What is opposition good for?

Abstract

Governments in representative democracies may have incentives to pursue policies that do not align with voters’ preferences. When voters lack information about the policy bias of the government and the consequences of policy alternatives, they will have difficulty holding the government accountable. I propose a formal model that explores whether an opposition party can help solve this problem by providing information about policy alternatives. The model acknowledges that opposition parties may have incentives to mislead voters because of their own policy biases or election concerns. Despite this challenge, the model shows that the presence of an opposition party may induce a biased government to adjust its policies. For this disciplining equilibrium to work, the reputations of the opposition and the government should be close to each other, or the voter should believe that one policy alternative is much more likely to be good for her than another alternative. In addition, the government should be sufficiently concerned about winning the elections, and the opposition should be sufficiently concerned about policy. Under the same conditions, however, misleading information on the opposition may cause an unbiased government to implement policies that are detrimental to voter welfare.

Keywords

Democratic representation legislative politics opposition parties

The pure idea of democracy, according to its definition, is the government of the whole people by the whole people, equally represented. Democracy, as commonly conceived and hitherto practiced, is the government of the whole people by a mere majority of the people exclusively represented. The former is synonymous with the equality of all citizens; the latter, strangely confounded with it, is a government of privilege in favor of the numerical majority, who alone possess practically any voice in the state.

(Mill, 1861)

The opposition has the responsibility of providing criticism and posing useful alternatives to government policies. This function, properly performed, helps government to set goals best qualified to produce public satisfaction. On matters of budget, welfare and other major concerns, criticism keeps the government responsive to the public and aware of weaknesses in its program.

(Apter, 1962)

1. Introduction

The merits of a democratic political system stem from the opportunities it provides for the representation of everyone in the polity; therefore, a sound and viable opposition is one of its indispensable elements. Opposition parties, obviously, serve as alternatives for discontented voters; however, their function is more than just providing another emblem on the ballot in the next elections. They provide information about the government’s policies, and point to their weaknesses. They express the demands and the interests of their constituencies, and contribute to the translation of these demands and interests into policy. Hence, in a political system with a functioning opposition, the government is expected to be more responsive to the demands of the population as a whole. In parliamentary systems, however, there are both institutional and motivational obstacles against the opposition’s performance of these ideal functions.

In parliamentary systems, opposition parties have very little, if any, chance of directly influencing policy decisions. The party or the coalition that has the majority of seats in the parliament has control over both legislative and executive power. Given high levels of party discipline, the party in government does not usually have difficulty passing the bills that it proposes and the opposition’s votes in the legislature cannot change the result. Evidence suggests that the direct influence of opposition parties on policy in parliamentary systems is rather limited (Powell, 2006). Nevertheless, opposition parties have the opportunity to participate in parliamentary debates, during which they can reveal their policy positions and offer alternatives to the government’s policy. The opposition’s criticism of the government’s policies may help voters acquire information about or have a new perspective on policy outcomes. In that case, the government may have to adjust its policies in accordance with the voters’ demands. Hence, opposition parties have the potential to influence policy decisions even when they do not have the majority of seats required to change the result of legislative voting.

While the information provision function of the opposition is promising for a more responsive political system, the incentives of the opposition parties may be incompatible with this function. The opposition may want to mislead the voters for policy or electoral purposes. If the opposition has information that would make it more difficult to justify its preferred policy, it may prefer to misinform voters in order to facilitate the adoption of its preferred policy. Similarly, if the opposition has information that would support the preferred policy of the government, it would not be willing to admit that the government is implementing the policy that is good for the public. Instead, it would be inclined to sabotage the reelection chances of the government. With these motivational obstacles in mind, in this paper, I ask whether the opposition can contribute to the responsiveness of the political system through its participation in parliamentary debates. More specifically, this question can be divided into two parts. (1) Under which conditions do opposition parties provide voters with useful information about the consequences of policies? (2) Do government parties have to adjust their policy decisions in accordance with newly available information?

To answer these questions, I propose a formal model that explores the effect of the opposition party on policy decisions in an environment where voters have limited information about the consequences of policies and about the policy bias of politicians. The model tackles two types of informational asymmetry between voters and politicians. First, there is a discrepancy in policy expertise, which makes it difficult for voters to discipline politicians. Second, politicians may be biased in favor of certain policies, irrespective of the consequences for voters. The model compares policy decisions that occur with and without parliamentary debate.

The following example illustrates the motivation for this paper. An investment decision must be made in a parliamentary system with two parties: a majority and a minority. The majority party in the parliament forms the government, so they have control over both the legislature and the executive. The majority party has an agenda that emphasizes economic development, whereas the minority party has an agenda that emphasizes environmental protection. Hence, the majority party is likely to discount the environmental costs of an investment, whereas the minority party is likely to discount economic benefits. The reason for this bias may be due to ideological concerns or the influence of interest groups. The voters have a more balanced view: they want the investment as long as the environmental costs are not too heavy; however, they have incomplete information about the costs of the investment. Given the institutional setup and high party discipline, the majority party seems to have all the power. The minority party cannot change the outcome by voting. In this paper, I explore the conditions under which (1) the minority party provides truthful information about the cost of investment to voters and (2) this information has an effect on the policy outcome.

In what follows, I start with a model where the opposition does not take any action. In the absence of debate, the voter only observes the policy decision of the government. The voter knows that the government may be biased in favor of the investment. If the reputation of the opposition is high enough, the voter can punish the government after observing an investment. In that case, a government with high reelection concerns will choose not to make the investment even when it is beneficial for the voter. If the reputation of the opposition is not high, the voter is not able to discipline the government since she cannot commit to punish the government after an investment decision.

In the model with debate, I introduce an opposition that makes a cheap-talk announcement before the government makes the policy decision. Since my focus is on whether the opposition can help the voter discipline the government, I only consider the equilibria where the voter rewards the government if the government decides to follow the opposition’s recommendation not to make an investment decision. I show that an equilibrium exists where the opposition always announces its preferred policy, and the government always follows the opposition’s recommendation against the investment decision. For this disciplining equilibrium to work, the reputation of the opposition and the government should be close to each other, or the voter should believe that one policy alternative is much more likely to be good for her than the other alternative. In addition, the government should be sufficiently concerned about winning the elections, and the opposition should be sufficiently concerned about policy.

2. Literature

The effect of legislative activity on policy outcomes has been the topic of several formal theoretical models. Using a cheap-talk signaling model, Austen-Smith (1990) explores whether legislators with different policy preferences would truthfully reveal their private information about the consequences of policy alternatives during legislative debate. The model shows that information transmission through debate is constrained by the dispersion of the legislators’ preferences. Given the assumption of three legislators with equal agenda-setting power and voting weight, the model does not capture the dynamics of partisan decision-making that arise from the inequality in seat share or procedural powers between the majority and the minority.

In the extreme case where the majority party has complete control over the agenda as well as the ability to discipline its members, the minority would have no chance of influencing the policy decision. Krehbiel et al. (2015) investigate the policy implications of reducing the discrepancies between the majority and the minority. They show that the resulting policies are more moderate when procedural rules allow the minority party to propose amendments or when the minority party has the means to provide side-payments to its members. Dewan and Spirling (2011) propose an agenda-setting model that shows that the minority can influence the policy even without any prerogatives to propose or amend policies. The critical component of their model is the presence of a commitment mechanism for the members of both parties to vote with their party. The results show that the members of the opposition party would be better off committing to vote against the government’s proposal instead of voting sincerely as long as the legislature is not completely polarized along party lines. When such a commitment exists, the party in government has to propose a policy that would be supported by a majority of its own members. Hence, the opposition party can influence the policy by committing to object to the government.

In this paper, I consider the possibility that the minority party will influence the decision of the majority party by changing the beliefs of voters about the consequences of policies, using an agency model with asymmetric information. In agency models, the principals face informational constraints that bring about two types of problem. First, the principal has limited information about agents; therefore, she faces the problem of choosing the agent who would make decisions in accordance with the principal’s preferences. Second, the principal lacks the policy expertise that the agent has; therefore, she faces the problem of monitoring the behavior of the agent. Depending on the action of the agent in the first period, the principal decides whether to retain the agent or replace him. The agency models that are the most relevant for my research question are the ones where voters are the principals and politicians are the agents.¹

As discussed, principals (voters) have limited information about agents (politicians), who come in different types. One characteristic that distinguishes politicians from one another relates to the quality of information that they have about the consequences of policy alternatives (Ashworth S and Shotts K, 2010; Ashworth S and Shotts K, 2011; Canes-Wrone et al., 2001; Prat, 2005). Another characteristic that distinguishes politicians is the level of competence in implementing policies (Dewan and Hortala-Vallve, 2017). Finally, politicians may differ in terms of whether their preferences are congruent with the voters’ preferences (Dellis, 2007; Lemon, 2005; Maskin and Tirole, 2004; Stasavage, 2007). The model in this paper addresses the issue of whether the voters can discipline incongruent politicians to act in accordance with the voters’ interests.

A main insight of the agency models is that elections may not be a sufficient tool for a responsive government when the voters face adverse selection and moral hazard problems simultaneously. When the voters have limited information about policy alternatives, they will not be able to demand the policy that is better for their welfare. Adverse selection further complicates this problem. In their efforts to signal to the voter that they are the good type, the politicians may pander, i.e. fail to choose the policy that they believe is the best for the voter (Canes-Wrone et al., 2001; Maskin and Tirole, 2004). Potentially, an opposition party may help the voter alleviate these problems; however, the opposition would also have policy preferences and election concerns, which do not always align with the voters’ interests.

The opposition in many of the principal–agent models is rather passive. It does not take any action that may affect its election chances. Hence, the only information source for the principal is the government (Canes-Wrone et al., 2001; Maskin and Tirole, 2004; Prat, 2005; Schultz, 2008). In some models, there is a third party, such as a newspaper or an auditor, that gives information about the government and the opposition (Ashworth S and Shotts K, 2011; Warren, 2012). The obvious difference in this setup is that the third party does not compete with the government. My models falls into another category, where the opposition makes an announcement about his policy preference before the elections (Ashworth S and Shotts K, 2011; Dewan and Hortala-Vallve, 2017; Lemon, 2005).²

The incentives of the opposition may not always be compatible with the roles it is expected to perform for a more responsive government. Dewan and Hortala-Vallve (2017) show one way in which the information provided by the opposition may be detrimental to the voters’ welfare. In their model, the government has to decide whether to implement a reform, the success of which depends on the government’s competence. When the governments’ reelection depends on the voters’ perception about its competence, the government may not make the optimum decision about reform. It may be reluctant to implement reforms that are likely to be successful or it may undertake reforms that are too risky. This problem becomes more severe if the opposition is also able to reveal information about its competence through an electoral campaign. Hence, the model shows that the salutary effect of opposition on the voters’ welfare cannot be taken for granted. This is not to say that the effect of the opposition is always negative. Ashworth and Shotts (2011) propose a model where the politicians can decide on the level of effort they put into acquiring information about policies. If the opposition is able to provide hard information, i.e. a signal verifiable by the voter, its message may help the voter by increasing the level of effort that the government is willing to exert to acquire information.

The problem that the voter faces in the model proposed in this paper does not result from the government’s incentives to signal its competence (Dewan and Hortala-Vallve, 2017) or from the government’s shirking (Ashworth S and Shotts K, 2011). In my model, the politicians have perfect information about the consequences of two policy alternatives but the voter only knows the probability that one alternative is better than the other. The voter has to decide whether to reelect the government based on her belief about whether the government is more likely to be congruent than the opposition. An incongruent government is biased in favor of a particular policy alternative, irrespective of its consequences for the voter, whereas a congruent government always prefers the policy that is good for the voter.³ In this setup, the government may choose the policy that is not good for the voter for two reasons. If the opposition’s reputation is very low, the voter cannot commit to punish the government for choosing the policy that is always preferred by the incongruent government. If the opposition’s reputation is high enough for such a commitment, the government will pander in order to signal its congruence.

The main question of this paper is whether the opposition may help the voter discipline the government by making a policy recommendation before the government’s decision. Lemon (2005) provides a good starting point to answer this question using a model where the information structure is similar to the one I described in the previous paragraph. The voter makes a probabilistic decision between an incumbent and a challenger after observing the challenger’s cheap-talk message and the incumbent’s policy decision. The model shows that the effect of debate on the voter’s welfare may differ, depending on the reputation of the politicians. One important difference in Lemon’s setup is about the policy preferences of the politicians. In his model, the bad politicians always prefer the policy that is bad for the voter. The most obvious example of the type of problem captured by this preference structure would be when corrupt politicians extract resources for their own consumption; however, it is not clear why a corrupt challenger would benefit from a bad policy decision that the government makes.

Many policy issues, such as the hypothetical example in the previous section, are not compatible with this preference structure. First, depending on the circumstances, biased politicians’ preferences may not be in conflict with the interests of the voters. The government party may prefer to make an investment because it is biased in favor of economic development yet in some cases making an investment is actually beneficial for the voters. Second, politicians differ from each other in terms of their policy preferences. The policy biases of the government and the opposition parties are usually in different directions. In my example, the bad government party always wants to make the investment whereas the bad opposition party always opposes the investment. Third, voters know the preferred policies of biased parties, which makes it easier for the voters to identify biased parties. Going back to my example, the voter knows that a biased government party will never choose not to make the investment except for reelection purposes. The model in this paper incorporates these aspects of the parties’ preferences. For the rest of the paper, I will assume that political parties are unitary actors. I will refer to the majority party as the government and the minority party as the opposition.

3. Model

There are three players in the model: a government (G), an opposition (O), and a representative voter (V). In the baseline model, the opposition has no role. In the deliberative model, the opposition sends a costless message $m \in {CON, LIB}$ about his preferred policy. In both models, the government chooses a policy $x \in {CON, LIB}$ . The outcome of the policy depends on whether the policy matches the state of the world $ω \in {CON, LIB}$ . The state of the world is observed by the government and the opposition but not by the voter. The voter only knows that the probability that $ω$ is $CON$ equals $α$ . The preferred policies of the government and the opposition depend on their respective types. The government and the opposition can be one of two types $t \in {b, g}$ . The bad government always prefers $x = CON$ whereas the bad opposition always prefers $x = LIB$ . The good government, the good opposition, and the voter all prefer the policy that matches the state of the world. The type of the government is private information. The opposition and the voter only know that the probability that the government is good equals $0 < β_{G} < 1$ . Similarly, the government and the voter only know that the probability that the opposition is good equals $0 < β_{O} < 1$ .

The timing of the game in the baseline model is as follows:

Nature chooses the government’s type, the opposition’s type, and the state of the world.

The government and the opposition observe the state of the world.

The government chooses a policy $x \in {CON, LIB}$ .

The voter decides whether to reelect the government or not.

The timing of the game in the model with debate is as follows:

Nature chooses the government’s type, the opposition’s type, and the state of the world.

The government and the opposition observe the state of the world.

The opposition announces $m \in {CON, LIB}$ .

The government chooses a policy $x \in {CON, LIB}$ .

The voter decides whether to reelect the government or not.

The timing of this model is a good approximation of the real world, where debate precedes the policy decision. One can argue that the government also participates in political debate before making its policy decision. If the government does not pay any cost for implementing a policy that is different from what it advocated during debate, the message of the government would not provide any information. The voters would take into account the policy decision rather than the message. A model where the government pays a cost for reversal is left for future research.

The utility functions of the players are the same for both games. The politicians’ utility has two components. First, they receive non-negative utility if their preferred policy is implemented. The government receives utility $b_{G}$ from its preferred policy, and the opposition receives utility $b_{O}$ from its preferred policy. Second, politicians receive utility of 1 from winning elections. I assume that $b_{G} < 1$ since this is a necessary condition for the voter to be able to discipline the government. The voter receives positive utility from her preferred policy and from electing a good politician. After having observed the opposition’s message m (if any) and the government’s policy x, the voter updates her beliefs about the types of the government and the opposition, and elects the politician that she believes more likely to be the good type.

The solution concept for the game is perfect Bayesian equilibrium. The opposition does not take any action in the baseline model. In the model with debate, the opposition’s strategy is indicated by $ϕ_{t, ω}$ , which is the probability that an opposition of type t chooses $m = CON$ after observing $ω$ . The government’s strategy will be indicated by $θ_{t, ω}^{m}$ , which is the probability that a government of type t chooses $x = CON$ after observing $ω$ and m (if any). In a perfect Bayesian equilibrium, the beliefs of the players should be consistent with the strategies of other players. When beliefs are not pinned down by Bayes’ rule, I calculate the beliefs, assuming that both the opposition and the government are purely policy-oriented. In the baseline model, the updated beliefs of the voter about the government and the opposition are denoted ${\hat{β_{G}}}^{x}$ and ${\hat{β_{O}}}^{x}$ , respectively. Similarly, in the model with debate, the beliefs are denoted ${\hat{β_{G}}}^{m, x}$ and ${\hat{β_{O}}}^{m, x}$ . Given these beliefs, the voter’s strategy is denoted $μ^{m, x}$ , which specifies the probability that the voter reelects the government after observing message m (only in the model with debate) and policy x.

4. Baseline model

In the absence of political debate, the voter does not acquire any information about the opposition. The only information she receives is the policy decision of the government, which may give her a clue about whether the government is good or not. The voter does not know the state of the world; however, she knows that the bad government prefers policy $x = CON$ , irrespective of the state of the world.⁴ Hence, the bad government has incentive to choose policy $x = LIB$ only if the reelection benefit of doing so exceeds the policy benefit ( $b_{G}$ ) of choosing policy $x = CON$ . The good government prefers the policy that matches the state of the world. Hence, the good government will have incentive to choose a policy that does not match the world only if the reelection benefit of doing so exceeds $b_{G}$ . After observing the policy decision of the government, the voter will reelect the government if her updated belief that the government is good is greater than her prior belief that the opposition is good.

First, I consider equilibria where the difference $μ^{LIB} - μ^{CON}$ is smaller than $b_{G}$ . In any such equilibrium, the bad government’s strategy is to always choose policy $x = CON$ , irrespective of $ω$ , and the good government’s strategy involves always choosing $x = LIB$ when $ω = LIB$ .⁵ Therefore, the voter will know for sure that the government is the good type if she observes policy $x = LIB$ . Given this belief, the voter should reelect government after observing $x = LIB$ , which implies that $μ^{LIB} - μ^{CON}$ is always positive and that the good government will always choose policy $x = ω$ . In other words, the strategy of both types of government is to choose their preferred policies. Given the government’s strategy, the updated belief of the voter after observing $x = CON$ can be calculated using Bayes’ rule. If the prior belief that the opposition is good ( $β_{O}$ ) is smaller than $\hat{β_{G}^{CON}}$ , then the voter’s strategy should include $μ^{CON} = 1$ . If $β_{O} = \hat{β_{G}^{CON}}$ , then $μ^{CON}$ can take any value greater than $1 - b_{G}$ . The equilibria are summarized next.

4.1. Undisciplined government equilibria

In the baseline model, there exist perfect Bayesian equilibria where the government always chooses its preferred policy. The strategy of the voter in such an equilibrium is one of the following:

The voter reelects the government, irrespective of the policy. This equilibrium holds if and only if $β_{O} < \hat{β_{G}^{CON}}$ .

The voter always reelects the government after policy $x = LIB$ but she reelects the government after policy $x = CON$ with probability greater than $1 - b_{G}$ . This equilibrium holds if and only if $β_{O} = \hat{β_{G}^{CON}}$ .

The updated beliefs of the voter are

\hat{β_{G}^{CON}} = \frac{α β_{G}}{1 - β_{G} + α β_{G}} and \hat{β_{G}^{LIB}} = 1

In the undisciplined government equilibria, the reelection incentive for the government is not sufficient for the voter to be able to discipline the bad government. This occurs when the reputation of the government ( $β_{G}$ ) or the voter’s belief that the state of the world is conservative ( $α$ ) is high, or when the reputation of the opposition ( $β_{O}$ ) is low. The voter’s belief that the government is good goes down when she observes policy $x = CON$ . If the initial reputation of the government is high enough or the voter believes that $ω$ is likely to be conservative, the updated belief about the government may still be higher than the reputation of the opposition. Therefore, the voter would not be able to commit not to reelect the government even after observing $x = CON$ . This poses a problem for responsiveness since a bad government would be able to get away with choosing a policy that is not good for the welfare of the voter. More specifically, the voter will have to endure a policy that she does not prefer with probability $(1 - β_{G}) (1 - α)$ , that is, when the government is bad and the state of the world is liberal. Table 1 shows the equilibrium policy in the undisciplined government equilibria with the preferred policy of the voter in bold letters.

Table 1.

Equilibrium policy in the baseline model.

	$ω =$ CON	$ω =$ LIB
Undisciplined government equilibria
Bad government	CON	CON
Good government	CON	LIB
Pandering government equilibria
Bad government	LIB	LIB
Good government	LIB	LIB
Mixed government disciplining equilibria
Bad government	CON/LIB	CON/LIB
Good government	CON/LIB	LIB

Next, I consider equilibria where the difference $μ^{LIB} - μ^{CON}$ is greater than $b_{G}$ . In any such equilibria, the reelection benefit of choosing policy $x = LIB$ exceeds the policy benefit of the preferred policy. As a result, the strategy of both types of government is to always choose $x = LIB$ . Since the voter will always observe policy $x = LIB$ in equilibrium, her updated belief about the government after observing $x = LIB$ will be equal to her prior belief about the government. The voter’s belief after observing $x = CON$ cannot be pinned down by Bayes’ rule. I calculate the voter’s belief, assuming that the policy $x = CON$ would only be chosen by a bad government (irrespective of $ω$ ) or by a good government when $ω = LIB$ . The voter’s updated belief about the government after observing $x = LIB$ will always be higher than her belief after observing $x = CON$ . If the reputation of the opposition falls between $\hat{β_{G}^{LIB}}$ and $\hat{β_{G}^{CON}}$ , the voter will always reelect the government after observing $x = LIB$ but will never reelect the government after observing $x = CON$ . If the reputation of the opposition equals either of the boundaries, the voter will be indifferent between the government and the opposition after having observed that particular policy. The equilibria are summarized next.

4.2. Pandering government equilibria

In the baseline model, there exist perfect Bayesian equilibria where the government chooses $x = LIB$ , irrespective of $ω$ . The strategy of the voter in such an equilibrium is one of the following:

The voter always reelects the government after policy $x = LIB$ but she reelects the government after policy $x = CON$ with probability smaller than $1 - b_{G}$ . This equilibrium holds if and only if $β_{O} = \hat{β_{G}^{CON}}$ .

The voter reelects the government only after policy $x = LIB$ . This equilibrium holds if and only if $\hat{β_{G}^{CON}} < β_{O} < \hat{β_{G}^{LIB}}$ .

The voter reelects the government after policy $x = LIB$ with probability greater than $b_{G}$ but she never reelects the government after policy $x = CON$ . This equilibrium holds if and only if $β_{O} = \hat{β_{G}^{LIB}}$ .

The updated beliefs of the voter are

\hat{β_{G}^{CON}} = \frac{α β_{G}}{1 - β_{G} + α β_{G}} and \hat{β_{G}^{LIB}} = β_{G}

For the pandering government equilibria to hold, the reputation of the opposition should be high enough to allow the voter to oust the government after observing policy $x = CON$ . When $β_{O}$ is higher than $β_{G}$ , however, the voter will face the problem of not being able to commit to reelecting the government after observing policy $x = LIB$ . Without the reelection incentive, the disciplining effect would not work. For a given value of $β_{G}$ , the pandering equilibria will hold for a wider range of $β_{O}$ as $α$ decreases. When the voter believes that $ω$ is likely to be liberal, her updated belief about the government after observing $x = CON$ will be small, thereby making it possible for the voter to commit not to reelect the government. As the name implies, the pandering government equilibria provide an imperfect solution to the voter’s challenge of keeping the government accountable. In their effort to signal to the voter that they are the good type, both types of government choose $x = LIB$ even when it is not beneficial for the voter. As seen in Table 1, the voter suffers from a loss of policy benefit with probability $α$ , that is, when the state of the world is conservative.⁶

Finally, I consider equilibria where the difference $μ^{LIB} - μ^{CON}$ equals $b_{G}$ . This condition makes the government indifferent between choosing $x = CON$ and $x = LIB$ when the preferred policy of the government is conservative, that is, when government is bad or the state of the world is conservative. The good government will choose $x = LIB$ when $ω = LIB$ since both the policy and the reelection benefit of $x = LIB$ is higher in this case. For $μ^{LIB} > μ^{CON}$ to be sequentially rational, $\hat{β_{G}^{LIB}}$ should be greater than or equal to $\hat{β_{G}^{CON}}$ . For $μ^{LIB} - μ^{CON} = b_{G}$ to be possible, the voter’s decision to reelect the government should be probabilistic after at least one of the policies. The following section summarizes the equilibria.

4.3. Mixed government disciplining equilibria

In the baseline model, there exist perfect Bayesian equilibria where the good government always chooses $x = LIB$ when $ω = LIB$ , and the government chooses $x = CON$ with probability $θ_{t, ω}^{*}$ otherwise.

The strategy of the voter in a mixed government disciplining equilibrium is one of the following:

If $\hat{β_{G}^{LIB}} > β_{O} = \hat{β_{G}^{CON}}$ , the voter always reelects the government after policy $x = LIB$ but she reelects the government after policy $x = CON$ with probability $1 - b_{G}$ .

If $\hat{β_{G}^{LIB}} = β_{O} = \hat{β_{G}^{CON}}$ , the voter reelects the government probabilistically after each policy such that $μ^{LIB *} - μ^{CON *} = b_{G}$ .

If $\hat{β_{G}^{LIB}} = β_{O} > \hat{β_{G}^{CON}}$ , the voter reelects the government with probability $b_{G}$ after policy $x = LIB$ but she never reelects the government after policy $x = CON$ .

The updated beliefs of the voter are

\begin{matrix} \hat{β_{G}^{CON}} = \frac{β_{G} \cdot α \cdot θ_{g, CON}}{β_{G} \cdot α \cdot θ_{g, CON} + (1 - β_{G}) \cdot [α \cdot θ_{b, CON} + (1 - α) \cdot θ_{b, LIB}]} \\ \hat{β_{G}^{LIB}} = \frac{β_{G} \cdot [α \cdot (1 - θ_{g, CON}) + (1 - α)]}{β_{G} \cdot [α \cdot (1 - θ_{g, CON}) + (1 - α)] + (1 - β_{G}) \cdot [α \cdot (1 - θ_{b, CON}) + (1 - α) \cdot (1 - θ_{b, LIB})]} \end{matrix}

The equilibrium policy of the mixed government disciplining equilibria are shown in Table 1. The mixed government disciplining equilibria seem to be a happy medium between the undisciplined government equilibria and the pandering government equilibria in terms of the voter’s policy benefit. I should note, however, that an equilibrium where the government always receives her preferred policy is possible if and only if the initial reputations of the government ( $β_{G}$ ) and the opposition ( $β_{O}$ ) are equal to each other. To see why, assume that the government always chooses the policy that matches the state of the world. In that case, the voter’s updated belief after observing $x = CON$ and $x = LIB$ are both equal to the government’s initial reputation. If the opposition’s reputation is higher than the government’s, the strategy of the voter is $μ^{LIB} = μ^{CON} = 0$ . If the opposition’s reputation is lower than the government’s, the strategy is $μ^{LIB} = μ^{CON} = 1$ . In either case, the bad government no longer has incentive to choose policy $x = LIB$ .

To understand the effect of the mixed government disciplining equilibria on the voter’s welfare, I consider two cases, shown in Table 2. The first case depicts an equilibrium where the bad government is partially disciplined, that is, it chooses policy $x = CON$ with probability $θ_{b, LIB}$ when $ω = LIB$ . For the purposes of a responsive government, $θ_{b, LIB}$ has to be as small as possible. As I explained previously, when $θ_{b, LIB} = 0$ , we have $\hat{β_{G}^{CON}} = \hat{β_{G}^{LIB}}$ . As $θ_{b, LIB}$ increases, $\hat{β_{G}^{CON}}$ decreases and $\hat{β_{G}^{LIB}}$ increases. When $θ_{b, LIB} = 1$ , the strategy of the government is to choose its preferred policy, and the updated beliefs are

\hat{β_{G}^{CON}} = \frac{α β_{G}}{1 - β_{G} + α β_{G}} and \hat{β_{G}^{LIB}} = 1

Table 2.

Cases of equilibrium policy in the mixed government disciplining equilibria.

	$ω =$ CON	$ω =$ LIB
Case 1
Bad government	CON	CON/ LIB
Good government	CON	LIB
Case 2
Bad government	CON	LIB
Good government	CON/LIB	LIB

Hence, the equilibrium policy depicted in the first case is possible for any value of $β_{O}$ between $α β_{G} / (1 - β_{G} + α β_{G})$ and 1. As $β_{O}$ moves away from $β_{G}$ , the voter’s policy loss from this equilibrium will increase.

Alternatively, I consider the second case where the bad government is always disciplined but the good government is pandering, that is, the good government chooses policy $x = CON$ with probability $θ_{g, CON}$ when $ω = CON$ . Ideally, the voter would like $θ_{g, CON}$ as large as possible. If $θ_{g, CON} = 1$ , we have $\hat{β_{G}^{CON}} = \hat{β_{G}^{LIB}}$ . As $θ_{g, CON}$ decreases, $\hat{β_{G}^{CON}}$ decreases down to 0 and $\hat{β_{G}^{LIB}}$ increases up to $β_{G} / (β_{G} + (1 - β_{G}) (1 - α))$ . Hence, the equilibrium policy of the second case is possible for any value of $β_{O}$ between 0 and $β_{G} / (β_{G} + (1 - β_{G}) (1 - α))$ . Like the first case, as the difference between $β_{O}$ and $β_{G}$ increases, the voter suffers a higher loss from the policy.

5. Model with debate

The previous section shows that there are no equilibria in the baseline model where both governments choose the policy that matches the state of the world. In a world with no debate, the voter’s lack of information limits her ability to discipline the government to make decisions in accordance with her interests. The focus of this paper is to explore whether this situation may be improved when the opposition gives the voter information about the state of the world. More specifically, I look into the existence of government disciplining equilibria with debate, that is, equilibria where the opposition’s message motivates the bad government to choose the correct policy in a situation where it would not have done so if the message had been different. It is important to note that disciplining the bad government becomes an issue only when $ω = LIB$ . When $ω = CON$ , the policy preferences of the government are already aligned with those of the voter. Hence, in this section, I am looking at situations where the opposition’s message $m = LIB$ induces the bad government to choose policy $x = LIB$ for election concerns.

In the model with debate, the voter observes the message of the opposition in addition to the policy of the government. Hence, the voter has a more refined tool to discipline the government. I consider equilibria where $- b_{G} < μ^{CON, LIB} - μ^{CON, CON} < b_{G}$ and $μ^{LIB, LIB} - μ^{LIB, CON} > b_{G}$ . In other words, the voter’s election decision after observing $m = CON$ does not discipline the government but her decision after observing $m = LIB$ gives the government sufficient incentive to choose $x = LIB$ . For such an equilibrium to improve the voter’s welfare from policy, the opposition should be willing to announce the message that matches the state of the world.

When $ω = LIB$ , the preferred policy of both types of opposition is liberal; therefore, their announcement decision will be the same. I disregard any possible equilibria where the opposition announces $m = CON$ after $ω = LIB$ because such an equilibrium would not bring any disciplining effect, given the strategy of the government and the voter. When $ω = CON$ , the opposition’s message determines the policy. If the opposition announces $m = CON$ , both types of government choose their preferred policy, which is $x = CON$ when $ω = CON$ . If the opposition announces $m = LIB$ , both types of government follow the message. The electoral benefit for the opposition of announcing $m = CON$ is $μ^{LIB, LIB} - μ^{CON, CON}$ . If the policy benefit of $x = LIB$ outweighs the electoral benefit of $m = CON$ , the bad government will announce $m = LIB$ , thereby misleading the voter. That bad government will announce the truth only if the electoral benefit of doing so exceeds the policy benefit of its preferred policy, that is, $μ^{LIB, LIB} - μ^{CON, CON} > b_{O}$ . When $ω = CON$ , the good government’s preferred policy is conservative; hence, it does not have any incentive to mislead the voter for policy purposes. However, for the good opposition to announce $m = CON$ , the electoral cost should not exceed the policy benefit, that is, $μ^{LIB, LIB} - μ^{CON, CON} > - b_{O}$ . I disregard any possible equilibria where both types of opposition announce $m = LIB$ after $ω = LIB$ because such an equilibrium would lead to an over-disciplining effect. In what follows, I only consider two possible strategies of the opposition: truthful opposition and partially truthful opposition.

First, I assume that the opposition is truthful, that is, both types of opposition’s message always match the state of the world. Given the government’s strategy, the voter will observe $(m, x) = (CON, CON)$ when $ω = CON$ , and $(m, x) = (LIB, LIB)$ when $ω = LIB$ . After observing either of these pairs of message and policy, the voter’s updated beliefs about the government and the opposition will stay the same as her prior beliefs. Unless $β_{G} = β_{O}$ , the voter’s strategy should have $μ^{LIB, LIB} = μ^{CON, CON}$ . Given the voter’s strategy, it will not be sequentially rational for the bad opposition to announce $m = CON$ when $ω = CON$ .

Second, I assume that the opposition is partially truthful, that is, the good opposition always announces the state of the world but the bad opposition always announces $m = LIB$ . In equilibrium, the voter will observe $(m, x) = (CON, CON)$ if and only if $ω = CON$ and the opposition is good. Accordingly, her updated beliefs will be $\hat{β_{G}^{CON, CON}} = β_{G}$ and $\hat{β_{O}^{CON, CON}} = 1$ , which implies that the voter’s strategy should include $μ^{CON, CON} = 0$ . The voter’s beliefs after observing $(m, x) = (CON, LIB)$ cannot be pinned down by Bayes’ rule. Considering only the policy incentives of the politicians, I set the updated beliefs after $(m, x) = (CON, LIB)$ to be the same as the updated beliefs after $(m, x) = (CON, CON)$ , in which case $μ^{CON, LIB} = 0$ .⁷ In equilibrium, the voter will observe $(m, x) = (LIB, LIB)$ if and only if $ω = LIB$ or the opposition is bad. Since the voter never observes $(m, x) = (LIB, CON)$ in equilibrium, I calculate the updated beliefs after $(m, x) = (LIB, CON)$ , assuming that both politicians are policy-oriented.⁸ We only consider equilibria where $μ^{LIB, LIB} - μ^{LIB, CON} > b_{G}$ , which implies that $μ^{LIB, LIB} > 0$ and $μ^{LIB, CON} < 1$ . Therefore, the equilibria hold only when $\hat{β_{G}^{LIB, LIB}} \geq \hat{β_{O}^{LIB, LIB}}$ and $\hat{β_{O}^{LIB, CON}} \geq \hat{β_{G}^{LIB, CON}}$ .

The final step in specifying government disciplining equilibria with debate is to check whether it is sequentially rational for the opposition to announce its preferred policy given the other players’ strategies. When $ω = LIB$ , the opposition can guarantee its preferred policy $x = LIB$ by announcing $m = LIB$ . If the opposition announces $m = CON$ , it will receive its preferred policy only if the government is good. The upside of announcing $m = CON$ for the opposition is to guarantee election. The opposition will forego the electoral benefit of announcing $m = CON$ if and only if the policy benefit of announcing $m = LIB$ exceeds its electoral cost, that is, $b_{O} (1 - β_{G}) > μ^{LIB, LIB *}$ . As discussed already, if $ω = CON$ , the good opposition announces $m = CON$ if and only if $μ^{LIB, LIB} - μ^{CON, CON} > - b_{O}$ . When $μ^{CON, CON} = 0$ and $μ^{LIB, LIB}$ , this condition is already satisfied. If $ω = LIB$ , the bad opposition announces $m = LIB$ if and only if $μ^{LIB, LIB} - μ^{CON, CON} < b_{O}$ . This condition is already satisfied if $b_{O} (1 - β_{G}) > μ^{LIB, LIB *}$ . In other words, given the strategies of the government and the voter and under conditions where the bad opposition announces $m = LIB$ after $ω = LIB$ , it will also announce $m = LIB$ after $ω = CON$ . The equilibria are summarized next.

5.1 Government disciplining equilibria with debate

In the model with debate, there exist perfect Bayesian equilibria where the government chooses its preferred policy after message $m = CON$ but it chooses policy $x = LIB$ after message $m = LIB$ . The strategy of the opposition is to always announce its preferred policy. The strategy of the voter is one of the following:

The voter never reelects the government after $m = CON$ . If $\hat{β_{G}^{LIB, LIB}} > \hat{β_{O}^{LIB, LIB}} > \hat{β_{G}^{LIB, CON}}$ , the voter always reelects the government after $(m, x) = (LIB, LIB)$ but she never reelects the government after $(m, x) = (LIB, CON)$ .

The voter never reelects the government after $m = CON$ . If $\hat{β_{G}^{LIB, LIB}} > \hat{β_{O}^{LIB, LIB}} = \hat{β_{G}^{LIB, CON}}$ , the voter always reelects the government after $(m, x) = (LIB, LIB)$ but she reelects the government after $(m, x) = (LIB, CON)$ with probability smaller than $1 - b_{G}$ .

The voter never reelects the government after $m = CON$ . If $\hat{β_{G}^{LIB, LIB}} = \hat{β_{O}^{LIB, LIB}} > \hat{β_{G}^{LIB, CON}}$ , the voter reelects the government after $(m, x) = (LIB, LIB)$ with probability greater than $b_{G}$ but she never reelects the government after $(m, x) = (LIB, CON)$ . The equilibria hold if and only if $b_{O} (1 - β_{G}) > μ^{LIB, LIB *}$

The updated beliefs of the voter are

\begin{matrix} \hat{β_{G}^{CON, CON}} = \hat{β_{G}^{CON, LIB}} = \hat{β_{G}^{LIB, LIB}} = β_{G} and \hat{β_{G}^{LIB, CON}} \\ = \frac{α \cdot (1 - β_{O}) \cdot β_{G}}{α \cdot (1 - β_{O}) + (1 - α) \cdot (1 - β_{G})} \\ \hat{β_{O}^{CON, CON}} = \hat{β_{O}^{CON, LIB}} = 1 and \hat{β_{O}^{LIB, CON}} = \hat{β_{O}^{LIB, LIB}} = \frac{(1 - α) \cdot β_{O}}{1 - α β_{O}} \end{matrix}

In the government disciplining equilibria with debate, the opposition is partially truthful (Table 3). When the message is conservative, the voter knows for certain that $ω = CON$ and the opposition is good. Given beliefs about the opposition after observing $m = CON$ , the opposition never reelects the government after $m = CON$ . When the policy benefit is sufficiently high for the opposition, it is not tempted by the electoral benefit of announcing $m = CON$ and announces its preferred policy. When the message is liberal, the voter can only conclude that $ω = LIB$ or the opposition is bad. She rewards the government for choosing $x = LIB$ after $m = LIB$ . For this decision to be sequentially rational, $\hat{β_{O}^{LIB, LIB}}$ cannot be greater than $\hat{β_{O}^{LIB, LIB}}$ , and $\hat{β_{G}^{LIB, CON}}$ cannot be greater than $\hat{β_{O}^{LIB, CON}}$ .

Table 3.

Equilibrium policy in the model with debate.

	Bad opposition		Good opposition
	$ω =$ CON	$ω =$ LIB	$ω =$ CON	$ω =$ LIB
Bad government	LIB	LIB	CON	LIB
Good government	LIB	LIB	CON	LIB

The shaded areas in Figure 1 show the range of $β_{G}$ and $β_{O}$ for which the government disciplining equilibria with debate holds, given different values of $α$ , which is the probability that $ω = CON$ . When the voter thinks that $ω$ is likely to be liberal, $m = LIB$ does not hurt the reputation of the opposition much but $x = CON$ damages the reputation of the government. For the equilibria to hold, the initial reputation of the government should be pretty high even for low values of the opposition’s initial reputation. The reverse is the case when the voter thinks that $ω$ is likely to be conservative. When the voter has a flat prior about $ω$ , the equilibria hold when the initial reputation of the government and the opposition are relatively close to each other.

Figure 1.

Conditions for government disciplining equilibria with debate.

The model shows that the reputation of the opposition ( $β_{O}$ ) does not need to be particularly high for debate to have a disciplining effect on the government. However, $β_{O}$ is critical for a disciplining effect to increase the welfare of the voter. The strategy of the bad opposition is to always announce $m = LIB$ , irrespective of $ω$ , which leads to policy $x = LIB$ . Hence, in the equilibrium with debate, the voter receives a policy that she does not want with probability $α (1 - β_{O})$ , that is, when $ω = CON$ and the opposition is bad.

6. Conclusions

The goal of this paper is to explore whether the participation of opposition parties in parliamentary debate has an influence on policy decisions. The premise of my argument is that the representative voter cares about the consequences of policies but that she has limited information on the mapping between policies and their consequences. In contrast, political parties have better information yet some political parties may be biased in favor of certain policies, irrespective of their consequences. Given this information and preference structure, the responsiveness of the political system is at stake. The inclusion of an opposition party in political debate may improve responsiveness in the following way. The opposition party may provide information to voters about the consequence of policies that the government is going to implement. If this information is credible enough to change the voters’ policy preference, the government may need to adjust its policy decisions accordingly. The model in this paper shows, however, that opposition parties have incentives to mislead voters, which prevents the existence of an equilibrium where the opposition party always tells the truth and the government does what is good for the voters.

The main finding of the paper shows an equilibrium where only the good opposition tells the truth and the opposition’s message has a disciplining effect on the government. Going back to the example, the good opposition protests the investment when the environmental costs exceed the economic benefits, whereas the bad opposition is against any investment, irrespective of its costs and benefits. In equilibrium, the government makes the investment only when the opposition supports it. The voter benefits from the disciplining effect when the investment is environmentally costly but suffers a loss when the government decides against an investment even though the economic benefits of the investment exceed the environmental cost. Since the disciplining effect works even when the opposition is misleading, the overall welfare effect of debate will depend on the probability that the opposition is good and the probability that the investment decision is beneficial for the voter.

For the disciplining effect to work, the government should be sufficiently concerned about winning elections, and the opposition should be sufficiently concerned about policy. This is because the voter rewards the government for choosing a liberal policy on the recommendation of the opposition, and rewards the opposition for making a conservative recommendation. Unless the opposition is sufficiently concerned about the policy, it will be reluctant to protest against the investment.

The model shows that, surprisingly, the disciplining effect works even when the reputation of the opposition is not particularly high. When both policies are equally likely to be good for the voter, the equilibrium holds when the reputation of the opposition and the government are relatively close to each other. The reputation of the government should be high enough (compared with the opposition) for the voter to be able to commit to rewarding the government after following the opposition’s liberal policy recommendation. The reputation of the opposition should be high for the voter to be able to commit to punishing the government if it does not follow the liberal policy recommendation.

When the voter’s beliefs on the consequences of the policy alternatives are lopsided, the conditions for the disciplining equilibrium change. When the voter thinks an investment is very likely to have high environmental costs, protesting an investment does not hurt the reputation of the opposition, and making the investment after a protest hurts the government’s reputation considerably. Therefore, the disciplining effect works only when the reputation of the government is high (relative to the opposition). When the voter places very low probability on environmental costs, only an opposition with high reputation can have a disciplining effect.

Footnotes

Acknowledgements

I would like to thank Randy Calvert, Brian Crisp, Justin Fox, Matthew Gabel, John Patty, Norman Schofield, audience members at the second Annual Formal Theory and Comparative Politics Conference, the 2015 Annual Meetings of the Southern Political Science Association and the Midwest Political Science Association, as well as the editors of the journal and the anonymous reviewer for their very helpful feedback. I am solely responsible for the errors.

Notes

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