, if π < π, all voters vote for policy 0. If π = π, all voters receiving s < 0 plus half of the voter receiving s > 0 vote for policy 0, while the other half of s > 0 voters vote for policy 1. As a consequence, policy 0 wins all the time if π ≤ π. This implies that we must have κ * (s, p, μ * ) = 0 for all s.

However, if π > π, all voters vote informatively, and thus the optimal policy always wins. It follows that in state 0 a majority votes for policy 0, while in state 1 a majority votes for policy 1. Hence, voters know that the policy that matches the state wins all the time. The belief about the state is π(s) = π if s ≥ 0, implying κ * (s, p, μ * )| s≥0 = π, and π(s) = 0 if s < 0, and hence κ * (s, p, μ * )| s<0 = 0. Could there be other pure strategy equilibria? μ * is uniquely determined, and hence also π(s, p, μ * ) is uniquely determined. But this implies that equilibrium vote shares are unique, leaving no room for beliefs κ(s, p, μ) that are consistent with these vote shares and that differ from the ones established before. Hence, if ∆ > 1, no other equilibrium in the voting subgame can exist. ∆ ≤ 1: First assume that κ(s, p, μ) is increasing in s in the sense that Sign [κ(s, p, μ) -κ] = Sign [s]. Then any voter with s < 0 chooses μ * = ∞, and thus all these voters hold belief π(s, p, μ * ) = 0 and vote for policy 0. Moreover, any voter with s > 0 chooses also μ * = ∞, and thus all these voters hold belief π(s, p, μ * ) = 1 and vote for policy 1. This implies that indeed the policy that matches the state always wins and we need to have κ(s, p, μ * )| s<0 = 0 as well as κ(s, p, μ * )| s>0 = 1, proving part 2 (a) of the proposition. Next, assume voters generally believe that policy 0 will be implemented, independent of the true state ω. Then κ(s, p, μ * ) = 0 for all s. Then any voter with s < 0 chooses μ * = ∞, and thus all these voters hold belief π(s, p, μ * ) = 0 and vote for policy 0. Moreover, any voter with s > 0 chooses μ * = 0. If and only if π ≤ π, this implies that indeed always a majority of voters votes for policy 0, and hence when π ≤ π there exists an equilibrium of the voting subgame in which policy 0 is always chosen. This proves part 2 (b). Now assume voters generally believe that policy 1 will be implemented, independent of the true state ω. Then κ(s, p, μ * ) = 1 for all s, and any voter with s > 0 chooses μ * = ∞, and thus all these voters hold belief π(s, p, μ * ) = 1 and vote for policy 1. Moreover, any voter with s < 0 chooses μ * = 0. If and only if π ≥ π, this implies that indeed always a majority of voters votes for policy 1, and hence when π ≥ π there exists an equilibrium of the voting subgame in which policy 1 is always chosen. This proves part 2 (c). Consider a situation in which beliefs are just as in the equilibrium discussed above for the case of ∆ > 1. That is, κ(s, p, μ) = 0 for all s. Then, as before, μ * (s) = ∞ and π(s, p, μ * ) = 0 if s < 0, and μ * (s) = 0 and π(s, p, μ * ) = q else. It follows that if q ≤ 1 1+β , a majority of voters always votes for policy 0. Hence, this is indeed an equilibrium. Consider next a situation in which beliefs are just opposite to what we have seen above, namely κ(s, p, μ) = 1 for all s. Then, μ * (s) = 0 and π(s, p, μ * ) = 1 if s > 0, and μ * (s) = 0 and π(s, p, μ * ) = q else. It follows that if q ≥ 1 1+β , a majority of voters always votes for policy 1. Hence, this is also an equilibrium. Finally, consider part 2 (d). An equilibrium in which the optimal policy never wins would imply policy 1 wins if ω = 0 and policy 0 wins if ω = 1. Hence, we would need to have κ(s, p, μ) weakly decreasing in s. Consider a voter with signal s > 0. It must be true that most of these voters vote for policy 0. Hence, it cannot be true that κ ≥ κ. If κ(s, p, μ) < κ, these voters all hold belief π. Next consider voters with s < 0. It must be true that most of these voters vote for policy 1, implying κ(s, p, μ) ≤ κ is not possible. Thus, because κ(s, p, μ) > κ, these voters all also hold belief π. If π > π, policy 1 always wins, contradicting that the optimal policy never wins. If π < π, policy 0 always wins, also contradicting that the optimal policy never wins. Finally, if π = π, in each state, each policy wins with 50%, and thus also the optimal policy wins with a chance of 50%.
This implies that the actual state is irrelevant for the probability of each policy winning, and thus we must have κ(s, p, μ) = 1 2 for all s. But then it is not possible that κ(s, p, μ) differs for voters with s > 0 and voters with s < 0. Hence, such an equilibrium of the voting subgame cannot exist. This complete the proof of the proposition. Follows from the discussion in the text. We first consider the case of severe climate change being catastrophic, ∆ > 1. The other case of severe climate change having only mild baseline welfare consequences will be considered thereafter. Note that π = q ≤ π in a symmetric pure strategy equilibrium. Suppose that off the equilibrium path voters observe p ∈ {{0, 1}, {1, 0}}. ∆ > 1: We know from Corollary 1 that π(s, p, μ * ) = 0 if s < 0 and π(s, p, μ * ) = π if s ≥ 0. Hence, π ≤ π, and thus no voter ever votes for policy 1, whereas policy 0 always wins at the ballot. It follows that κ * (s, p, μ * ) = 0, with μ * (s) as described in Lemma 1. Thus, the unique equilibrium is candidates choosing p * = (0, 0). This is supported by κ * (s, p * , μ * ) = 0 and μ * (s) as described in Lemma 1. ∆ ≤ 1: Assume first κ(s, p, μ) = 0 for all s. Then it follows from Corollary 1 that π(s, p, μ) = 0 if s < 0 and π(s, p, μ) = π = q if s > 0. Because q ≤ 1 1+β , a majority of voters always votes for policy 0. It follows from Proposition 2 that no candidate has an incentive to campaign on p = 1. Consequently, p * = (0, 0), κ(s, p * , μ * ) = 0, and μ * follows from Lemma 1. Suppose next that ∆ < 1 and that κ > κ if s > 0 and κ < κ if s < 0. Note that this means that we must have ∆ < 1. Then it follows from Corollary 1 that π(s, p, μ) = 0 if s < 0 and π(s, p, μ) = 1 if s > 0. Hence, all voters all the time vote informatively, and thus the policy that matches the state wins, implying κ = π(s, p, μ). It follows from Proposition 2 that, if candidates expect voters to behave this way, they have an incentive to choose the socially optimal policies. Hence, p * = (ω, ω), κ(s, p * , μ * ) = π(s, p * , μ * ), and μ * follows from Lemma 1. Now suppose that ∆ = 1. Moreover, suppose an efficient equilibrium exists also in this case, with κ(s, p, μ) = 1 = κ if s > 0, and κ = 0 < κ if s < 0. Then it follows from Corollary 1 that π(s, p, μ) = 0 if s < 0, and thus any voter with s < 0 votes for policy 0. For voters with s > 0, μ * = µ, and thus these voters hold perfect Bayesian beliefs. This implies, by Assumption 2, that voters vote informatively. However, then the right policy is chosen in any state, and thus we need to have κ(s, p, μ) = π(s, p, μ). But π(s, p, μ) < 1, and therefore voters with s > 0 would choose μ = 0 instead of μ = µ. Hence, when ∆ = 1, no efficient equilibrium exists. It follows from Proposition 1 part 2 (d) that no equilibrium can exist in which always the wrong policy is chosen. Hence, we now only need to show that no equilibrium, in which policy 1 always wins, can exist. Suppose to the contrary that voters believe that policy 1 wins with certainty, κ(s, p, μ) = 1 ≥ κ for all s. Then it follows from Corollary 1 that, if ∆ < 1, π(s, p, μ) = q ≤ π if s < 0 and π(s, p, μ) = 1 if s > 0. Therefore, all voters with s > 0 always vote for policy 1. If sufficiently many voters with s < 0 also vote for policy 1, policy 1 wins all the time. This is the case iff q ≥ 1 1+β . However, this contradicts Assumption 1. A similar argument shows that p = (1, 1) cannot be equilibrium, either, if ∆ = 1. Hence, it follows that no equilibrium, in which policy 1 is always chosen, exists. This proves the proposition. Take the belief about ω of a voter who receives s and chooses α:

. Anticipatory utility is defined as before in (2). Hence, it's derivative with respect to α is

and zero else. This proves the result. It follows from Lemma 2 that independent of the true state ω, a majority of voters prefers to vote for policy 0 when offered the choice. The proof then follows from Proposition 2. We focus on pure strategy equilibria. It then follows from Lemma 1 that when s > 0, a voter would either like to choose μ = ∞, or μ = µ. Moreover, when s < 0, a voter would either like to choose μ = 0, or μ = µ. Next have a look how a voter's objective function changes with s:

and hence W (s, p, μ) strictly decreases in s for all μ. Note that when μ = 0, then the realization of s is irrelevant as the belief is π(s, p, μ)| μ=0∧s>0 = q. Hence, the voter with the greatest incentive to distort µ has s → ∞.
For this voter, the payoff of not distorting and instead choosing μ = µ is W (s, p, μ)| μ=µ∧s→∞ = -β(1 -κ(s, p, μ)) -∆. If, to the contrary, any such voter chooses μ = 0, the payoff is W (s, p, μ)| μ=0∧s>0 = -κ(s, p, μ)(1 -q) -q(β(1 -κ(s, p, μ)) + ∆) -γ. If γ ≥ γ + ≡ (1 -q)(β(1 -κ(s, p, μ)) + ∆ -κ(s, p, μ)), then no voter with s > 0 has an incentive to distort the issue's complexity. Otherwise, that is, if γ < γ + , then there exists a unique signal realization s = s + > 0 such that a voter receiving this signal is indifferent between choosing μ = 0 and μ = µ. The payoff of a voter choosing to not distort a signal s is W (s, p, μ)| μ=µ = -κ(s, p, μ)(1 -q) + q(β(1 -κ(s, p, μ)) + ∆)e σ 2 ln 1 + γ q(β-γ+∆-(β+1)κ(s,p,μ)(1-q)-q(β+∆))

. This is smaller than π if

The belief of a voter who chooses μ = µ and receives signal s > 0 is π(s, p, μ) = q q + (1 -q)e -2sµ σ 2

. The signal at which such a voter starts to vote for policy 1 is the signal such that π(s, p, μ) = π. In particular, this signal realization is s * , where s * ≡

is the CDF of the normal distribution with mean µ and standard deviation σ, the share of voters voting for policy 1 if ω = 1 is

Recall that s + 0 is increasing in γ, and hence V 0 is monotonically increasing in γ. When γ = 0, we know from our earlier analysis that voters all vote for policy 0 despite s > 0. If γ → ∞, no voters distorts µ and, by Assumption 2, a majority votes for policy 1 iff ω = 1. By continuity, there is a unique γ such that a majority votes for policy 0 if and only if γ < γ. To see incentives, first consider how W (s, p, μ) changes with μ, when μ ≥ µ. It is easy to show that W (s, p, μ) is strictly concave in μ and thus an interior equilibrium exists for all s. The FOC for an interior optimum is ∂W (s, p, μ)

∂ μ (1 -q) (σ 2 + 2μs) -qe 2 μs σ 2 (2μs -σ 2 )

which is the case iff Ω = (1 -q) (σ 2 + 2μs) -qe 2 μs σ 2 (2μs -σ 2 ) < 0. If s = 0, Ω| s=0 = σ 2 > 0, and hence μ * (s) is decreasing. Moreover, lim s→-∞ Ω = -∞. Thus, if Ω is monotone in s, then there is a unique s -< 0 such that μ * (s) increases in s if s < s -and it decreases in s if s ∈ (s -, 0]. We have ∂Ω ∂s = 2μ 1 -q -q 2μse

2 μs σ 2 σ 2 > 0. This proves the existence of a unique s -. Moreover, because |Γ| decreases in c, the absolute deviation from µ decreases in the cost c.

Next consider s > 0, implying μ < µ. Rearranging the FOC yields σ 2 + q -1 This is negative when s = 0. Hence, if we can show that Ω ′ is convex, we prove the existence of a unique s + . Take the second derivative with respect to s:

and thus Ω ′ is indeed convex in s. Thus, there exists a unique s + > 0 such that μ * (s) increases in s if s > s + and it decreases in s when s ∈ [0, s + ). Moreover, because |Γ ′ | decreases in c, the absolute deviation from µ decreases in the cost c. This proves the lemma. The proof basically follows along the lines of the discussion in the text. We know from Lemma 4 that |μ(s) -µ| decreases in c. Moreover, lim c→∞ μ(s) = µ, because then both Γ = 0 and Γ ′ = 0 (see the proof of Lemma 4). Moreover, as c ↘ 0, we are back in the scenario of Proposition 3. Finally note that both μ(s) and π(s, p, μ) are continuous functions of both s and c, and thus so is the share of voters voting for policy 1 in state ω = 1 if p 1 ̸ = p 2 . Hence, there must exist ĉ such that the share of voters V 0 voting for policy 1 in state 1 is just 1 2 . Moreover, Sign [c -ĉ] = Sign V 0 -1 2 . This proves the proposition. 2. This assumption is not without loss of generality for the model's conclusions. Allowing for q ≥ 1 1+β would imply that the set of possible equilibria is larger. I chose to assume q < 1 1+β , because it seems realistic that voters need to be convinced to support anti-climate change policies. Moreover, as a second benefit, Assumption 1 keeps the paper's exposition more concise. This could be justified, for example, because candidates have types as well. An ideological candidate always chooses p i = i-1, i ∈ {0, 1}. A strategic candidate chooses the policy that is expected to maximize the probability to win the election. A model in which each candidate i is ideological with probability γ ∈ (0, 1) and non-ideological with probability 1 -γ would yield the same results regarding the platform choices of office-motivated candidates as the assumption of non-informative deviations. See https://rebellion.global/ (accessed on 24/09/2024). See https://www.pewresearch.org/science/2023/10/25/how-americans-view-future-harms-fro m-climate-change-in-their-community-and-around-the-u-s/. See https://ccpi.org/. See https://www.oecd.org/en/data/indicators/trust-in-government.html

See https://www.germanwatch.org/en/cri

Note that the theoretical analysis is valid only for democracies.
However, because all countries in the sample are classified either as Democracy or Full Democracy in the Polity IV data series, and because the sample size is very small, I do not control for polity scores in the regressions.