Presidential veto power

Presidential veto power Oliver Board and Tiberiu Dragu October 5 Abstract The presidential veto is a vital component of the system of checks and balances established by the American Constitution. To analyze the impact of this veto power on the legislative process, we examine a cheap talk game between three players: an expert committee which drafts a bill and sends it to the floor; the legislature, which can modify the bill before voting on a final version; and the president who can then veto or not. We show that, depending on the strength and direction of the president s bias compared to that of the committee, more or less information may be transmitted than if the president has no veto power. A striking implication of this result is that the president may actually be harmed by his own veto power and suffer an overall loss of utility. Furthermore, the very existence of the veto threat can sometimes induce the legislature to use what information they have less effectively. [The Presidential veto] establishes a salutary check upon the legislative body, calculated to guard the community against the effect of faction, precipitancy, or any impulse unfriendly to the public good...the injury which may possibly be done by defeating a few good laws, will be amply compensated by the advantage of preventing a number of bad ones. (Alexander Hamilton, Federalist No. 73) Introduction The process of legislation can have a dramatic effect on policy and consequently on overall social welfare. Legal rules shape incentives and provide a framework within which firms and individuals can engage in economic interactions. The standard normative approach to policy analysis views the entire legislative process as a social-welfare-maximizing black box, exactly as the neoclassical theory of production and supply views We are grateful to Meg Gleason, Ana Espinola-Arrendondo, Alexander Gümbel and Lucy White for helpful comments. Department of Economics, University of Pittsburgh, Pittsburgh, PA 56, ojboard@pitt.edu DepartmentofPoliticalScience,StanfordUniversity,Stanford,CA9435,tdragu@stanford.edu

the firm as a profit-maximizing black box. However, there are political failures as well as market failures, often rooted in informational problems distortions potentially arising from an asymmetric distribution of relevant information among the agents of the public decision-making process. Indeed, uncertainty and asymmetry of information are prevalent in the legislative process. When legislators enact policies they do not always know their precise effects. Also, different legislators may have different information regarding the consequences of enacted policies. Moreover, the interests of such informed legislators may not coincide with those of the median voter in the legislature. Consequently, these legislators could use their informational advantage strategically with possible undesirable effects on the final choice of policies. As we shall see, the extent to which this occurs depends on the constitutional framework that regulates the legislative process. The passage of federal legislation in the United States (US) is a case in point. Although bills originate on the floor of the House or the Senate, almost all of them are actually drafted by specialized standing committees before returning to the floor. If passed by the Congress, the President can either sign the bill into law or veto it. If the President issues a veto, the bill is sent back to the floor where a two-thirds majority can override the veto. However, such overrides in the US Congress are extremely rare and unlikely. From 789 until the present day, 35 Presidents exercised their veto authority 55 times. Congress challenged the President s veto 37 times and succeed in overriding only on 6 occasions. Uncertainty and asymmetry of information are pervasive in the US legislative process. First of all, the relationship between policies and outcomes is not straightforward. The precise impact of a bill depends on many factors, and without detailed investigation it is hard to predict its consequences. Typically, the committee drafting the bill carries out this investigation and therefore has access to better information about its likely outcome than those who vote on it. Committees hold many hearings and acquire a degree of knowledge not necessarily enjoyed by the other legislative agents. Several papers (see e.g. Gilligan and Krehbiel [], [] and Krishna and Morgan [3]) have analyzed the amount of information passed from the informed committee to the uninformed floor, building on Crawford and Sobel s [9] seminal analysis of strategic information transmission. These papers provide an informational rationale for the (internal) organization of the legislature, focusing on the comparison between different rules that govern the interaction between the committee and the floor. A key result is that any divergence of interest between the committee and the floor(inwhichcasewesaythecommitteeisbiased) can adversely affect the flow of information. The role of the presidential veto, however, is not considered. In this paper we provide an analysis of how presidential veto power affects the transmission of information within the legislative process and consequently policy choices. To address this issue, we need to understand how this constitutional provision shapes the incentives of the main legislative body. We use the tools of game theory to show that the veto power can have a substantial impact on the final outcome. First, the Stiglitz [7] discusses this issue in more detail. Austen-Smith and Riker [3] were the first to emphasize the importance of this distinction.

presidential veto directly influences the bills passed by Congress which needs approval from the president before their bills become law; second, this has an indirect (though potentially large) effect on the information transmission process. Depending on the strength and direction of the president s bias compared to that of the committee, more or less information may be transmitted. Counterintuitively, it is even possible that the president may be harmed by his own veto power: although the president is able to veto bills he dislikes, if the committee s draft bill is sufficiently less informative, he might suffer a welfare loss overall. Furthermore, the very existence of the veto threat can sometimes induce Congress to use what information it has less effectively (from its point of view) than would otherwise be the case. The framers of the American Constitution intended the veto as a guard against ill-conceived legislation an institutional weapon given to the president to wield in the legislative process. For instance, James Madison saw the presidential veto as an auxiliary precaution against usurpation by the necessarily predominant branch of republican government (Federalist No. 5). Additionally, presidents often use their power of veto because they believe that if a particular bill becomes a law, it will produce negative effects on the population (or part of it). However, to our knowledge the informational impact of the veto on the legislative process has not previously been considered. Our formal model has relevance beyond the US legislative process. Other constitutions also grant the elected president a veto over legislation. Although the nature of the veto power varies enormously across the range of such presidential systems, the veto is the president s most consistent and direct connection with the legislative process. Even the European Union (EU) legislative process with its atypical institutions, the European Commission, the Council of Ministers and the European Parliament, can be analyzed with our formal model. More generally, the model can be applied to any situation in which one party is given a yes or no vote over a proposal but has no ability to formulate the proposal itself. This suggests several applications in corporate governance where shareholder approval is required for major decisions. In the U.S., changes to a company s corporate charter work in this way. And in Germany even minority shareholders are afforded veto power: any block of 5% or more can veto corporate charter amendments, supervisory board changes, and profit and transfer control agreements. Similar arrangements exist in other countries. Our results may shed some light on the likely effects of such veto power, and thus contribute to the debate over the appropriate extent of shareholder power (see e.g. Bebchuk and Fried [5]). Such alternative applications of our model will be discussed in the concluding section. The paper proceeds as follows. In section two we describe the US legislative process in more detail. Section three introduces our formal model, and section four provides the formal analysis and states our key results. Section five discusses related literature, and in the final section we consider possible extensions and provide some concluding remarks. 3

The US legislative process The Constitution creates a system of separate institutions sharing functions and (sometimes) even competing for predominant influence in exercising them. The framers of the Constitution desired a strong and effective national government, but at the same time they wanted to avoid concentrating too much power in the central government. The framers believed that limits on government could be achieved by dividing power among different branches of government. Such division of power would ensure both policy conflict and cooperation, because it makes officials in the various branches of government responsive to different constituencies and perceptions of public welfare. In the legislative process, Congress s own legislative power is effectively checked by the president s veto the laws Congress passes may be vetoed in turn by the president. The Constitution names Congress as the first branch of government, assigns it all legislative power, and grants it explicit and implicit responsibilities through the so-called elastic clause (Section 8 of Article I). This clause empowers Congress to make all Laws which shall be necessary and proper for carrying into Execution. Draft bills may originate in either the House of Representatives or the Senate. Although any member of either chamber can introduce a legislative proposal, the bill is almost always referred to the appropriate committee for consideration. Decision-making is decentralized: responsibility for specific subject areas is dispersed among different congressional committees. Committees provide the division of labor and specialization needed to handle the roughly ten thousand measures introduced biennially. Each committee s jurisdiction is divided into certain subject matters under the rules of each body, and all measures affecting a particular area of the law are referred to the committee with jurisdiction over that subject matter. For example, the Committee on the Judiciary in the House has jurisdiction over measures relating to judicial proceedings generally, as well as seventeen specific categories, including constitutional amendments, immigration and naturalization, bankruptcy, patent, copyrights, and trademarks. A member seeks election to the committee that has jurisdiction over a field in which she feels she is qualified. For example, the Committee on the Judiciary is traditionally composed almost entirely of lawyers. Many members are nationally recognized experts in the speciality of their particular committee. Action by the committees is perhaps the most important phase of the legislative process. The committees provide the most intensive consideration of a proposed measure as well as a forum in which members of the public are given the opportunity to voice their opinions. A tremendous volume of work is carried out by members in this phase. The drafting of legislation is an art that requires great skill, knowledge and experience. Committees acquire detailed information during the course of often very lengthy formal hearings congressional committees sometimes draft bills after studies and hearings covering a period of a year or more. Committee membership also entitles legislators to certain resources, such as expert staff assistance, which also puts them at advantage compared with other colleagues outside the committee. In addition, each committee is provided with a professional staff to assist it in the innumerable legislative details involved in 4

the consideration of bills. 3 If the committee votes to report the bill to the floor, the committee staff writes a report. The report describes the purpose and scope of the bill and reasons for its recommended approval. Generally, a sectionby-section analysis is conducted explaining precisely what each section is intended to accomplish. Committee reports are the most detailed element of the legislative history of a law. They are used by the courts, the executive department, and the public as a source of information regarding the purpose and meaning of the law. A reported bill is given consideration by the entire membership of the body of Congress in which it originates. Debates are governed principally by the rules adopted at the opening of each Congress. After a general debate, the second reading of the bill begins. The second reading is a section-by-section reading during which time germane amendments may by offered to each section when it is read. Under the standard open amendment process, a member is permitted five minutes to explain a proposed amendment; members may also offer an amendment to an amendment, for a separate five-minute debate. Each substantive amendment and amendment thereto is put to a vote for approval. The Constitution establishes a major legislative role for the President by requiring his approval of measures passed by Congress. Although the President does make legislative proposals, Congress is usually under no constitutional obligation to put the proposal to a vote: the President has no formal power to propose legislation. Moreover, the President cannot veto specific pieces of a legislative act: line-item vetoes are unconstitutional. 4 Rather, the Constitution allows the President to veto a bill in its entirety only, perhaps striking down many provisions of which he approves in order to eliminate one he opposes. Within ten days after a bill is presented to the President, he must either: ) sign it into law; ) veto it and return it to the house of Congress in which it originated along with a message explaining his action; or 3) take no action on it, in which case it becomes a law without his signature at the end of ten days. If the President issues a veto, the bill is sent back to the floor where a two-thirds majority in each chamber can override the veto. 5 3 A model of the information transmission in the legislative process 3. The Players, Preferences and Information Our model assumes that policies and outcomes are fundamentally distinct and that the consequences of policies are uncertain. Many factors in the environment affect the relationship between legislative decisions 3 Legislative functions that are exercised by committee in the US Congress may be fulfilled by other agents in other political systems. For instance, in parliamentary democracies, ministries rather than committees acquire policy expertise and draft legislation. Thus one can argue that there is a functional equivalence between congressional committees and ministries in parliamentary democracies. 4 Under the line-item veto law, P.L. 4-3, which took effect on January, 997, President Clinton became the first president empowered to veto specific items within a bill (and only then in appropriations bills). But on June 6, 998, in the case of Clinton v. City of New York, this law was declared unconstitutional by the United States Supreme Court, which held that a constitutional amendment would be required to grant a line-item veto. 5 For a much more detailed account of congressional procedures, see Oleszek [5]. 5

and policy outcomes. Legislative initiatives may produce unintended and possibly undesirable consequences. The political and economic environment in which policy consequences are realized may be subject to random variations beyond the control of legislative decision-makers. For example, macroeconomic policy decisions mustbetakeninaveryuncertainenvironment.theuncertaintycomesinmanyforms,suchasuncertainty about the structure of the economy, for example the linkage between excess demand and inflation. Also policies are vulnerable to the vicissitudes of implementation. Public agencies charged with implementing the policies have specific expertise about the details of implementing such policies. Congress may lack a thorough understanding about how agencies work, or may not appreciate the complexities of implementing the statutes they write. The model incorporates such uncertainty by assuming that there is a stochastic and linear relationship between a bill and its outcomes: x = b θ. Formally, we consider a game with three players, the committee, c; the (unicameral) legislature, l; and the president, p. There is asymmetric information: while the committee has acquired specific expertiseand so knows the outcome a given bill will produce (i.e. the committee is assumed to know the exact value of a random variable θ), the legislature and the president make the policy in the absence of such knowledge and know only that a given policy produces outcomes distributed over a specified range. The committee proposes a draft bill and sends it to the legislature for approval. The legislature updates its beliefs and chooses a bill, perhaps, but not necessarily, the committee s drafted bill. Then the president can either veto or accept the legislature s chosen bill. Finally, the outcome is realized as a function of the legislature s policy choice and the presidential veto. Payoffs are awarded to the three players the committee, the legislature, and the president as a function of the closeness of the realized policy to their most preferred policies. Formally, the move order of the game is as follows:. Nature chooses the value θ of a random variable. θ U [, ].. The committee observes θ and sends a draft bill, d R to the legislature. 3. The legislature observes d but not θ and passes a bill b R. 4. The president observes d and b but not θ, and can veto the bill or not. All players care only about the final policy outcome x. Preferences are given by the following quadratic loss functions: U c = (x c x) ; U l = x ; U p = (x p x) Each player has a preferred policy, or ideal point, x c, and x p for the committee, legislature and president respectively. x c and x p can therefore the thought of as the bias of the committee and the president relative to the legislature. The assumption that the players have different preferred policies represents the fact that they have different constituencies. The members of the Congress represent constituencies that vary in geographical area, population, economic structure, and social composition. Every member of Congress depends for re-election on constituency-based political forces. Therefore, different members speak for different 6

economic, social, and geographical interests, and all members are necessarily somewhat parochial in their policy orientation. In contrast, the president s constituency is the entire nation. The president can claim to speak authoritatively on behalf of the national interest or to act for various inarticulated or unorganized interests not adequately represented in Congress. Without loss of generality, we assume that x c >, and consider the following three cases: (a) x c > >x p ; (b) <x p <x c ; and (c) <x c <x p. In case (a) the president and the committee have opposing biases; in cases (b) and (c), they are biased in the same direction, with the committee more biased than the president in case (b), and the reverse in case (c). As mentioned, the random variable θ represents uncertainty as the effects a given bill will produce: the resulting outcome if bill b is passed and ratified by the president is x = b θ; if the bill is vetoed, the status quo, b remains in place, and the outcome x = b θ. We can re-write player utilities as: U c = (x c b + θ) U l = ( b + θ) U p = (x p b + θ) 3. Strategies and Equilibrium Concept A strategy for the committee, d(θ), specifies a draft bill given the state of the world. These bills have no value other than the information they convey: they are cheap talk. A strategy for the legislature, b(d), specifies which bill they pass given the draft bill sent by the committee: they are free to amend the draft in any way they choose. Finally, a strategy for the president involves a decision A(d, b), which takes the value when the president approves the bill and the value when he vetoes it. In addition, the legislature and the president form a posterior distribution μ l (b) and μ p (b) over the state space, which depend on the committee s draft bill. In a (perfect Bayesian) equilibrium of the game, the draft bill sent by the committee maximizes its expected utility given the anticipated responses of the legislature and the president. Next, the legislature chooses the bill which maximizes its expected utility given its beliefs about the value of θ (conditional on the committee s draft bill) and the anticipated response of the president; finally, the president vetoes the bill if and only if it leads to a worse outcome for him than the status quo, given his beliefs about θ. The legislature s and the president s calculations are assumed to be consistent with beliefs updated from their priors on θ according to Bayes rules. It can be shown that every equilibrium is of a particular type: a partition equilibrium. A partition equilibrium is a partially pooling equilibrium, in which some but not all of the committee s information is revealed. More precisely, the committee s strategy choice partitions the state space into a finite number of intervals, with the draft bill chosen revealing only in which element of the partition the actual value of θ lies. This represents the committee s optimal compromise between including enough information in the draft bill 7

to induce the legislature and the president to respond to it and holding back enough information so that this response is as favorable as possible from the committee s point of view. 6 There are typically several types of partition equilibria of this kind, with varying degrees of information being revealed by the committee. As is standard in cheap talk games, we focus attention on the most informative of these, which we call a legislative equilibrium with veto. The informativeness of an equilibrium measures how finely the partition divides up the state space. More precisely, suppose that bills are chosen to minimize the variance of the final policy outcome, x, given only that the information θ lies somewhere in the relevant element of the partition 7.Clearlyafiner partition will result in a lower variance, so the variance of x can be used as a measure of informativeness. Given a partition P which divides the state space into n intervals [,θ ), [θ,θ ),...,[θ n, ], we define: informativeness (P) = var (ˆx) where ˆx (θ) = θ i + θ i θ for θ [θ i,θ ). We are now in a position to present the formal definition of our equilibrium concept: Definition A legislative equilibrium with a veto is a set of strategies, d ( ), b ( ), A (, ), and beliefs μ l ( ) and μ p( ), such that:. For all θ [, ],d (θ) arg Z max d U c (b (d),a (d, b),θ). For all d, b (d) arg max b U l (b, A,θ) μ l (θ d)dθ θ Z 3. For all d, b, A (d, b) arg max A U p (b (d),a,θ) μ p(θ d)dθ, where A = {, } Z θ 4. For all d such that dθ >,μ i satisfies: μ i (θ b) = θ dθ, where θ d = {θ d (θ) =d}, for i = l, p. θ d d 5. There is no other more informative equilibrium. To analyze the precise effect of the presidential veto, we compare this to the most informative equilibrium of the game in which the president has no veto power, a legislative equilibrium without veto. Here, the legislature maximizes its expected utility given its beliefs about the state, θ, which are updating by Bayes rule on observing the draft bill sent by the committee. At the same time, the chosen draft bill of the committee maximizes its expected utility given the legislature anticipated responses. Formally, Definition A legislative equilibrium without a veto is a set of strategies, d ( ), b ( ), and beliefs μ l ( ), such that: 6 For example, suppose that the committee chooses one of a finite number n of draft bills, d {d,d,..., d n }, with d i chosen whenever θ [θ i,θ i ) (in fact, the precise values of d,d and d 3 do not matter; what is important is that a different bill is sent in each interval, so that by observing the value of d the legislature can figure out which interval θ must be in). The legislature and the president interpret the draft bill d i to mean that θ i 6 θ<θ i+ for some set of numbers {θ,θ,..., θ n} such that θ =and θ n =. 7 In fact, this will typically not be the case in equilibrium, because of the tension between preferences of the legislature and the president. We discuss this in more detail in the next subsection. 8

. For all θ [, ],d (θ) arg Z max d U c (b (d),θ).for all d, b (d) arg max b U l (b, θ) μ l (θ d)dθ Z θ 3. For all d such that dθ >,μ l satisfies: μ l θ d 4. There is no other more informative equilibrium. (θ d) = θ dθ, where θ d = {θ d (θ) =d}. d 3.3 Informational losses versus distributional losses. The players are involved in a collective decision-making process that has both conflict of interests and prospective gains from cooperation: they typically find themselves in situations that are neither purely conflictual nor win-win. For one, reducing the uncertainty about the relationship between policies and outcomes is collectively beneficial and distinct from the distributional effects (the private benefits for each player) of a chosen bill. All agents, the committee, the legislature, and the president, benefit fromhaving more information about the consequences of legislation if such information can be attained prior to the choice process. But the players have different preferences and are concerned with the distribution of benefits under alternative policy choices. With such a divergence in the players preferred outcomes, some players may incur gains at the expense of others. Note that the (expected) utility of each player can be decomposed into two elements, the first representing the informational losses which arise because (in equilibrium) the bill b chosen is not perfectly responsive to the state θ, causing some variance in the final policy outcome x (θ); and the second representing distributional losses, which arise when the expected value of final outcome is not equal to the player s ideal value: U i = var (x ) (E [x ] x i ) for i {c, l, p} (where x l =). 8 Note that the first term of this expression, var (x ), is not thesameasthemeasureoftheinformativeness of a partition used above. In the definition of informativeness of a partition, bills were chosen to minimize the variance of x, i.e. each bill was the midpoint of the corresponding interval. Although these bills represent the legislature s ideal choices given its information, it will sometimes be forced to choose differently to avoid a presidential veto. This results in additional informational losses. To clarify, informational losses result from two sources. First, the committee holds back some of its information, revealing imperfectly the value of θ. Depending on his bias relative to that of the other players, we shall see that the president can either alleviate or worsen this effect. Second, given the information revealed by the committee, the preference divergence between the president and the legislature produces 8 The derivation of this formula is as follows: U i = E E [x ] E [x ] x i + x i = var (x ) (E [x ] x i ). (x i x ) = x i +E [x ] x i E x = E x E [x ] 9

another informational distortion: in some intervals, bills are chosen in accordance with the legislature s preferences; in others, the president s veto power pulls the chosen bill closer to his ideal; the overall effect is a higher variance in the outcome than would result if the legislature alone made the choice. Given that a higher variance is harmful for all the players, ceteris paribus, thisdistortioneffect represents a clear inefficiency. 3.4 Formal analysis 3.4. Committee and President have opposing biases (x c > >x p ) We consider first the case where the committee and the president have opposing biases. The key result of this section is that the legislative equilibrium without veto is at least as informative as the legislative equilibrium with veto (Theorem ). A striking implication of this result is that the ability to veto bills not to his liking may actually harm the president. One the one hand his veto threat causes the legislature to propose bills that are more favorable to him, for fear that their preferred choices will be vetoed; but on the other the original bill drafted by the committee is less informative, and therefore the actual bill passed is less responsive to the state, resulting in greater uncertainty in the final outcome. Using the terminology introduced above, the president s distributional losses will be reduced if he has veto power, but his informational losses will increase. As we shall demonstrate below, the overall effect is ambiguous. The legislature is always worse off under the legislative equilibrium with veto: not only is the draft bill from the committee less informative, but they are also constrained in what bills they can pass by the threat of a veto from the president. To understand in more detail the precise effects of the president s veto power, suppose that the legislative equilibrium without veto partitions the state space into n steps: [,θ ), [θ,θ ),...[θ n,, ] ; in the ith step, the committee sends draft bill d i and the legislature chooses bill b i. In each case b i is chosen to minimize utility losses: since the legislature s (updated) belief on receiving draft bill d i is uniform on [θ i,θ i ), it will adopt b i = θ i +θ i, the midpoint of the interval. Now let us reintroduce the presidential veto, and ask whether the original partition still constitutes an equilibrium. In electing whether or not to use his veto power against a particular bill b i, the president is effectively making a choice between the b i and the status quo, b. Since his preferred bill is θi +θi + x p, he will exercise his veto whenever b is closer to this bill than is b i, i.e. whenever b θ i + θ i + x p < θ i + θ i + x p b i. Substitution b i = θi +θi and using the fact that x p < gives us b <b i <b x p. In words, the president will veto any bill between b and b x p. If none of the bills passed by the legislature in the legislative equilibrium without veto fall in this region, then it is also a legislative equilibrium with

veto. If one or more of the bills passed in the original equilibrium do fall in this region, however, we have a new equilibrium. Suppose first that the legislature does not adjust its actions, so that bill b i (say)itvetoedby the president, and the status quo b remains in place. The original intervals were constructed so that when the state is θ i, the committee was indifferent between b i and b i+, with strict preference for b i when θ<θ i and strict preference for b i+ if θ>θ i ; but if b i is vetoed by the president in favor of b, the committee will now strictly prefer b i+ when the state is θ i or slightly less. For these values of θ, it does better to draft bill d i+, undermining the original equilibrium. To compute the legislative equilibrium with veto, we must take into account the effects of the presidential veto when constructing the indifference conditions for the committee (recall that these indifference conditions determine how the state space can be partitioned). This is not simply a matter of replacing any bill which the legislature would like to pass in the interval (b,b x p ) with b itself. The legislature will anticipate likely vetoes by the president and may adjust its actions accordingly. To see how, let E [θ d i ] denote the legislature s and the president s expectation of θ on receiving draft bill d i from the committee. 9 The legislature s preferred bill is E [θ d i ], while the president wants E [θ d i ]+x p. We consider three (exhaustive) possibilities: (a) E [θ d i ] 6 b or E [θ d i ] > b +x p. The legislature can pass its preferred bill b i = E [θ d i ] without fear of veto by the president. (b) b <E[θ d i ] 6 b x p. Any bill above b will be vetoed by the president, since the president s preferred bill is E [θ d i ]+x p <b ; and any bill below b is worse for the legislature than b itself. The legislature can do no better than pass its preferred bill b i = E [θ d i ] and accept the president s veto, with the status quo b remaining in place. (c) b x p <E[θ d i ] <b x p. The president will veto any bill that is further from the status quo than his preferred bill, i.e. any bill above E [θ d i ]+x p b ; since this value is still less than E [θ d i ], it is the closest the legislature can get to its preferred bill. Figure below shows the bill that will result as a function of E [θ d i ]. 9 The definition of an equilibrium requires that the legislature and the president have the same beliefs about θ on the equilibrium path, i.e. ifd i is actually chosen by the committee for some value of θ. Off the equilibrium path this need not be the case. This issue, which does not affect the current analysis, is discussed in more detail in the proof of Theorem. Passing a bill b i = b results in the same outcome, with no need for a presidential veto.

b i 45 b b x p b x p E[θ d i ] Figure : bill chosen as a function of expected value of θ To clarify the intuition behind the effects of the presidential veto, we present an example before providing a formal statement of the results. Example Suppose the committee s bias is x c =, the president s bias is x p = 5, and the status quo b = 3. Without veto: The legislative equilibrium without veto is characterized by the intervals, 5, 5, 7 5 and 7 5,, which partition the state space into three sections. The committee drafts a different bill, d,d or d 3, depending on whether θ lies in the first, second or third interval respectively. Since there is no fear of presidential veto in this case, the legislature chooses its favorite bill based on the information learned from the committee. For instance, if draft bill d is sent, the legislature knows that θ must lie between and 5 ; it will choose bill b = 5 (the mid-point of the interval) to minimize distributional losses. And in response to draft bills d and d 3 the legislature will adopt bills b = 9 3 and b 3 = 5 respectively. It remains to check that the original strategy of the committee is optimal given these bills chosen by the legislature. Recall that the bias of the committee (its ideal outcome) is x c. Thus when the state is θ, the committee s ideal bill is b = x c + θ. Since draft bill d induces bill b from the legislature, and draft bill d induces bill b, we must check that whenever θ, 5, the committee prefers b to b, and whenever θ 5, 5 7, it prefers b to b. This will be true as long the committee is indifferent between the two bills

when θ is on the borderline between the two intervals (θ = 5 ). At θ = 5, the committee s ideal bill is + 5 = 6, which is precisely the midpoint between b and b : the committee is indeed indifferent between the two bills. Similar analysis shows that d 3 is optimal when θ 7 5,, as required. With veto: It is clear that this cannot be an equilibrium with veto: in the last interval the president prefers the status quo b = 3 (this is in fact his ideal policy, given his expectation of θ) to the equilibrium action of 5, so he would exercise his veto power if b 3 = 5 were passed by the legislature. This in turn alters the incentives of the committee. For values of θ between 3 3 and 7 5 (the original cutoff point) the committee now prefers to send draft bill d 3, resulting in a finalbillof 3, rather than draft bill d whichinducedafinal bill of 9 3. The legislative equilibrium with veto is characterized by the intervals, 8 75, 8 75, 3 75 and 3 75,, resulting in bill b = 4 75,b = 39 5, and b 3 = 3 respectively. In the first two intervals, the legislature is choosing its favorite bill, since the president s veto threat is not credible when his own preferred bill is so far from the status quo. In the third interval, however, the legislature would like to choose bill b 3 = 53 75 while the president s ideal bill is 38 75. Any bill b> 3 will be vetoed, so the best bill from the point of view of the legislature which will not be vetoed is b 3 = b = 3 itself. The partitions, which represent the amount of information transmitted in each case, are shown figure below along with the resulting bills. The final outcomes are shown in figure 3. Legislative equilibrium without veto b = 5 b = 9 3 b 3 = 5 7 5 5 8 3 75 75 θ / b = 4 75 / 3 b = 5 / b 3 = 3 Legislative equilibrium with veto Figure : Information transmitted and bills passed (example ) 3

x Without veto With veto 6 θ 6 3 Figure 3: Outcomes (example ) It is clear from example that the veto power reduces the amount of information transmitted: although there is the same number of intervals in each case, they are more evenly spaced in the equilibrium without veto. Theorem shows that this result is not just a feature of this specific example, but applies whenever the committee and the president have opposing biases, regardless of the position of the status quo. Theorem If the committee and the president have opposing biases, then the legislative equilibrium without veto is at least as informative as the legislative equilibrium with veto. We relegate the proof of this proposition to the appendix, but it is worthwhile providing some intuition here. First recall that, in the model without veto threats, a more informative equilibrium is possible when the agents interests are more closely aligned. Although our comparison between the equilibria with and without veto fixes preferences and focuses on the impact of the president s veto threat, something similar is going on. When the president has the opposite bias to the committee, his veto power can force the legislature to choose bills that are closer to his own interests than they would like; and these bills are further away from the committee s interests, effectively driving a larger wedge between the bills chosen by the legislature and the committee s preferred choices than there would be if there were no veto power. The next two results show how the presidential veto impacts on the utility of the legislature and the president respectively. 4

Corollary If the committee and the president have opposing biases, the president s utility may be higher, lower or the same in the legislative equilibrium without veto as in the legislative equilibrium with veto. To understand Corollary, recall that we can decompose the president s expected utility into informational losses and distribution losses: U p = E(x p x) = var [x] (E [x] x p ) = (informational losses + distributional losses). Informational losses arise because the committee holds back some information in their draft bill, and so the bill chosen by the legislature is not perfectly responsive to changes in the state, θ, causing fluctuations in the final outcome x. Distributional losses arise because given their beliefs about θ,the legislature typically chooses bills that are not ideal from the point of view of the president. Veto power mitigates these distributional losses, allowing the president to veto bills that are unfavorable to him; but informational losses are increased because the committee, now facing a greater divergence between its preferred outcome and the bill actually chosen, withholds more information than before. Depending on which of these effects dominates, the president may be either better or worse off. To prove the corollary, we compute the President s utility levels in example with and without the veto, for three different values for the status quo, b. Table describes the results. no veto veto, b = veto, b = veto, b = 3 informational.59.88.59. distributional.4.36.4.97 overall.559.64.559.59 Table : Presidential utility losses in different equilibria Corollary If the committee and the president have opposing biases, the legislature s utility is at least as high in the legislative equilibrium without veto as in the legislative equilibrium with veto. Corollary follows easily from Theorem, which states informational losses are at least as high in the legislative equilibrium with veto as without veto; since distributional losses for the legislature are zero in the legislative equilibrium without veto, they can only increase when the veto is introduced, giving us the desired result. 3.4. Committee and President have like biases, with the committee more biased (x c >x p > ) The next case we consider is when the committee and the president are biased in the same direction, with the president less biased than the committee. As might be expected, the effects of the veto are reversed compared with the case of opposing biases. Again, this result holds whatever the value of the status quo. 5

Theorem If the committee and the president have like biases, with the committee more biased than the president, then the legislative equilibrium with veto is at least as informative as the legislative equilibrium without veto. The intuition behind Theorem is basically the opposite of the intuition behind Theorem : for certain regions of the state space, the presidential veto forces the legislature to pass bills that are closer to the committee s preferred choices than it would if there were no veto power, resulting in a closer alignment of effective preferences between the two bodies and therefore (potentially) a more informative equilibrium. Figure 4 illustrates this point, detailing the committee s ideal bill (θ + x c ), along with the bill that will actually be chosen in the presence of presidential veto power. b i committee s preferred bill bill chosen by legislature x c 45 b x p b x p b E[θ d i ] Figure 4: Effective preference alignment in the presence of presidential veto power Example provides a direct comparison of the legislative equilibrium with and without veto for specific parameter values. Example Suppose the committee s bias is x c =, the president s bias is x p = 3, and the status quo b = 3. Without veto: The legislative equilibrium without veto is exactly the same as in example, since the committee s bias is the same and the president plays no role: the state space is partitioned into three 6

intervals,, 5, 5, 7 5 and 7 5,, resulting in bills b = 5,b = 9 3, and b 3 = 5 respectively. With veto: This cannot be a legislative equilibrium with veto, since in the second interval the president would veto the bill b in favor of the status quo b = 3, which is in fact his preferred bill. This in turn induces the committee to prefer draft bill d, signaling that θ lies in the first interval, for values of θ of 5 and slightly higher. In the legislative equilibrium with veto, the boundary of the first interval shifts to the right, pushing the second interval to the right as well. The new partition is, 45 7, 7 45, 45 and 45, (see figure 5 below). Legislative equilibrium without veto b = 5 b = 9 3 b 3 = 5 7 5 5 7 45 45 / b = 7 9 / b = 3 / 67 b 3 = 9 θ Legislative equilibrium with veto Figure 5: Information transmitted and bills passed (example ) The utility implications of the presidential veto in this case are summarized by the following corollaries. Corollary 3 If the committee and the president have like biases, with the committee more biased than the president, then the president s utility will be at least as high in the legislative equilibrium with veto as in the legislative equilibrium without veto. Corollary 3 follows immediately from Theorem : if the president s veto power has any effect, it increases the informativeness of the equilibrium; even if the legislature chose its preferred bills given this extra information, the president would be better off. Further, in some intervals the threat of presidential veto may constrain the legislature to choose bills that are closer to the president s ideal, resulting in an additional increase in his utility. 7

Corollary 4 If the committee and the president have like biases, with the committee more biased than the president, then the legislature s utility may be higher, lower or the same in the legislative equilibrium with veto as in the legislative equilibrium without veto. Corollary 4 is proved by comparing the legislature s utility values with and without the veto. Intuitively, the presidential veto will reduce its informational losses at the expense of increased distributional losses, with an ambiguous effect overall. Table shows the informational and distributional losses for the legislature in example, with and without the veto, showing that the legislature is better off with the veto in place. With a status quo of b =, on the other hand, the president s veto power would have no effect, and the legislature would be exactly as well off in the legislative equilibrium with veto as without veto. no veto veto, b = 3 informational.59.45 distributional.. overall.59.45 Table : Legislature s utility losses in different equilibria Finally, to show that the veto can harm the legislature, consider an example with x c = 3,x p = 4, and b = 3 4. No information can be transmitted (with or without the veto), because the committee is so biased. In the legislative equilibrium without veto, the legislature chooses bill b = ; in the legislative equilibrium with veto, on the other hand, any bill below 3 4 will be vetoed by the president: thus the status quo remains in place. Without the veto, the legislature s loss is.833, while with the veto its loss is.458. 3.4.3 Committee and President have like biases, with the president more biased (x p >x c > ) The final case we consider is when the committee and the president are biased in the same direction, but the president is more biased than the committee. In this case the effect on information transmission is ambiguous. A president with similar bias to the committee can cause the legislature to pass bills closer to the committee s own ideal choice, increasing the amount of information in equilibrium; but if the president is much more biased than the committee, the legislature may be compelled to pass bills even further from its favorite than the committee would like, potentially reducing the amount of information transmitted. We state this result formally, and then prove it by means of an example. Theorem 3 If the committee and the president have like biases, with the president more biased than the committee, then the legislative equilibrium with veto may be more, less, or just as informative then the legislative equilibrium without veto. Distributional losses are.3774, or. to four decimal places. 8

Example 3. Suppose the committee s bias is x c = 5 and the status quo b = 3. Legislative equilibrium without veto. The legislative equilibrium without veto is characterized by the intervals, 5, 5, 5 6, and 6 5,. The informativeness of this equilibrium, var [x] =.. We now prove the theorem by holding constant the committee s bias and the status quo and introducing the presidential veto, with two different levels of presidential bias. President s bias x p = 5. In this case, the legislative equilibrium with veto is more informative than the legislative equilibrium without veto. The legislative equilibrium with veto is characterized by the following intervals,, 6 45, 6 45, 3 45, and 3 45,. It is interesting to delve into the mechanics of this equilibrium. In the second interval, the legislature would like to choose b = 47 9. However, the president s ideal policy is 47 9 + 5 = 65 9, and thus he would veto this bill. There is nothing the legislature can do better than to choose b = 47 9 instead, knowing that this will be vetoed and the status quo will remain in place. The presidential veto does not constrain the legislature in the first and third intervals, where it chooses b = 8 45 and b 3 = 38 45 respectively. It remains to check that the committee s boundary types are indifferent between the bills adopted in equilibrium. The boundary type θ = 6 6 45 has an preferred bill of 45 + 5 = 9 45, which is equal to 8 45 + 3 = 9 45, the midpoint of the resulting bills in the first and second intervals. Similarly, the boundary type θ = 3 45 has an preferred bill of 3 45 + 5 = 34 45, which is equal to 3 + 38 45 = 34 45,the midpoint of the resulting bills in the second and third intervals. The informativeness of this equilibrium is var [x] =.93, which is more informative than without the veto. President s bias x p = 3. Next, consider the same parameters except that x p = 3 (i.e. the president is very biased). In this case, the legislative equilibrium with veto is characterized by the following intervals:, 3 45, and 3 45,, bills b and b passed in the first and second intervals respectively. The three-step equilibrium under the legislative equilibrium without veto becomes a two-step equilibrium since the president will veto any bill smaller than the status quo. Specifically, he would veto the first two bills, b = 3 and b = 7 3, chosen in the legislative equilibrium without veto. The informativeness of this equilibrium is var [x] =.5, which is less informative than without the veto. Corollaries 5 and 6 point out the possible effects of the presidential veto on the utilities of the legislature and the president himself. In both cases, the effects are ambiguous. We prove these results by computing utility losses in equilibria with different values of x p (tables 3 and 4). In each case, x c = 5 and b = 3. Corollary 5 If the committee and the president have like biases, with the president more biased than the Note also that for the parameter values in this example, the original three-step equilibrium is still an equilibrium but it is less informative than the legislative equilibrium with veto constructed above; and the partition, 5, 5, 7 5, 7 5, forms another equilibrium. The result is interesting also from a theoretical perspective. Recall that Crawford and Sobel [9] prove that there is exactly one partition equilibrium with n steps. In the case where the president is more biased than the committee, this result no longer holds. As shown in our example, there may be two different three-step equilibria (with one being more informative than the other). See [6] for a more detailed discussion of this issue. 9