[Work
in progress; please do not quote without the written consent of the authors]
In
Search of The Uncovered Set:
A New Technique for Estimating the Uncovered Set in
Real-world Legislatures,
With Application to Characterizing the Impact of
Party Organizations in the
Contemporary U.S. Congress©
William T. Bianco
Dept. of Political Science
Penn State University
Ivan Jeliazkov
Dept. of Economics
Washingon University in St. Louis
Itai Sened
Dept. of Political Science
Washington University in St. Louis
Abstract
_____________________________________________________________________
© Prepared for the William H.
Riker Conference at Washington University in St. Louis, December 2001.
1.
Introduction
In a nutshell, our aim here is to fill an important gap in the literature on voting games and their application to real-world legislatures. Scholars who use these games to make sense of real-world legislative politics rely on the uncovered set as a solution concept to predict the set of feasible outcomes – enacted bills, rules, etc. – given the preferences of elected legislators. In other analyses, the concept of the uncovered set (and the expectation that the agenda-setting and voting strategies used by rational voters will converge on this space) is used to justify the power of legislative leaders, to explain stability in legislative outcomes, and to demonstrate a relatively small role for strategic behavior in a legislative context.
The problem is, no one knows what the uncovered set looks like. While the uncovered set is easy to define and can be located within a subset of the space containing proposals and preferences, we lack a general result or even useful examples that characterize the size and shape of the uncovered set. Some oversimplified analyses notwithstanding, no one has ever determined what the uncovered set looks like for a real-world situation, such as specific sessions of the U. S. House of Representatives or any other legislative body for that matter. Without these results, we simply do not know whether our intuitions about the uncovered set or the dynamics of actual legislative proceedings are true or false.
In this paper, we develop and implement a brute-force algorithm for determining the size and shape of the uncovered set for a typical real-world legislative, the contemporary U. S. Congress. (A later version of this paper will show how the size and shape of the uncovered set varies given changes in the variance and bias of legislators’ ideal points, as well as with the number of points.) We use NOMINATE scores as estimates of legislators’ preferences, yielding uncovered sets in a two-dimensional space. Our analysis shows that the uncovered set is easily simulated for such examples. Thus far, the principle surprise is the size of the set -- somewhat larger that intuition would suggest -- and its shape -- roughly egg-shaped, with the long axis oriented towards the median ideal points of the two parties in Congress.
The second part of this paper uses these findings to address a central question in contemporary legislative studies: the impact of party organizations in the legislative process. Our results suggest that within the confines of the uncovered set, which in turn defines the limits of majority-driven action in the legislative context, the majority party has substantial room to alter both the legislative agenda and the content of legislative proposals. However, our findings also show that some of the positive findings about the impact of party in House proceedings during the last generation are in fact spurious, the result of changes in the size and shape of the uncovered set during this period. Put another way, our analysis provides a way to distinguish between changes in outcomes that are the product of party-based agenda-setting, and those that are driven by changes in the distribution of legislators’ preferences caused by retirements and defeats
2.
Background: The Uncovered Set
Over the last generation, a central preoccupation in formal models of committees (legislatures) and elections has been to develop institution-free solution concepts – that is, to predict what kind of outcome will emerge given voters’ (committee members, legislators) preferences and no agenda limitations. A series of seminal theoretical results arrived at in the 1970’s led the scientific community to accept that no such equilibria exist in multi-dimensional setting (McKelvey, 1976; Schofield, 1978; McKelvey, 1979; McKelvey and Schofield, 1987), suggesting that outcomes in real-world politics are highly sensitive to factors that shape agendas, methods of voting, and the set of participants (Shepsle, 1979). . This literature is exemplified by the so called Chaos Theorem (McKelvey, 1976; Schofield, 1978; McKelvey, 1979; McKelvey and Schofield, 1987) and the claim associated with it that majority based decision making procedures, unchecked by agenda setting or other institutional constraints, can lead almost any committee or legislative body to prefer any outcome in the policy space to any other outcome in this space.
Further work suggested that these predictions of inherent chaos in voting situations were overdrawn. Working independently, a number of scholars showed that if voters (legislators or citizens) are far-sighted enough to consider the ultimate consequences of their behavior (rather than choosing myopically between alternatives as they are presented), outcomes of social choice situations will cluster in the uncovered set.[1] This set was shown to be a relatively small subset centrally located in the policy space of voter ideal points and to collapse to the core in the rare cases in which a core exists in such social choice environments (McKelvey, 1986; for a broader review, see Feld, Grofman, and Miller, 1989). These results have promoted the uncovered set to become, as a solution concept, the basis of both numerous explanations for observed stability in real-world legislatures and a central tool in analyzing abstract games used to develop predictions and expectations for real-world behavior (e.g., Shepsle, and Weingast 1984, 1994).
Most importantly, in the study of real-world legislatures, the uncovered set was used to support the conclusion that the range of possible outcomes in a legislative bodies is likely to be restricted to a relatively small set located at the center of legislators’ ideal points in the policy space (Shepsle and Weingast, 1984, 1994; Ordeshook and Schwartz, 1987). In substantive terms, this conclusion answers the question “why so much stability,” – why legislative proceedings do not reflect the chaos predicted by previous abstract models (Cox 1990; Erikson and Romero 1990; Krehbiel and Rivers 1990). Other analyses used the uncovered set to explain why we observe so little strategic maneuvering in floor proceedings (e.g., saving and killer amendments): such strategies are intended to yield relatively extreme outcomes that, given the equilibrium logic that underlies the uncovered set, would never be chosen by rational, far-sighted actors (Bailey and Brady 1998). Finally, the uncovered set has also been used as a rationale for the power of legislative leaders, parties and committees – the assumption being that they are empowered by their caucuses or the structures of their parliaments to use agenda-setting, lobbying powers and coalition bargaining to implement outcomes within the uncovered set (Aldrich 1994; Rohde 1994; Sened 1996; Snyder 1992).
- The Uncovered Set: Definition and Known
Properties
Let X be the set of all possible outcomes and let x,y,zÎX be arbitrary elements of this set. Then we can define the uncovered set as follows:[2]
Definition 1: A point xÎX is covered if there exists a point yÎX that beats x and any point zÎX that beats yÎX beats xÎX as well.
Definition 2: The uncovered set is the set of points
not covered.
The attractiveness of the uncovered set as a solution concept relies on the following set relations (McKelvey, 1986; Ordeshook 1986: 184-5): let W(x) be the set of points that defeat x; I(x) be the set of points that tie x; and D(x) the set of points that x defeats. Similarly let W(y) be the set of points that defeat y; I(y) be the set of points that tie y; and D(y) the set of points that y defeats. Then if y covers x then the following set relations hold:
(1) I(y)
Ì
W(x) È I(x)
(2)
D(x) Ì D(y)
So, if y covers x, y dominates x as an outcome of the voting game because y defeats x and any outcome that ties y defeats or ties x and any outcome that defeats y also defeats x. Therefore, strategic agents should eliminate all covered points because they are ‘strategically’ dominated. It follows that in legislative voting games covered point should be eliminated and only the uncovered set will survive this strategic elimination process.
This simple
algorithm suggests that in some analytical sense the feasible set that
may be implemented by a legislative body is expected to be restricted to the uncovered
set.
With all its analytical appeal, the uncovered set has defied, so far, all the effort at general characterization. All we know about the uncovered set is that it is a centrally located compact set that collapses to the core if a core exists. This led theorists to conclude that majority rule does not lead to chaos but to a centrally located feasible set (Ordeshook, 1986: 187). This led theorist to try and provide more precise boundaries of the uncovered set. Unfortunately, all that is know in this respect is that if indifference curves are concentric circles, the uncovered set is contained within a circle that has a radius of 4r where r is the radius of the so called yolk: the smallest circle that intersect all median lines of ideal points of the voting members of the committee or legislative body (Ordeshook, 1986: 187) as shown in Figure 1.
*** Figure One Here ***
4.
The Problem: What Does the Uncovered Set Look Like?
Our paper begins with two observations about the literature centered on the uncovered set. First, for all of the attention given to the uncovered set, there have been few attempts to characterize the relationship between a set of ideal points of committee or legislative bodies and the size and approximate shape of the associated uncovered set (Miller, personal communication). One specific set of results establishes that in a two-dimensional space the uncovered set lies more-or-less in the center the distribution of legislators’ ideal points (McKelvey, 1986). Beyond this result, we know that the size of the uncovered set tends to get smaller as the number of legislators increases. This and a series of examples, usually drawn with very few committee members (one of the most commonly reproduce in the literature can be found in Ordeshook, 1986: 186, Figure 4.21) led some to believe that the uncovered set ‘shrinks’ rapidly in large size legislative bodies to a very small set, the shape and exact location of which depend on the distribution of ideal points in ways that, to this day, are unknown (Grofman, Feld, and Miller, 1989). Our computations of the uncovered set of several U.S. Houses of representative demonstrate that the uncovered set tend to be relatively large and less sensitive to the exact distribution of the ideal points of the members of the House.
The second problem associated with the use of the uncovered set as a solution concept – a predictor of outcomes – is that no algorithm exists to actually specify its shape in any actual social choice environment such as the U. S. House or any parliamentary system. The problem is not a lack of good data on legislators’ preferences: NOMINATE scores are widely-used as a summary indicator, and are available for the entire history of the Congress (Poole and Rosenthal, 2000), and can be calculated for other legislatures using programs that are in the public domain (e.g. Ofek, Quinn and Sened 1998; Quinn, Martin and Whitford, 1999; Schofiled and Sened, 2002). Rather, the problem is that no one has used these ideal points to calculate an uncovered set for a given legislative session or sessions. The reason is not clear. In any case, without such characterization, it is impossible to tell whether our expectations about legislative processes, based on the theoretical concept and game theoretic derivations of the uncovered set have any empirical relevance in studying legislative behavior.
In sum, the literature on legislative proceedings relies on an abstract solution concept that no one understands – understands in the sense of knowing how the concept would apply to the actual study of legislatures. Our project aims at filling this important gap. We have devised an algorithm that enables us to calculate, via brute-force simulation, what the uncovered set looks like given any set of legislators’ ideal points. Such an analysis would have been prohibitive given the limits of computing power even a couple of years ago, but our calculations show that the advent of Pentium 4 desktops has overcome this technical constraint as it provides us with sufficient computation speed and capacity to calculate uncovered sets for legislatures as large as the contemporary U.S. House of Representatives and the U.S. Senate. That is our task here.
5. Applying
the Technique: The Party in the Legislature
As noted later, our technique for estimating uncovered sets has many potential applications in the study of legislative proceedings and elections, both in the United States and elsewhere. To illustrate, in this paper, our applications focus on assessing the power and influence of the majority party in the contemporary U. S. House.
In a series of works, Aldrich and Rohde, working separately (Rohde 1991, Aldrich 1995) and together (1998, 1999) present evidence for a theory of conditional party government: the idea that homogenous majority party caucuses can and act to move policy outcomes away from the floor median towards the preferences held by the median legislator in the party caucus. The majority party’s power stems from its control of the agenda, rules of debate, and congressional institutions such as the committee system. When there is disagreement within the majority party over the desirability of different outcomes, these powers are not deployed. But when party members can agree on what is to be done, they empower their leaders to translate this consensus into legislative proposals and policy outcomes. Along the same lines, Cox and McCubbins argue that, "the majority party acts as a structuring coalition, stacking the deck in its own favor – both on the floor and in committee – to create a kind of 'legislative cartel' that dominates the legislative agenda" (1993, 270). In both cases, these works suggest that caucus majorities and the party leaders they empower are often the source of legislative strategies and agendas.
These authors also argue that these changes in the importance of the majority party are the product of a generation-long electoral realignment in American national politics. Simply put, as Southern Democrats at the mass and elite level gradually became Republicans, the Democratic and Republican Caucuses in the House became more homogenous internally and more distinct from each other (Rohde 1991). The result is a legislature where the members of each caucus are increasingly likely to agree amongst themselves about desirable courses of legislative action – and to disagree with the consensus in the other caucus. The result, argue these authors, is an increasingly partisan Congress, where party leaders attempt to shape the agenda in line with the central tendency in their caucuses, and where support and opposition for a proposal will typically break along partisan lines. Although this conception of the contemporary Congress does not posit that the party caucuses determine everything, it certainly contradicts Mayhew’s (1974, 27) generation-old claim that, “…no theoretical treatment of the United States Congress that posits parties as analytic units will go very far.”
The Aldrich-Rohde-Cox-McCubbins description of legislative parties is by no means a consensus view.[3] Another group, typified by Schickler (2000), King (1997), Gilligan and Krehbiel (1987a, 1987b, 1990), and Krehbiel (1993, 1995, 1997a, 1997b, 1998, 1999, 2000) argues that legislative structures and outcomes over the last generation are best explained in terms of floor majorities, with political parties having no role save as a mechanism for the exercise of majority power.[4] In this view, proposals and rules might originate in the majority party, but their content reflects the need to satisfy the entire legislature (i.e., the floor median) rather than the majority caucus (i.e. the caucus median). In general, this debate has focused on the “post-reform House” – the period following the institutional changes of the early 1970’s – however scholars on both sides of the debate have extended their arguments to earlier periods (e.g., Cox and McCubbins 1993 pp-pp, Schinkler 2000, 269-283).
The debate between these two conceptions of party in the legislatures has centered on a variety of data and estimation techniques, including comparisons of preferences within each caucus, voting behavior of legislators on amendments and final passage, committee assignments, composition, and outputs, and even the communications that the members of each caucus have with their constituents. Despite all this evidence, we believe that a calculation of House uncovered sets provides unique and important insights into this debate – and a modified picture of the party influence in the contemporary House.
The utility of the uncovered set in addressing these questions is born of the fact that the uncovered set identifies the range of feasible outcomes in the legislature. Regardless of whether outcomes are shaped by party deliberations or a free-for-all on the floor of the legislature, the expectation is that rational legislators will ultimately arrive at some outcome within the uncovered set. Thus, the size and shape of the uncovered set establish limits on what the majority caucus can do; that is, what outcomes it can hope to achieve. Put another way, once we know what the uncovered set looks like in a particular legislature, we can tell whether there is a lot of room for the majority caucus to be influential, or whether the distribution of preferences leaves little room for party action.
For example, a small uncovered set provides little room for direct party influence on policy outcomes. Given a small uncovered set, the majority caucus may try to translate the caucus consensus into policy outcomes, but unless this consensus is included as one of the small number of outcomes in the uncovered set, no amount of manipulation or arm-twisting will make it enactable. Put another way, under these conditions, outcomes are essentially driven by the policy preference of legislators on the floor. The only option for the majority party lies in its control of the agenda: it can prevent some proposals from coming to the floor for a vote, or advancing other proposals that, after floor consideration, will move outcomes closer to the preferences of caucus members.[5]
Conversely, a large uncovered set is more likely to be associated with party influence. Under these conditions, members of the majority party have more leeway in deciding what to do – as long as they choose something within the uncovered set, they can devise a legislative strategy (i.e., a special rule) that will receive majority support and lead to the enactment of their preferred proposal. Put another way, a large uncovered set enables the majority party to shape the content of policy proposals as well as determine the policy agenda within the legislature.
Finally, examination of the uncovered set in the contemporary House also allows us to address a fundamental debate in the literature on legislative parties: whether the alleged influence of the majority party is actually driven by changes in the distribution of preferences in the legislature. For example, suppose Democrats are in the majority and we observe outcomes moving in a liberal direction over time. One explanation is that the Democratic Caucus is using its power over House floor proceeding to move policies in this direction. However, another reasonable possibility is that the caucus is ultimately powerless, with the direction of policy change being driven by the fact that constituents are electing more liberal legislators (or fewer conservative legislators) as time goes by, thereby shifting the uncovered set and feasible outcomes in a liberal direction. Such arguments are difficult to resolve given data on vote decisions or legislator preferences, as it is hard to determine how these individual-level data translate into outcomes. With data on the uncovered set, however, we can measure the feasible set directly, and determine whether changes in the distribution of preferences have indeed shifted the range of enactable outcomes.
6. The
Uncovered Set in the Contemporary House
This section reports the results of our analysis. The current version of the paper reports uncovered sets for the 81st (49-50), 86th (59-60), 91st (69-70), 96th (79-80), and 101st (89-90) sessions of the House. Details on the algorithm used to calculate the uncovered set for each legislative session can be obtained from the authors upon request. The Poole-Rosenthal NOMINATE scores were used as data on legislator preferences. In order to facilitate interpretations across sessions, we use the common-space scores, which report results for House members, Senators, and the President across different legislative sessions using a common metric. These scores vary from –1 to 1 in each dimension; in our figures, the horizontal dimension captures the classic left-right liberal-conservative economic distinction (positive scores = more conservative), while the vertical dimension captures positions on civil rights (positive scores = more conservative, e.g., Southern Democrats).
To give a sense of what our results look like, Figure 2 shows legislators’ ideal points and the uncovered set for the 81st House. The uncovered set is the gray blotch in the middle of the figure; the white circle within the uncovered set is the median legislator. The two dimensions capture the entire –1 to 1 range of the feasible space.
*** Figure 2 Here ***
Three facts are immediately apparent from figure two. For one thing, the uncovered set is not smoothly-shaped; rather, the perimeter in irregular, reflecting the distribution of ideal point. The uncovered set is also not located in the center of the distribution of points; rather, it appears to be skewed towards the ideal points of majority Democrats. And finally, while the uncovered set does not occupy anything like the entire space, it contains a substantial proportion of feasible outcomes, including the ideal point of the median legislator. More specifically, the height and width of the uncovered set are roughly the same as the standard deviations of ideal points on each dimension (.31 on X, .41 on Y).
A similar picture is revealed in Figure 3, showing the uncovered set for the 96th House.
*** Figure Three here ***
Here the distribution of ideal points is somewhat different, reflecting the demise of Southern Democrats, whose preferences typically placed them at the top of the vertical dimension and the middle of the horizontal dimension, and their replacement by Republicans, typically located at the right-hand, bottom of the figure. The impact of these changes is to shrink the size of the uncovered set and move it in a south-west direction. Even so, the uncovered set is still ‘irregular,’ still skewed away from the center, and still occupying a nontrivial portion of the space.
Insights about changes in the size and shape of the uncovered set over time, as well as conclusions about the impact of legislative parties on house proceedings over the last generation, are contained in Figure 4, which shows uncovered sets for all of the congresses in our analysis (note: 106th excluded from this draft).
*** Figure 4 Here ***
The individual figures omit legislators’ ideal points, and cut off the outer halves of each ideological dimension (i.e., the range is from -.5 to .5). The white circle in each uncovered set is the ideal point of the median legislator.
These figures provide strong but not compelling support for theories that posit a strong role for the majority party in the contemporary House. Most importantly, the uncovered sets are consistently large. Thus, there is considerable room for partisan maneuvers – the majority caucus has a wide range of outcomes from which to choose. However, Figure 4 also shows that the size and location of the uncovered set has moved over time in a general south-west direction. Thus, insofar as policy outcomes in the House mirror this trend, they could create the illusion of party-centered action, when in fact they might well be the product of a slow evolution in congressional preferences.
7.
Future Research
This project is at a very early stage. Thus far, our focus has been on establishing the feasibility of our technique and presenting a few initial results. Our aim is to progress along two fronts: to show how the size and shape of the uncovered set varies with the distribution of legislators’ ideal points, and to use our findings to address additional questions about the operation of real-world legislatures.
Abstract Results. With regard to the first research agenda, our aim is to develop a general characterization of the uncovered set. That is, we will show, using multiple simulations based on random draws of ideal points, how the size of the uncovered set shrinks as the number of legislators increases. We will also show how the uncovered set varies with changes in the distribution of ideal points. What happens, for example, when most legislators hold relatively extreme ideal points vs. a situation where most legislators are moderates? We will also explore cases where the distribution of ideal points is bimodal, corresponding (roughly) to the contemporary U.S. House of Representatives.
These simulations are intended to put meat on the bones of the uncovered set – to sharpen scholars’ intuitions about how this concept applies to real-world situations. Up to now, the widespread cites to the uncovered set have not been matched with a clear understanding of what this concept tells us about real-world legislatures. That is, insofar as the uncovered set defines the set of possible outcomes in a legislature, what kinds of outcomes can we expect in a large – or small legislature? To what extent does it matter that the distribution of ideal points is bimodal or polarized? Does simple variance matter? Finally, we wish to use our technique to clarify the relationship between the uncovered set and related concepts such as the heart promoted by Schofield (1996), that is probably more appropriate and appealing in the study of parliamentary systems with multiple parties Austen-Smith, 1996 and Schofield and Sened, 2002).
Legislative
Politics. Our technique for constructing uncovered sets given the
preferences of real-world legislators will enable us to address a variety of
questions in legislative studies. In
essence, given a set of legislatures, the uncovered set is a prediction
about what sort of outcomes are likely when the group votes using majority
rule. Therefore, by calculating the uncovered
set for different subgroups of legislators, we can analyze the nature of
conflict within a legislature and how institutions and outcomes are shaped by
this conflict.
Our initial work, presented here, shows
that our characterization of real-world uncovered sets provides deep
insights into the evolution and influence of legislative parties n the
contemporary Congress. Many other
applications exist. For example, our
techniques can address questions of the nature of the congressional committee
system – the extent to which committees are dominated by “outliers” or members
whose preferences are extreme relative to their colleagues (e.g. Cox and
McCubbins 1993, Diermeier 1994, Krehbiel 1991, Owens 1997). Essentially all research on this question is
based on the analysis of roll call votes, a problematic technique given that
the proposals being voted on are endogenous to expectations about committee and
floor preferences. Our analysis, based
on a characterization of the committee and floor uncovered sets, can
approach this question using a more fundamental and reliable source of data on committee
and floor preferences – a source that incorporates the essential fact of
legislative action, the need to build majority support on the committee and the
floor for policy proposals.
A third use for our simulation based characterization of the uncovered set in the U.S. House and U.S. Senate is to track changes that occur over-time in the size and shape of this set as a measure of the potential for policy shifts and the impact of elections on the policy process. In terms of government policy, elections are a shock that elects some number of new representatives and thereby changes the range of enactable government policies. One fundamental question about elections, then, is how large a shift in policy can be expected given a set of election returns? Put another way, to what extent is legislative turnover – or changes in legislative majorities – correlated with shifts in the size and shape of the chamber’s uncovered set?
Most analyses of elections assume that one sort of shift invariably yields the other – that high turnover in any given election portend large shifts in government policy. Our analysis will provide new measures of the impact of elections on the policy process, and allow us to reevaluate the conventional wisdom concerning elections over the last several generations. Were, for example, elections such as 1964, 1974, 1980, and 1994 as revolutionary as the conventional wisdom suggests? Or did other elections with smaller levels of turnover produce larger changes in the feasible set? (Preliminary work will focus on the post-World War II Congresses, but preference data exists back to the Founding, and we intend to ultimately analyze it.)
We have only begun to consider the range of questions that our project can address. The techniques we developed can address other important questions in American politics such as the relative power of the House and Senate in cross-chamber bargains, and the ability of the President to implement his or her preferences given the requirement of legislative action.
Comparative Politics. A central
characteristic of parliamentary systems is the centrality of coalition
formation as the focal point of parliamentary politics. This fact has not escaped modern students of
politics who spent much time and effort to study the process and implications
of coalition formation in parliamentary systems (Riker, 1962; Browne and
Franklin, 1973; Budge and Laver, 1985; Austen-Smith and Banks, 1988; Laver and
Schofield, 1990, Laver and Shepsle, 1990, 1996; Strom, 1990; Schofield, 1995;
Sened, 1996). In recent years,
attention has focused on the trade-off between office-related and
policy-related payoffs that serve as the two main currencies in coalition
bargaining processes (Budge and Laver, 1985; Laver and Schofield, 1990; Sened,
1996, Schofield and Sened, 2002). While
office related perquisites are relatively easy to assess by counting portfolios
(Browne and Franklin, 1973) or different measures of budget allocated to
departments controlled by different ministers (Nachmias and Sened, 1999), the
measures of policy-related payoffs are harder to establish (Laver and Shepsle,
1996).
There are actually two difficulties associated with
measures for policy-related payoffs.
First, even if we can establish some estimates of the ideological
distances from implemented policy positions and the ideal policy positions of
the parties (Ofek, Quinn and Sened, 1998), the value that each party attaches
to such distances is subjective and impossible to measure or estimate. The second problem is to predict the set of
feasible outcomes in parliamentary, multiparty systems. This is a similar task to the one we
emphasized in our discussion of the U.S. Congress. Multiparty parliamentary politics is highly volatile, due to the
number of players involved and the tricky job of establishing and then
maintaining long-term coalition governments. If a core exists in the game then
a prediction can be made that the core of the game will be implemented. A core may exist if one is willing to assume
that portfolio holders in the cabinet have full and perfect control on policies
in their jurisdictions and will implement their ideal point on this
dimension. If this were the case,
parties would compare all possible coalitions by comparing the points in space that
the ministerial portfolio distribution implies. A coalition would form by parties that prefer a particular point
in space implied by a particular composition of portfolio allocations by a
particular coalition to all other possible permutations. The policy that such a coalition would
implement is the intersection of all uni-dimensional coordinates determined by
the ideal points of the parties who control the different ministries with
jurisdiction on the respective dimension of the policy space (Laver and
Shepsle, 1990, 1996).
An alternative way to model coalition formation in multiparty parliamentary systems is to take parliaments as the deciding body more seriously. But if we look to the parliament to make majority rule decisions on policy implementation we encounter the same problem as in the U.S. Congress: the core of the parliament may often be empty. Schofield (1995) has shown that strong central parties often impose their will on the rest of parliament by their central position and weight of seats. Given some distribution conditions on the weights and positions of other parties such dominant parties may capture what Schofield (1986) calls the structurally stable core of parliament. In simple terms, such central, dominant parties establish a critical mass of their own members around their ideal points. Other parties, presumably distributed all around the dominant party are unable to promote any alternative policy position that would be preferred by a majority to the ideal point of the strongest party. The Christian Democrats and the parties that colluded with them to form most of the coalition governments in Italy between 1949-1987 are one notable example to this phenomenon (Mershon, 1996), the rule of the Labor party in Israel between 1948-1977 and again between 1992-5 is another (Sened, 1996).
But what happens in the absence of such a core parties, as has been the case both in Italy and in Israel after 1987 and 1977 respectively? In such cases the uncover set or the heart are once again an attractive solution concept to help determine the set of feasible outcomes of the parliamentary social choice weighted voting game (Schofield 1996; Sened, 1996; Schofield and Sened, 2002). The advantage of using the uncovered set or the heart as solution concepts in such environment is two fold. First, it by passes the first problem of the subjective values of ideological distances between the expected policy positions that may be implemented by a coalition and the ideal policy positions of different parties, because it relies on a pair-wise comparison of two points at each determination of which point may win a majority rule contest. Second, it overcomes the second problem of predicting a feasible set of outcomes in parliament in the absence of a clear structurally stable core or a ‘Condorcet winner.’[6]
The empirical relevance and additional complexities of new models of coalition formation that incorporate both policy-related and office related payoffs in modeling coalition formation processes (Austen-Smith and Banks, 1988, Laver and Schofield 1990, Sened, 1996; Schofield and Sened, 2002) can be tested only on the basis of reliable prediction of the feasible sets of outcomes in multiparty parliamentary systems. When the core is not empty the obvious prediction of the policy position that any coalition may implement is the core point. When the core of the parliamentary system is empty, only two cooperative game theoretic concepts have been promoted with some success as alternative solution concepts that may help determine the feasible set: the uncovered set (Miller, 1981) and the heart (Schofield, 1996). The exact nature of the way the two concepts are related has never been established, nor was any kind of clear advantage of using one over the other, as a general solution concept to use in these environments (Austen-Smith, 1996). Both are known to be centrally located and to collapse to the core when a core exists (McKelvey, 1986; Schofield, 1996; Austen-Smith, 1996). Our tool-box can actually generate both for any multiparty parliamentary system based on the seat distribution among parties and estimates of ideal points of parties in parliament.
By calculating the
uncovered set and the heart for multiparty parliaments we hope to
accomplish three interrelated objectives.
First, we can establish a better understanding of the relation between
the two competing solution concepts.
Second we can provide clear predictions of policy implementation in
multiparty parliamentary systems.
Finally, we can enhance the study of such systems as well as the
empirical relevance of so many theoretical efforts that have so far stopped
short of empirical tests for lack of clear empirical estimates of the feasible
set of policy outcomes in multiparty parliamentary systems when the core of the
parliamentary game is empty.
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Figure Four. Uncovered Sets, 86th
–101st House
