1. The model

We consider a model with an Incumbent (I), a Challenger (C), and a Voter (V).Footnote ² In each of two periods, $t\in\{1,2\}$, the politician in office chooses a counterterrorism policy, $p_t \in \mathbb{R}_+$. An increasing and strictly convex function c(p) measures the social costs of choosing p, which can be thought of as the cost of curtailing civil liberties in order to ensure higher security from terrorism. Incumbent also cares about re-election and receives an additional payoff B > 0 if reelected, and 0 if not reelected.

Terrorism occurrence is a binary variable, $a_t\in\{0,1\}$, with $a_t=1$ denoting a successful terrorist attack and $a_t=0$ denoting no terrorist attack. Let $u(a_t)$ denote the payoff received by Incumbent and Voter if the outcome in period t is $a_t\in \{0,1\}$, and $s\equiv u(0)- u(1) \gt 0$ denote the net benefit of security from terrorism.

The probability of a successful attack is given by the function $\pi(\theta_i, p)$, which is decreasing and convex in p and decreasing in the politician’s competence (θ_i, where $i\in\{I,C\}$). In this context, one can think of Incumbent’s competence, among other things, as her managerial ability to set the general direction and tone of the federal bureaucracy in charge of terrorism prevention. There is symmetric uncertainty about Incumbent’s ability, which is drawn from the set $\Theta=\{\underline{\theta}, \overline{\theta}\}$, with $\overline{\theta} \gt \underline{\theta}$, and it is common knowledge that $Pr(\theta_i=\overline{\theta})=\gamma$.Footnote ³ We assume that $\frac{\partial \pi(\overline{\theta}, p)}{\partial p}=\frac{\partial \pi(\underline{\theta}, p)}{\partial p}$, meaning that the size of the effect of a change in counterterrorism policy on the probability of a terrorist attack does not depend on the politician’s competence.Footnote ⁴

Finally, if Incumbent is not reelected, she will receive a payoff of zero; if she is reelected, in the second period, she receives a policy payoff given by the cost of curtailing civil liberties and the outcome of the fight against terrorism (i.e., occurrence or absence of a terrorist attack). Call this policy payoff $u^2_P$ and call $r=B+u^2_P \gt 0$ the cumulative benefit of holding office, on which we focus for the remainder of the paper.Footnote ⁵

After Incumbent’s choice of p ₁, Voter observes whether or not there is a terrorist attack but does not observe the counterterrorism policy, p ₁.Footnote ⁶ Voter chooses whether to reelect Incumbent or to elect Challenger, who is randomly drawn from the same pool of candidates as Incumbent. Voter also cares about the performance on other policy issues, captured by the parameters w_C and w_I for Challenger and Incumbent respectively, which are realizations of independent draws from a random variable W. Since Incumbent might not know the identity of Challenger she will face, we assume Incumbent does not know w_C before choosing p ₁. The difference $w_I-w_C$ is itself a random variable, distributed according to a strictly increasing CDF that we denote by F, with density function f. Lastly, to capture the salience Voter attaches to terrorism prevention relative to other policy consideration, we weigh the payoff related to terrorism prevention by a parameter $\psi \in (0,1)$, while we weight the benefit from other policy considerations by $(1-\psi)$.Footnote ⁷ In summary, Voter’s per-period utility function is as follows:

\begin{equation*} U_V =\psi\big[u(0)-\mathbb{E}[\pi(\theta_i,p_t)]s-c(p_t)\big]+(1-\psi)w_i, \end{equation*}

where i denotes the identity of the politician holding office in that period.Footnote ⁸

Incumbent’s (expected) payoff is as follows:

(1)\begin{equation} U_I=u(0)+v(0;p_1)r-\mathbb{E}[\pi(\theta_I,p_1)](s+\Delta(p_1) r)-c(p_1), \end{equation}

where $v(j;p_1)$ is the reelection probability following a = j, with $ j \in \{0,1\}$, and $\Delta(p_1)\equiv (v(0;p_1))-v(1;p_1)))$ is the difference between the reelection probability if a = 0 and if a = 1, when the Incumbent chooses counterterrorism policy p ₁.

Note that Voter and Incumbent have the same preference for the benefits and the costs of terrorism prevention, $\mathbb{E}[\pi(\theta_I,p_t)]s-c(p_t)$. This allows us to investigate whether or not democratic responsiveness increases when performing well in terms of terrorism prevention becomes more critical to secure reelection.

After the electoral decision of voter, the (new) Incumbent chooses a new policy, p ₂, and then the game ends with the new outcome. To summarize, the timing of the game follows.

Period 1

1. (1) Nature draws Incumbent’s and Challenger’s abilities, θ_I and θ_C.

2. (2) Incumbent chooses counterterrorism policy p ₁.

3. (3) A terrorist attack happens with probability $\pi(\theta_I,p_1)$.

4. (4) Voter observes whether or not a terrorist attack occurs, $a_t\in \{0,1\}$, observes the realizations of w_I and w_C, and decides whether to reelect Incumbent or to elect Challenger.

Period 2

1. (1) The elected politician $i\in\{I,C\}$ chooses counterterrorism policy p ₂.

2. (2) A terrorist attack occurs with probability $\pi(\theta_i,p_2)$.

3. (3) Utilities are realized, and the game ends.

To show our main result that increased electoral salience leads to less congruence between Voter’s preferences and the policy implemented by elected representatives, our analysis proceeds as follows. First, we pin down what Voter’s preferred counterterrorism policy would be. Then, we analyze the strategic interaction between Voter and Incumbent, to derive Incumbent’s equilibrium policy choice. In the model with Incumbent, we solve for the Perfect Bayesian Equilibria of the game. Finally, we analyze how an increased electoral salience of terrorism prevention affects the congruence between Voter’s and Incumbent’s policy choices.

2. Salience vs congruence

First, from Voter’s standpoint, the optimal counterterrorism policy choice in each period, denoted by $p^{\ast}_{V}$, solves,

(2)\begin{equation} -\frac{d}{d p_t}\mathbb{E}[\pi(\theta,p_t)]s-c'(p_t)=0. \end{equation}

The optimization problem is strictly concave in p, and thus there is a unique $p^{\ast}_{V}$.Footnote ⁹

Moving to the case in which Incumbent chooses p while Voter decides whether or not to reelect Incumbent, recall that the only difference in incentives between Incumbent and Voter is the desire of the former to be in office. As such, with no accountability mechanism in place, in the second period the politician in office (either Incumbent or Challenger) will choose a counterterrorism policy that is identical to the one that Voter would choose. That is, in the absence of electoral incentives, Voter’s preferences and the politicians’ preferences are perfectly aligned.

Moving backwards, let us analyze the election stage. After observing the outcome a = j in the first period, Voter reelects Incumbent if and only if

\begin{equation*} \mathbb{E}[ U_V(p_2)\mid I, a=j]\geq \mathbb{E}[U_V(p_2) \mid C], \end{equation*}

where the expectation is over θ_i given that candidate $i \in \{I,C\}$ is in office. Due to the absence of complementarities or substitutabilites between p and θ, Incumbent’s and Challenger’s policy choices at t = 2 do not depend on Voter’s and/or Incumbent’s posterior beliefs about Incumbent’s ability.

As a result, Voter’s reelection rule becomes

(3)\begin{equation} w\ge \frac{\psi}{1-\psi}s\Big[\mathbb{E}[\pi(\theta_I,p_2\mid a=j, \tilde{p}_1)]-\mathbb{E}[\pi(\theta_C,p_2)]\Big] \end{equation}

where $w=w_I-w_C$ is the utility difference (from Voter’s perspective) between Incumbent and Challenger on policy issues other than terrorism, and $\tilde{p}_1$ is the policy that Voter, who does not observe p ₁, expects Incumbent to choose. As w is a random variable from Incumbent’s perspective, denoting by $v(a=j;\tilde{p}_1)$ the probability Incumbent is reelected given the outcome a = j, for $j \in \{0,1\}$ and expected policy $\tilde{p}_1$, we have,

(4)\begin{equation} v(j;\tilde{p}_1)=1- F \bigg( \frac{\psi}{1-\psi}s\Big[\mathbb{E}[\pi(\theta_I,p_2\mid a=j, \tilde{p}_1)]-\mathbb{E}[\pi(\theta_C,p_2)]\Big]\bigg). \end{equation}

Voter updates her beliefs about Incumbent’s competence from observing the outcome. If Voter observes a terrorist attack, using Bayes’ Rule, Voter believes Incumbent is competent with probability given by,

\begin{equation*} Pr(\theta_I=\overline{\theta} \mid a=1, \tilde{p}_1)=\frac{\pi(\overline{\theta},\tilde{p}_1)\gamma}{\pi(\overline{\theta},\tilde{p}_1)\gamma+\pi(\underline{\theta},\tilde{p}_1)(1-\gamma)}, \end{equation*}

where γ is the prior probability that $\theta_I=\overline{\theta}$. Similarly, if Voter observes no terrorist attack, Voter believes Incumbent is incompetent with probability given by,

\begin{equation*} Pr(\theta_I=\overline{\theta} \mid a=0, \tilde{p}_1)=\frac{(1-\pi(\overline{\theta},\tilde{p}_1))\gamma}{(1-\pi(\overline{\theta},\tilde{p}_1))\gamma+(1-\pi(\underline{\theta},\tilde{p}_1))(1-\gamma)}. \end{equation*}

Given these posterior beliefs, we have the following result.

If Voter observes no terrorist attack, she becomes more optimistic about Incumbent’s ability to stop terrorism in the next period, while a successful attack induces her to become more pessimistic about Incumbent’s competence. As a consequence, terrorism prevention yields both a direct, s, and an indirect, $\Delta r$, benefit for Incumbent. Importantly, when terrorism prevention becomes more prominent in Voter’s decision, stopping attacks becomes even more crucial for Incumbent, whose electoral fortunes hinge more and more on it.

We can now move to Incumbent’s optimal choice. Recall that r is Incumbent’s cumulative benefit of reelection. Given Voter’s re-election rule, Incumbent’s problem is,

(5)\begin{equation} \max_{p_1 \in[0,\overline{p}]} u(0)+v(0;\tilde{p}_1)r -\mathbb{E}[\pi(\theta_I,p_1](s+\Delta(\tilde{p}_1) r)-c(p_1). \end{equation}

Incumbent chooses the level of p ₁ that satisfies the following first order condition:

\begin{equation*} -\frac{d}{d p_1}\mathbb{E}[\pi(\theta,p_1)](s+\Delta(\tilde{p}_1) r)-c'(p_1)=0 \end{equation*}

The optimization problem is strictly concave in p, as the second derivative is negative.Footnote ¹⁰ Therefore, denote by $p_{I}(\Delta)$ Incumbent’s best response function, and notice that it is increasing in Δ. The equilibrium level of p ₁, which we denote by $p_ I^*$ then solves the following

(6)\begin{equation} p_1=p_I(\Delta(p_1)). \end{equation}

Now, we can compare Incumbent’s equilibrium choice with Voter’s preferred policy choice and determine whether there is more or less policy congruence when the salience of the main policy issue increases. We turn to this analysis in the next section.

3. The effect of salience on policy congruence

We first show that, unsurprisingly, Incumbent is not a perfect representative of Voter due to her inherent interest in remaining in office. This implies a divergence between Incumbent’s enacted policy and the policy preferences of Voter. We establish the presence of such divergence in the following result.

The result in Proposition 3 identifies the distortionary effects of electoral incentives on the optimal counterterrorism policy choice. While in his choice of p Voter takes into account only the basic trade-off between security and liberty, Incumbent also tries to improve her electoral prospects. Since ensuring security from terrorism helps her reelections chances, Incumbent’s electoral concerns lead her to choose a further reaching counterterrorism policy than Voter would prefer.

The main question is how variation in the salience of terrorism prevention on Voter’s reelection calculus affects this divergence between the enacted policy and Voter’s preferred policy. The following proposition provides an answer to this question.

Proposition 4 indicates that the gap between enacted policies and the preferences of Voter widens when terrorism prevention becomes more electorally salient. In other words, heightened salience undermines representation. Below, we explore the implications of this result within the realm of security policy and counterterrorism. Subsequently, we discuss how our findings reveal the broader impact of electoral salience on policy congruence.

The democratic foundations of counterterrorism measures have been widely debated since the 9/11 attacks, particularly regarding their impact on fundamental rights and liberties. A common empirical pattern following terrorist attacks is for governments, regardless of partisan orientation, to adopt legislative measures that grant executive officials broad discretion to implement counterterrorism policies, all in the name of protecting voters from the looming threat of terrorism. This trend is evident in laws such as the USA Patriot Act of 2001, passed after 9/11 in the US.

These legislative acts, which increase executive officials’ discretionary power, have led to the development of counterterrorism policies, like surveillance programs, that were created and enacted behind closed doors and shrouded in secrecy.Footnote ¹¹ Such policies are often justified by a perceived public demand for greater security. The fear and devastation caused by events like 9/11 heightened public concern over terrorism, prompting calls for more effective counterterrorism strategies, even if they require trading off certain rights and liberties.Footnote ¹²

While the electoral process is often viewed as a check on excessive counterterrorism powers relative to what voters would accept (Posner and Vermeule Reference Posner and Vermeule2011), our analysis challenges the assumption that public demand for security aligns with majoritarian interests. Heightened public concern about terrorism may lead elected officials to enact policies that deviate from voters’ security preferences. This divergence raises concerns about the democratic accountability of counterterrorism measures enacted by executive officials, particularly surveillance policies, in the aftermath of terror attacks when terrorism prevention is highly salient.Footnote ¹³

Our analysis demonstrates that increased salience undermines policy congruence and, consequently, representation. This finding broadly extends to issues where voters seek specific policy outcomes that depend (stochastically) on unobservable policy inputs and the competence of policymakers, and where voters typically evaluate elected representatives using simple observable data, such as success or failure in achieving desired outcomes. These types of issues are often categorized as valence issues—areas where there is widespread agreement on policy goals, such as enhancing national security, reducing crime, or promoting economic growth and recovery.

In the context of security from terrorism, voters do not observe the policymaking process in detail because most security and counterterrorism measures are conducted behind closed doors, cloaked in secrecy, and shielded from public scrutiny. In other valence policy domains, while the details of policymaking might, in theory, be observable, the complexity and technical nature of such policies mean that the typical median voter faces significant learning costs in understanding the intricacies of economic and social policy. Additionally, voters often exhibit limited interest and face high opportunity costs in dedicating time and effort to grasp these details, especially in highly technical and arcane policy areas.

Indeed, a well-established body of literature indicates that voters are rationally ignorant (Carpini and Keeter Reference Carpini and Keeter1996), often lacking basic knowledge about the policymaking process, including the names of their representatives, let alone the specifics of complex, multi-dimensional legislative acts such as the Health Care Act or the Economic Recovery Act. Whether due to secrecy, lack of expertise, an unwillingness to invest time in understanding the political process, or a combination of these factors, voters often remain unaware of the detailed workings of policymaking in significant valence policy areas. Consequently, they base their electoral decisions on simple, observable heuristics, such as the perceived success or failure of the incumbent in delivering the desired outcome. In such settings, our analysis extends to valence issues beyond just increasing security from terrorism.

In our analysis, we assume that voters and elected representatives face identical benefits and costs when enacting counterterrorism policies. This assumption is motivated by two considerations. First, we examine how the electoral salience of counterterrorism affects policy congruence between elected officials’ actions and voters’ preferences. Specifically, we highlight how elections fail to check excessive counterterrorism powers and, in fact, how electoral demands for security can undermine representation. Second, the assumption aligns with the definition of valence issues, which focus on elected officials’ competence in achieving a desired outcome rather than ideological disagreement. We aim to show that even when the costs and benefits of security policies are identical for voters and officials, electoral incentives tied to heightened security salience undermine policy congruence. This helps explain, for example, the contrast between Obama’s counterterrorism stance before the 2008 presidential election—when he expressed concerns about civil liberties—and his policies as president, when he supported and renewed aggressive counterterrorism measures, such as surveillance, that he had previously criticized.Footnote ¹⁴

More generally, our analysis shows that when an issue becomes more electorally salient, politicians adopt more interventionist policies, as they become less concerned with the costs of enacting them. This framework extends beyond counterterrorism to explain how salience shapes policy congruence and representation, even when voters and elected officials face different costs and benefits. We suggest that as an issue’s salience increases, elected officials are incentivized to pursue more aggressive policies to appear competent to voters. If the costs of enacting policies are the same or lower for officials than for voters, greater salience always leads to increased policy divergence. However, if enactment costs are higher for officials, increased salience may push them to enact policies in the ideological direction of the voters’ ideal policy. Whether this improves or weakens policy congruence depends on the relative positions of voter and official preferences and the policies enacted in response to higher electoral salience.Footnote ¹⁵

4. Conclusion

Should we expect greater congruence between voters’ preferences and enacted policies on more electorally salient issues? In this paper, we address this critical question regarding the theory of representation in democracies. We show that as the salience of a policy issue increases, the congruence between enacted policies and voters’ preferences decreases. While this result has broad applicability to other valence issues, we derive it within the context of security policy and terrorism prevention, one of the most prominent policy issue since the turn of the century.