2. Institutional and electoral constraints on executive power in the literature

Theoretical models of unilateral action focus primarily on either institutional or electoral constraints. The former camp extends the pivotal politics framework (Krehbiel, Reference Krehbiel1998), situating the president as a first-mover in a spatial bargaining game (e.g., Chiou and Rothenberg, Reference Chiou and Rothenberg2017; Howell, Reference Howell2003; Judd and Rothenberg, Reference Judd and Rothenberg2020). Endowed with exogenous discretion, the executive can set policy subject to revision by the legislature or court, which often enables him to secure more preferable policy than were he simply a veto player. While these models isolate first-mover advantage and highlight the limited institutional constraints on executive power, they do not consider the threat, and disciplining effect, of electoral sanction (Christenson and Kriner, Reference Christenson and Kriner2017, Reference Christenson and Kriner2020; Reeves and Rogowski, Reference Reeves and Rogowski2016, Reference Reeves and Rogowski2018, Reference Reeves and RogowskiForthcoming).

Beyond securing policy goals, unilateral action may benefit the executive electorally. Building on models of pandering (Canes-Wrone et al., Reference Canes-Wrone, Herron and Shotts2001; Maskin and Tirole, Reference Maskin and Tirole2004) and career concerns in separation-of-powers settings (Fox and Van Weelden, Reference Fox and Van Weelden2010; Buisseret, Reference Buisseret2016), these models see the executive unilaterally increasing his power (Howell and Wolton, Reference Howell and Wolton2018) or using unilateral action to mobilize high policy demanders (Kang, Reference Kang2020) to secure reelection. Especially relevant is Judd (Reference Judd2017), which models an executive who can choose between default policy or unilateral action that reveals policymaking skill. In equilibrium, unilateral action is necessary for some executives to win reelection, even when the default policy would provide higher welfare. Like Judd (Reference Judd2017), I show that unilateral action may be sufficient for the executive to win reelection when he uses it to signal his congruent type. Importantly, though, it is not necessary. When the legislator proposes mutually agreeable legislation, the executive can increase voter welfare and win reelection without exercising unilateral authority.

This paper is at home alongside a growing subset of models that combine institutional and electoral constraints on unilateral action. One similar model is Stephenson and Nzelibe (Reference Stephenson and Nzelibe2010), which examines voter welfare under three separation-of-powers settings. Using a contracting model, the authors find that voter welfare is highest when the executive can choose between legislation or unilateral action as this arrangement allows the voter to design the most flexible punishment strategy. My results support this finding, but do so in the context of a signaling model that combines selection and sanctioning (see Fearon, Reference Fearon1999). This model also compliments Foster (Reference FosterForthcoming), which highlights the understudied “second-mover” advantages of unilateral action. There, the legislator can anticipate unilateral action and may decline to act in order to dodge sanction from a third-party actor. Like Foster (Reference FosterForthcoming), I model a strategic legislator who takes on the role of first mover. However, a divergent legislator cannot avoid sanction from the voter by declining to legislate. Rather, the relative transparency of unilateral action may incentivize the divergent legislator to head off electorally damaging unilateral action by proposing welfare-enhancing legislation, which the congruent executive always accepts.

3. A model of separated powers and policymaking

This section introduces the model under Checks and Balances. I proceed to analyze equilibrium strategies and beliefs before moving to Unilateralism.

3.1 The policy environment

Both settings feature three players: the executive (E), a median legislator (L), and a representative voter (V). I refer to the executive and legislator collectively as the politicians i, where i ∈ {L,  E}. In each period t ∈ {1,  2}, the legislator (she) privately selects a policy $x_L^t \in \{ -1,\; \, 1\}$. These labels, − 1 and 1, represent left and right policy respectively and should be thought of as representing different policy domains between periods.Footnote ¹ The legislator's selection is revealed to the executive (he) who privately selects a policy from the same binary space, $x_E^t \in \{ -1,\; \, 1\}$. If the executive selects the same policy as the legislator, that policy becomes the period-t policy outcome, x ^t. If the executive selects the opposite policy, gridlock occurs and a default policy, x ^t = 0, is imposed.Footnote ² Admissible policy outcomes are x ^t ∈ { − 1,  0,  1}. Without loss of generality, I assume the voter (he) prefers the right policy alternative in each period, which ensures the politicians have an incentive to play the policymaking game. The voter's per-period payoff is the period-t policy outcome:

$$u^t_V( x^t) = x^t.$$

To simplify the presentation of the model, the voter does not discount the future.

A key assumption of the model is that the voter does not observe politicians’ individual policy selections ($x_i^t$). He does learn the ultimate policy outcome (x ^t) in each period, but only after the policy selection stage has ended. In practice, this means that if new policy is enacted (i.e., x ^t ∈ { − 1,  1}), the voter correctly infers that both politicians selected that policy. If gridlock occurs (i.e., x ^t = 0), the voter knows the politicians have chosen different policies, but he does not know which politician selected $x_i^t = -1$. Substantively, this assumption could be justified in two ways. First, voters typically pay little attention to politics and do not follow debates in Washington (see e.g. Bartels, Reference Bartels1996; Cameron, Reference Cameron2012; Carpini and Keeter, Reference Carpini and Keeter1996), but they do learn about policy changes retrospectively (e.g., Fiorina, Reference Fiorina1981). Second, one could imagine the private selection of $x_i^t$ happening behind closed doors (e.g., a group of legislators privately meet with the president at the White House to debate the details of a bill), followed by an unmodeled stage in which the politicians announce their policy selections. Ultimately, these announcements would be unverifiable and could be dismissed as cheap talk until policy is enacted. If new policy were enacted, the voter could be sure that both politicians did support that policy. If gridlock occurred, the voter might be uncertain about who is at fault. For example, both politicians could claim to support infrastructure projects but disagree over how much to spend. If gridlock occurred, each side might claim that the other was never actually interested in infrastructure and was bargaining in bad faith. In that case, the voter would not be sure who was telling the truth, making the original announcements meaningless. In the “Extensions and robustness” section, I also discuss an extension of the model in which I relax this assumption and instead posit that the voter observes each politician's individual policy selection with positive probability. As the probability of observing the individual selections increases, unilateral action loses its relative transparency advantage and the welfare-enhancing effects of Unilateralism are reduced or even reversed in more extreme cases.

In light of the previous discussion, this model would be most appropriate when analyzing either policies over which the two parties hold un-polarized positions (e.g., infrastructure and veterans benefits but not immigration or healthcare) or executive-legislative bargaining in the context of unified government where party cannot serve as a heuristic for policy positions. In those settings, both politicians would seem to hold similar policy preferences and gridlock might truly lead to voter confusion. By contrast, a voter is unlikely to be confused under divided government when the two parties fail to agree on, say, immigration policy.

3.2 Uncertainty about politician types

Both the executive and legislator have preferences over policy conditional on their type, θ _i ∈ {C,  D}. A politician with type θ _i = C is congruent: their preferences over policy align with the voter's. A politician with type θ _i = D is divergent: their preference ordering is opposite the voter's. At the beginning of the game, these types are drawn independently from different distributions; they are revealed to the politicians but not the voter.Footnote ³ However, the voter knows the distributions from which the types are drawn and holds beliefs that the legislator is congruent with $\Pr ( \theta _L = C) = \pi > {1\over 2}$ and the executive is congruent with $\Pr ( \theta _E = C) = \gamma > {1\over 2}$.

Politicians receive per-period, policy-specific payoffs conditional on their type and the enacted policy x ^t. If the politician is congruent, their period-t policy-specific payoff is x ^t. A divergent politician receives − x ^t. Politicians also receive per-period office-holding rents, β _i, a random variable drawn for each politician from a uniform distribution.Footnote ⁴ Note, β _i is not redrawn between periods if i is reelected. As with politicians’ types, the voter does not know politicians’ realizations of β _i, only the distribution from which β is drawn. Together, a congruent politician's period-t payoff is given by:

$$u_i^t = ( x^t;\; \theta_i = C,\; \beta_i) = x^t + \beta_i.$$

For a divergent politician:

$$u_i^t = ( x^t;\; \theta_i = D,\; \beta_i) = -x^t + \beta_i.$$

For simplicity, politicians do not discount the future, and in the event they leave office, their second-period payoff is normalized to 0. Table 1 summarizes all notation used throughout the paper (some of which will be introduced later).

Table 1. Notation

.

4. Checks and Balances

I begin my analysis of the Checks and Balances setting in the second period. As there is no future election, both politicians choose their type-preferred policy. Congruent politicians choose $x_i^2 = 1$ and divergent politicians choose $x_i^2 = -1$. The voter can maximize his second-period payoff by reelecting congruent politicians and replacing divergent ones.

While the voter may be uncertain about each politician's type in the election stage, he can make inferences about those types conditional on x ¹ and retain a politician only if the posterior probability they are congruent exceeds the prior probability a random challenger would be congruent. I focus on the following retrospective voting rule: reelect both politicians when x ¹ = 1 and replace both politicians otherwise. This voting rule is trivial for congruent politicians who maximize their policy payoff by enacting x ¹ = 1. Divergent politicians must choose between policy benefits today or reelection tomorrow. To constitute a Perfect Bayesian equilibrium, the retrospective voting rule must be sequentially rational for the voter following Bayes Rule, which I verify below.

The intuition behind each politician's first-period policy decision is as follows. If both politicians are congruent, they naturally choose x ¹ = 1. Recall that politicians know one another's types, so coordination in this respect is feasible. Doing so also ensures the voter's posterior belief about their types is weakly greater than the respective priors.

Now suppose one politician is congruent and the other is divergent. The congruent politician prefers x ¹ = 1 for policy and electoral reasons. The divergent politician faces a choice. By pooling on x ¹ = 1, they suffer policy defeat but win reelection and cause gridlock in the second period. By choosing x ¹ = −1, they cause gridlock in the first period and both politicians lose the election. For the divergent politician, if β _i < 1, the cost of passing x ¹ = 1 outweighs future office-holding rents. If β _i ≥ 1, the opposite is true.Footnote ⁵ To illustrate this logic, suppose the executive is congruent and the legislator is divergent. Under the proposed voting rule, the executive's choice is straightforward—choose $x_E^1 = 1$. The inequality to solve for the legislator's optimal policy decision is given by:

$$\eqalign{u_L( 1,\; -\!1;\; \beta_L) = 2\beta_L -\! 1 & \geq \beta_L = u_L( -\!1;\; \beta_L) \cr \beta_L & \geq 1.}$$

Recall β _i is uniformly distributed on $( 0,\; \, \bar \beta )$. In both regimes, I set $\bar \beta \equiv {3 + \pi \over 2}$. This threshold is chosen to ensure unilateral action is separating under Unilateralism, which allows me to focus more directly on the signaling dynamics of the game.Footnote ⁶ Given $\bar \beta$, the probability $\beta _i < 1 = {2\over 3 + \pi }$. Despite the sequential nature of the policymaking game, the threshold of β _i = 1 is the same irrespective of which politician is divergent.

When both politicians are divergent, the legislator's choice determines the policy outcome. If the legislator's office-holding benefit is large and she would prefer to pool with congruent types, her choice of $x_L^1 = 1$ forces the executive to either accept x ¹ = 1, win reelection, and enact x ² = −1 in the second period or choose $x_E^1 = -1$, which leads to gridlock and electoral defeat. The executive optimally chooses $x_E^1 = 1$ regardless of his office-benefit. A similar logic applies when the legislator's office-holding benefit is small and she chooses $x_L^1 = -1$. The legislator's optimal decision again depends on the cutoff of β _L = 1 as:

$$\eqalign{u_L( 1,\; -\!1;\; \beta_L) = 2\beta_L & = \beta_L + 1 = u_L( -\!1;\; \beta_L) \cr \beta_L & = 1.}$$

For these strategies and beliefs to constitute a Perfect Bayesian equilibrium, the voting rule must be sequentially rational. To see that it is, consider: if x ¹ = −1, both politicians are divergent with probability 1, and the voter would replace them. If x ¹ = 1, his belief that both politicians are congruent is weakly greater than the respective prior probabilities of drawing new congruent politicians. Finally, if x ¹ = 0, the voter can conclude one politician is congruent and one is divergent, but without observing individual policy choices, he cannot know which one. The voter's posterior belief the executive is congruent conditional on observing x ¹ = 0 is given by:

$$\Pr( \theta_E = C \vert x^1 = 0) = {\gamma ( 1 - \pi) \left({2 \over 3 + \pi} \right)\over \gamma ( 1 - \pi) \left({2 \over 3 + \pi} \right) + ( 1 - \gamma) \pi \left({2 \over 3 + \pi} \right)} = {\gamma - \gamma \pi\over \gamma + \pi - 2\gamma \pi} < \gamma\; \hbox{ iff } \pi > {1\over 2}.$$

The voter concludes that the current executive is less likely to be congruent than a new executive when the prior probability that the legislator is congruent is greater than 1/2, which is true by definition. Thus, the voter optimally replaces the executive with a challenger on observing gridlock. A similar logic holds for $\Pr ( \theta _L = C \vert x^1 = 0)$. The proposed voting rule is sequentially rational and the above strategies and beliefs constitute a Perfect Bayesian equilibrium.

Proposition 1 characterizes the equilibrium under Checks and Balances. To construct Proposition 1 (and later Proposition 2), I define a series of relevant thresholds on β _i as follows. When β _L ≥ 1, the legislator is said to have high office benefit. When β _L ∈ [2γ − 1,  1), she is said to have moderate office benefit. Finally, when β _L < 2γ − 1, she is said to have low office benefit. For the executive, high, medium, and low office benefit are defined as β _E ≥ 1, $\beta _E \in [ {1\over 2},\; \, 1)$, and $\beta _E < {1\over 2}$, respectively. Proofs can be found in the supplemental appendix.

Following Proposition 1, voter welfare (W _C) is given by Equation (1), where each term represents the expected payoff of a given politician-type combination.

(1)$$\matrix{ & W_C \ \equiv \ \gamma \pi ( 2) + \gamma ( 1 - \pi) \left[{2\over 3 + \pi} ( \gamma + \pi - 1) + ( 1 - {2\over 3 + \pi}) \right]\cr & \quad + ( 1 - \gamma) \pi \left[{2\over 3 + \pi} ( \gamma + \pi - 1) + ( 1 - {2\over 3 + \pi}) \right] + ( 1 - \gamma) ( 1 - \pi) \left[{2\over 3 + \pi} ( \gamma + \pi - 2) \right]. }$$

The first term in Equation (1) says that with probability γπ, Nature draws two congruent politicians who enact x ¹ = 1 in both periods for a total payoff of 2. The second term indicates that Nature draws a congruent executive and divergent legislator with probability γ(1 − π). Inside the brackets, with probability ${2\over 3 + \pi }$, the legislator has, at most, moderate office benefit, and gridlock occurs. The voter nets 0, replaces both politicians, and draws two congruent politicians for a payoff of 1 with probability γπ or a payoff of − 1 with probability (1 − γ)(1 − π). With probability $1 - {2\over 3 + \pi }$, the legislator has high office benefit, the politicians enact x ¹ = 1, both are retained, and x ² = 0, for a total payoff of 1. The third and fourth terms are constructed similarly.

5. Unilateralism

I turn to an alternative separation-of-powers regime in which the executive has the choice to play the Checks and Balances game as previously described or, after observing the legislator's choice, unilaterally enact either policy. However, the exercise of unilateral power is both more transparent and more costly than legislation. This transparency gives the executive additional leverage to both implement his preferred policy and reveal information about his, and the legislator's, type. However, the cost allows the legislator to strategically manipulate the policy offer to counteract electorally damaging unilateral action.

5.1 Sequence of play under unilateralism

The sequence of play under Unilateralism generally follows that of Checks and Balances, however, during Step 3 when the executive proposes his policy, $x_E^1$, he also chooses a method of proposing the policy, α ^t ∈ {0,  1}. If the executive proposes legislative policy (α ^t = 0), play proceeds as normal. If the executive proposes unilateral policy (α ^t = 1), his choice is immediately implemented such that $x_E^t = x^t$, irrespective of the legislator's choice. However, choosing α ^t = 1 is costly; unilateral directives involve bureaucratic transaction costs (e.g., Rudalevige, Reference Rudalevige2012; Turner, Reference Turner2020), are less durable than legislation (Thrower, Reference Thrower2017), and risk reversal by courts (Howell and Wolton, Reference Howell and Wolton2018). Thus, the executive pays a private cost of ${1\over 2}$ when setting α ^t = 1. In “Extensions and Robustness,” I discuss two extensions, one in which this private cost varies on the interval (0,  1), and one in which the second-period private cost is prohibitively high. Neither of these changes substantially alter the main result. The executive's updated per-period utility is given by:

$$u_E^t( x^t,\; \alpha^t;\; \beta_E) = \left\{\matrix{ x^t - {1\over 2} \alpha^t + \beta_E \hfill & \hbox{if }\theta_E = C\hfill \cr - x^t - {1\over 2} \alpha^t + \beta_E \hfill & \hbox{if } \theta_E = D. \hfill }\right.$$

The voter's utility function is given by u _V(x ^t,  ɛ) = x ^t − α ^tɛ, where ɛ is a cost close to 0 when the executive acts unilaterally.Footnote ⁷ Analytically, this cost plays little role in equilibrium outcomes but is necessary to ensure the voter has an incentive to select a congruent legislator. Substantively, it can be thought of as stemming from constitutional qualms (Kang, Reference Kang2020; Reeves and Rogowski, Reference Reeves and Rogowski2018). Consistent with Checks and Balances, the voter does not observe the politicians’ individual selections. However, the voter does observe α ^t, which allows him to infer the executive's policy choice when unilateral action is exercised. Given their contentiousness, unilateral acts do garner news coverage and criticism from members of Congress (see e.g., Christenson and Kriner, Reference Christenson and Kriner2017; Reference Djourelova and DuranteDjourelova and Durante, N.d), which could attract the voter's attention.

Analysis of unilateralism

In the second period, each politician selects their type-preferred policy. If both politicians share the same type, they will choose that type's preferred policy legislatively (recall, unilateral action is costly). If the types differ, the executive will unilaterally enact his preferred policy as the cost does not outweigh the policy benefit. In the supplemental appendix, I consider an extension in which the cost does outweigh the benefit. See “Extensions and robustness” for a discussion.

Lemma 1 (Unilateralism Second Period Strategies) If the executive and legislator share types, they legislatively enact that type's preferred policy. If their types differ, the executive unilaterally enacts his type's preferred policy.

Before the election, the voter will observe both x ¹ and α ¹, giving him additional information on which to base his choice. I propose the following retrospective voting rule (which I later verify is sequentially rational): if the policy x ¹ = 1 is passed legislatively, reelect both politicians and replace both politicians given any other legislative outcome. If x ¹ = 1 is implemented unilaterally, reelect the executive and replace the legislator, and replace the executive and reelect the legislator when x ¹ = −1 unilaterally.

Turning to the politicians’ first-period strategies, if both are congruent, the choice is simple: pass the voter's preferred policy legislatively. When the executive is congruent and the legislator is divergent, however, unilateral action has the power to substantially increase the voter's welfare. In fact, in this type of combination, the voter always gets his preferred policy in both periods. If the legislator has at most moderate office benefit, just as in Checks and Balances, she proposes $x_L^1 = -1$. Unlike Checks and Balances, though, gridlock does not ensue. Instead, the executive unilaterally enacts x ¹ = 1. Under the retrospective voting rule, the voter replaces the legislator and reelects the executive. In the second period, following Lemma 1, if the new legislator is congruent, then the politicians pass x ² = 1 legislatively. If the new legislator is divergent, the executive passes x ² = 1 unilaterally.

If, on the other hand, the first-period divergent legislator has a high office benefit, she would like to stay in office more than she would like to pass her type-preferred policy. To ensure the executive does not act unilaterally, revealing her type and leading to her replacement, she proposes $x_L^1 = 1$ when:

$$\eqalign{u_L( 1,\; -\!1;\; \beta_L) = 2\beta_L - \!2 & \geq \beta_L - \!1 = u_L( -1;\; \beta_L) \cr \beta_L & \geq 1.}$$

As unilateral action is costly, the executive also proposes $x_E^1 = 1,\; \, \alpha ^1 = 0$:

$$\eqalign{u_E( ( x^1_E = 1,\; \alpha^1 = 0) ,\; ( x^2_E = 1,\; \alpha^2 = 1) ;\; \beta_E) & = 2\beta_E + {3\over 2}\cr > u_E( ( x^1_E = 1,\; \alpha^1 = 1) ,\; ( x^2_E = 1,\; \alpha^2) ;\; \beta_E) & = 2\beta_E + 1 + {\pi\over 2}.}$$

The voter retains both politicians, and in the second period, the executive unilaterally implements x ² = 1.Footnote ⁸ Ultimately, when the divergent legislator sufficiently values holding office, she strategically manipulates the attractiveness of legislation such that the executive does not act unilaterally and reveal information about the politicians’ types.

Suppose the executive is divergent and the legislator is congruent. Here, the legislator proposes $x_L^1 = 1$. Under Unilateralism, the executive has the capacity to circumvent the legislator and implement the voter's least-preferred policy. However, only divergent executives have an incentive to unilaterally impose x ^t = −1 and doing so would reveal his type, leading to certain replacement. If he instead follows the legislator in proposing $x_E^1 = 1,\; \, \alpha = 0$, he can win reelection and unilaterally implement his preferred policy in the second period. The executive resolves this choice in favor of pooling on x ¹ = 1 when his office-holding benefit is weakly greater than 1.

Finally, if both politicians are divergent, they maximize their policy benefit by legislatively implementing x ¹ = −1. But again, doing so would lead to their dismissal. Unlike Checks and Balances, the legislator's office holding benefit is not determinative.Footnote ⁹ Even if the legislator has a high office benefit and proposes $x_L^1 = 1$, an executive with low office benefit may still enact x ¹ = −1 unilaterally if $\beta _E < {1\over 2}$. However, if the legislator proposes $x_L^1 = -1$, the executive always proposes $x_E^1 = -1$ legislatively.

For these strategies and beliefs to constitute a Perfect Bayesian equilibrium, the voter's decision rule must be sequentially rational. Regarding legislation, only divergent politicians enact x ¹ = −1 and congruent politicians are more likely to enact x ¹ = 1, so these beliefs accord with the decision rule. Of particular interest is the voter's posterior beliefs after the executive acts unilaterally. As only congruent executives enact x ¹ = 1 unilaterally, and only when the legislator is divergent, observing x ¹ = 1,  α = 0 gives the voter complete information about the politicians’ types, and he is justified in reelecting the executive and replacing the legislator. Only divergent executives unilaterally enact x ¹ = −1, however, the outcome occurs when the legislator is both congruent and divergent. As it is more likely to occur when the legislator is congruent (the threshold is β _E < 1 when the legislator is congruent and $\beta _E < {1\over 2}$ when divergent), the voter is justified in replacing the executive while reelecting the legislator. Finally, gridlock is never observed in equilibrium. Sequential rationality in this case relies on what the voter would believe were he to observe gridlock. In the supplemental appendix, I discuss an adaptation of the Intuitive Criteria to this non-standard signaling game and find that the voter should believe both politicians are congruent with probability 0 when observing gridlock. Thus, the decision rule is sequentially rational. Proposition 2 summarizes the equilibrium. Proofs can be found in the supplemental appendix.

Proposition 2: There exists a Perfect Bayesian equilibrium in which the voter retains both politicians when observing his preferred policy legislatively and replaces both politicians when observing any other legislative outcome. When the voter observes his preferred policy unilaterally, he reelects the executive and replaces the legislator. When he observes his least preferred policy unilaterally, he replaces the executive and reelects the legislator. Both politicians choose their type-preferred policy in the second period and enact it following Lemma 1. In the first period:

1. 1. both politicians choose the voter's preferred policy legislatively if: (a) both are congruent, (b) one is divergent and has high office benefit, or (c) both are divergent and the legislator has high office benefit while the executive has at least moderate office benefit;

2. 2. both politicians select the voter's least-preferred policy legislatively if both are divergent and either (a) the executive has at least moderate office benefit while the legislator has at most moderate office benefit or (b) both politicians have low office benefit.

3. 3. the executive unilaterally enacts the voter's preferred policy when he is congruent while the legislator is divergent and has at most moderate office benefit; and

4. 4. otherwise the executive unilaterally enacts the voter's least-preferred policy: if (a) he is divergent and has at most moderate office benefit while the legislator is congruent, or (b) he is divergent and has low office benefit while the legislator is divergent and has at least moderate office benefit.

Following Proposition 2, voter welfare is given by Equation (2), where each term represents the expected payoff of a given politician-type combination.

(2)$$\matrix{ & W_U \equiv \gamma\pi( 2) + \gamma ( 1 - \pi) ( 2) + ( 1 - \gamma) \pi \left[{2\over 3 + \pi} ( 2 \gamma - 2) \right]\cr & \quad + ( 1 - \gamma) ( 1 - \pi) \left[\left(1 -\left(\left(1 - {2\over 3 + \pi} \right)\left(1 - {1\over 3 + \pi} \right)\right)\right)( 2\gamma - 2) \right]. }$$

The first two terms of Equation (2) reveal that when the executive is congruent, the voter always gets his preferred policy outcome. Although the voter may sometimes suffer when the executive is divergent, office-holding rents constrain the divergent executive in many cases.

6. Voter welfare under alternative separation-of-powers settings

It is not surprising that the voter stands to gain from unilateral action when the executive shares his policy preferences. But voters do not know the executive's type ex ante, necessitating the separation of powers in the first place. The relevant question is: in which institutional framework are voters better off after relaxing assumptions of universalism?

A reasonable hypothesis would be that the voter fares best in the setting that empowers the politician who is more likely to be congruent. That is, if the legislator is more likely to be congruent, perhaps voter welfare is higher under Checks and Balances. Similarly, if the executive is more likely to be congruent, then perhaps welfare is higher under Unilateralism. To investigate this question, I construct a function $\tilde \gamma ( \pi )$, which is derived by setting the two welfare equations equal to one another and solving for γ. I plot this function in Figure 1. The x-axis is π and the y-axis is γ, and every point along the curve is a pair (π,  γ) at which voter welfare is equivalent in each setting. At points above the curve (white), welfare is higher under Unilateralism. At points below the curve (gray), welfare is higher under Checks and Balances. I also plot a dashed 45-degree line, representing the baseline assumption that the voter prefers the regime that favors the more-likely congruent actor.

Fig. 1. A comparison of voter welfare under Checks and Balances and Unilateralism. The x-axis tracks π, the prior on legislator congruence, while the y-axis plots γ, the prior on executive congruence. The solid line is $\tilde \gamma ( \pi )$, the threshold at which the voter is indifferent between either regime type for the given prior probabilities of congruence. The area above (below) the curve indicates where voter welfare is higher under Unilateralism (Checks and Balances) for the given combination of prior probabilities of congruence. The dotted line is the 45-degree line.

As hypothesized, when one politician is especially likely to be congruent and the other is especially likely to be divergent, the voter prefers the regime favoring the more-likely congruent actor. However, were this always true, $\tilde \gamma ( \pi )$ would fall squarely along the 45-degree line. Instead, we see that this function always falls weakly below the 45-degree line, indicating that for several (π,  γ) pairs in which the legislator is more likely to be congruent than the executive, the voter nonetheless prefers Unilateralism. The wedge area represents a primary contribution of the model. Even when universalism does not hold—that is, the executive is less likely to be congruent the legislator—the expected benefits of unilateral action can outweigh the risks.

The driving force behind these results are as follows. First, gridlock is a key source of welfare loss under Checks and Balances. It lowers the voter's policy payoff and incentive compatibility constraints require that he dismiss both politicians even though one must be congruent. Under Unilateralism, gridlock is replaced by unilateral action, which both leads to policy change and provides the voter with additional information. However, the use of unilateral action is asymmetric between congruent and divergent executives. When the executive is congruent, he can always act unilaterally to deliver the voter's preferred policy if the legislator is not willing to propose welfare-increasing legislation. When the executive is divergent, unilaterally enacting the voter's least-preferred policy is electorally costly, which acts as a constraint. Ultimately, gridlock clouds responsibility and the voter is not able to draw precise inferences. Unilateral action increases the risk of a divergent policy outcome, but its relative transparency constrains divergent executives who prize reelection rents.

7. Extensions and robustness

In the supplemental appendix, I undertake four extensions of the baseline model which I briefly discuss here. First, I relax the assumption that the voter observes only x ^t, allowing him to instead observe $x_L^t$ and $x_E^t$ with exogenous probability τ, which could be variously interpreted as capturing complexity, salience, or media coverage of the policy domain (e.g., Canes-Wrone and Marchi, Reference Canes-Wrone and de Marchi2002). I find that as τ increases, the welfare gains from Unilateralism decrease relative to Checks and Balances. Larger values of τ allow the voter to screen out divergent politicians with more precision under Checks and Balances, limiting the welfare-reducing consequences of gridlock. For low or moderate values of τ, the welfare conclusions hold but are attenuated. When τ is large, the Checks and Balances regime becomes preferable when γ and π are similar. Signaling gains from increasing executive power seem partially dependent on voter attention to the policymaking process—a promising direction for future research on this topic.

In the second extension, I consider the possibility that unilateral action may simply be too costly to pursue by setting the cost κ to ${3\over 2}$ in the second period. This higher cost could stem from the perceived risk of a court reversal (see e.g., Howell and Wolton, Reference Howell and Wolton2018) or the expectation that an ideologically opposed future executive might unilaterally revoke that policy (Thrower, Reference Thrower2017). By setting κ > 1, the second-period executive never acts unilaterally. Intuitively, this makes the voter worse off when the executive is congruent and legislator is divergent, but improves welfare in the opposite case. Yet, this change does not alter the main finding of the paper—that Unilateralism is preferable even in some instances when π > γ. The first-period signaling and policy gains benefit the voter while the possibility of gridlock in the second period may be welfare-increasing or decreasing.Footnote ¹⁰ Foreclosing the possibility of second-period unilateral action encourages more divergent unilateral action in the first period (since the divergent executive cannot count on future unilateral gains), but also more congruent unilateral action as the congruent executive can only gain policy benefits in the second period by encouraging the voter to remove a divergent legislator.

In a third extension, I allow the voter's loss from his least favorite policy to vary on the interval ( − c,  1) where c ∈ ( − 1,  ∞). Intuitively, if c < 1, the cost of a divergent unilateral act poses little danger and Unilateralism remains preferable. However, as c increases above 1, even small risks of divergent unilateral action can offset the gains of congruent unilateral action, making Checks and Balances increasingly preferable. Surely, the Framers were considering these asymmetric costs and benefits when designing the Constitutional system. However, congressional teamsmanship and gridlock (Lee, Reference Lee2016) may leave us with outdated status quos that are costlier than any solution the executive might propose.

Finally, I relax the uniform distribution assumption on β _i, allowing β _i to be drawn from any strictly increasing CDF. The main result is that the wedge area favoring Unilateralism increases as it becomes more probable that β _i < 1. Although the risk of divergent unilateral action increases as $\Pr ( B_i < 1)$, this risk is offset by policy and signaling gains from a congruent executive breaking through welfare-reducing gridlock that is more likely to occur under Checks and Balances.