1. Introduction

The unidimensional model of party systems which locates political parties at different points or in a given order on a left-right scale seems today as widely rejected as it was formerly accepted, but nevertheless it has shown a remarkable capacity for survival as a parsimonious descriptive and explanatory device.

The traditional point of view may be represented by R. M. Maclver's bold assertion that "political parties, apart from aberrations due to special circumstances, fall regularly along a single alignment, whether the two-party or the multiple-party system prevails".1 Taken at f ace-value that statement was probably never true, but essentially the same single-dimensional model was later raised to theoretical prominence by Anthony Downs² whose spatial model of party competition was in turn severely attacked, especially by D. E. Stokes' well-founded criticism.3 Stokes' critique is often quoted with approval,4 but the fact remains that single-dimensional scales are still frequently used in the analysis of party systems without persuasive empirical justification. For instance, authors often tend a priori to assume the existence of a left-right political spectrum within which parties are naturally placed,5 or give a few rather unsatisfactory reasons to support a proposed location of parties along the continuum.6 Of course, a number of authors are indeed aware of the problems involved,⁷ but only occasionally is empirical evidence invoked to support the common assumption of a continuous left-right scale.⁸

In Denmark - as in most European countries — the left-right conception is a significant characteristic of popular political language, and, as might be expected, it has also permeated scientific vocabularies. But even if Danish political science literature is sparse, agreement does not prevail concerning the scientific utility of left, center, right and their related concepts. After a short review of the ideologies and policies of Danish parties, Poul Meyer concludes⁹ that one cannot use the concepts of right and left or socialist and liberal because they have no unequivocal meaning. According to his view, classifications of Danish parties can only be made by taking account of several factors not necessarily producing the same spacing of parties.10

This last point is conceded by Erik Rusmussenll in a discussion of the unidimensional

model: "If one wishes to use the right-left continuum as an objective and absolute scale ... one has to do so for each individual politically significant subjectmatter category and may use it generally only on occasions where a high degree of coincidence of specific continua occurs, as can be said to be true with respect to the four 'old parties' during most of the inter-war period". Rasmussen comments further, however, that the weaknesses of the left-right continuum must not obscure the fact that "parties often perceive themselves and are perceived by voters as differently placed in relations to each other, and consequently the possibilities of majority formation within the system are delimited by those perceptions. In other words, the continuum could also be used by means of the behavior of parties as a subjective and relative scale. Thereby it becomes a scientifically usable device in the sense that the designations refer to relative distances observed by behavior."

While the two Danish authors mentioned above work exclusively with unidimensional concepts, they nevertheless differ as regards the complexity of their arguments. While the former is stressing the point that the external observer, e.g. the political scientist, cannot indicate methods by which a single, undisputed, and unequivocal left-right ranking of Danish parties could be established, the latter tries to save the traditional position by means of some kind of reasoning which unfortunately opens up a Pandora's box of tricky problems.

Firstly, Erik Rasmussen's argument is based upon a reification of the party. This may be justifiable in some contexts, particularly when we are dealing with long established, cohesive, and institutionalized parties. Thus, parties can exist in the minds of their followers and antagonists as 'abstract entities' apart from their members and leaders,¹² and it then becomes a relevant research problem to investigate what kind of predispositions, motives, etc. individuals are inclined to ascribe to these entities, be it their 'own' party or other parties. So far, only a little research is reported in this field; what has been done concentrates on general descriptions of the party images among the electorate,¹³ and only a few serious discussions of the concept of psychological distances among parties have been reported thus far.l4

Erik Rasmussen's argument implies, however, that the parties as political actors, i.e. especially the parliamentary leaders of Danish parties, have formed images of the parties in the political system, and this position is a bit more problematic. Apart from mentioning in passing the difficulties in indicating methods by which one could perform valid measurements at this level, we should like to put forward the hypothesis that the tendency to reify parties decreases when we move from the electorate level to the elite level. It is plausible to suggest that the perceptions, expectations, and relations are highly personalized at the upper level of Danish politics among the few politicians who are powerful. Important decisions are made in the 'smoke-filled rooms' in Denmark as in most other countries, and the prevailing methods of cabinet formation and compromising₁₅ make it very plausible that perceptions of distances among the parties are more diffuse and less important factors influencing the behavior of party leaders.l6

This brings us to the second and most evident weakness in Erik Rasmussen's

argument. Even if party images involving psychological distances exist in the minds of voters and leaders, this finding would only lead to the question of what the relationship might be between image and behavior. The rationale for the introduction of the concept of distance is to help us explain behavior of politicians and parties. The real dilemma in the argument is that there is a serious risk that the existence of perceived party distances will be inferred by the scholar from precisely that kind of behavior he wants to explain by means of the concept. The trap of circular reasoning is almost impossible to escape under these circumstances.¹⁷

With the possible exception of a study by Hans Jørgen Nielsen,¹⁸ the left-right model has not as yet been systematically tested against the reality of Danish politics. Nielsen scrutinizes results from Danish Gallup surveys on foreign policy attitudes of the electorate broken down according to the party preference of the respondent. He tentatively concludes that a certain ordering does exist among voters of different parties in the foreign policy issue-area.

2. Approaches to the Study of Party Distances

This paper deals with a particular aspect of party distances and dimensionality of party systems. In order to make our aim clear at the outset, we shall briefly try to place the object of our analysis in its proper perspective. Generally speaking, a variety of approaches to the problem of analyzing party distances would appear possible. In Table I we have listed some of these approaches by combining different units of analysis with various sources and types of data. The unifying feature of these approaches is that all of them, in one way or another, allow for inquiring into some aspect of 'distance' and dimensionality. The scheme could easily be extended and further differentiated, and a collection of appropriate methods for a data analysis could also be added. For the present purpose, however, we need not elaborate on this point since we are primarily concerned with the following types of general questions: Is it possible by truly empirical methods to order political parties on a unidimensional scale? And furthermore, is it possible to measure the exact intervals between parties on such a scale? Or alternatively, do measures of party distances demonstrably conform to a single-dimensional scale? In principle, at least, the approaches indicated in Table I could be used to investigate the questions mentioned. And, in fact, a number of studies have either treated or touched upon some of the questions. A few examples will suffice to illustrate the richness of research possibilities and also some diversity in possible results.

Olavi Borg¹⁹ has undertaken a content-analysis of Finnish party programs from which he obtained a series of ideological variables. In order to determine the leftright 'coloring' of the variables they were correlated with the common left-right ordering of parties. (The use of that scale was supported by a survey of voters' opinions on the average image of parties.) He then proceeded with a factor

analysis of all the variables and extracted a number of distinct factors. Although the first factor, termed 'Capitalistic vs. socialistic economic system' appeared to constitute "some kind of a general factor of the value contents of party ideologies" explaining more than one third of the variance, the addition of five other factors increased the percent variance explained to more than 90. Because of this, and as not all factors had a clear ideological 'coloring', one is tempted to conclude that a unidimensional model cannot fully represent the basic structure of Finnish party ideologies.

Electoral behavior studies ordinarily contain questions on party preference orderings, policy attitudes, etc., but the results generally show, in the words of Philip Converse, "that the assumption of a single primary dimension along which both voters and parties are located turns out to cover a distressingly small part of reality".²⁰ Bo Särlvik²¹ has done an interesting study in which he uses voting change as a measure of distance and dimensions in the Swedish party system, and while his conclusions are not without reservations they demonstrate a 'most important' left-right dimension.

The authors of The Legislative System22 found to their surprise "that Democratic and Republican legislators differ quite sharply in ideological terms". In trying to account for this fact, however, they also found that ideological homogeneity within the parties was rather low, as well as being uncorrelated with indices involving party orientations. Their findings suggest that there is in general no association between ideological and party thinking.

In his study of the Canadian parliament, Allan Kornberg23 states that: "Although the left-wing and right-wing members of the legislative parties do not quite live up to the attitudes popularly ascribed to them, they do hold fairly distinct attitudes on policy issues". In view of the general problems considered in this paper, however, it is interesting to note that the 'attitudes towards extension of cultural dualism' resulted in an ordering of parties different from that obtained by questions of attitudes towards 'Welfare statism' and 'political participation and tolerance'.

Roll call studies have seldom used the total set of roll call votes to examine the
similarities and differences in legislative voting behavior. Most studies entail the

analysis of samples of roll call votes.²⁴ And while, e.g., Guttman scaling may show a common underlying attitude towards a particular area of public policy, we are not aware of studies which have found a common dimension underlying a considerable number of issue areas, not to say all possible issue areas. Of course, the very reason to distinguish between different policy areas is to study hypothesized differences in voting behavior in different policy areas. But if one wishes to test the universal single-dimensional left-right model, one must of necessity use total populations. (This is what we intend to do in this study of (anonymous) divisions, as will be explained below.)

In addition to survey studies of legislators' policy attitudes and roll call analysis, the left-right model could also be tested by asking members of legislative parties to rank-order other parties, but to the best of our knowledge no reports on this topic have so far been published.25

In legislatures where party cohesion is high it makes sense to study the aggregate party votes by use of methods that are analogous to traditional methods of roll call analysis. This approach, as we shall see in a moment, can lead to a meaningful concept of party distance, but so far this method has not been widely used.26

Finally, coalition theorists have increasingly realized the necessity of developing appropriate measures of distance between parliamentary parties to contribute in explaining cabinet coalitions formed.²⁷ Although some progress is discernible, much remains to be done.28

Thus there are ample opportunities for studying party distances, and a very interesting question is, to what extent different empirical approaches produce similar results, and to what extent a given approach produces similar or comparable results when applied to various kinds of data.

Our critique of previous Danish literature is not an attempt to refute the concept of perceived party distances. What we wish to attach importance to is that a congruence of the perceived and the observed cannot be assumed a priori, but has to be tested by means of empirical methods that do not require inferences from one level to another. Confusion is bound to arise if one fails to separate analytically distinct meanings of the term 'distance'.

The research we are going to report: here is concerned with the study of observable behavior, thus moving exclusively at one level. Our intention is to discuss the possibility of fitting the behavior of Danish legislative parties to various types of spatial models, and in particular we are trying to demonstrate that a model has to be at least two-dimensional in order to fit the kind of data we use. Why parties behave in such a way that multidimensional models are required, is another question which we desist from exploring in this context.

Apart from this primary purpose two other goals are set. We wish to observe the behavior patterns of parties over time in order to examine possible fluctuations. In popular political conversations parties are often described as 'moving' relatively. A prominent typology of party systems is in the same way based upon the existence of fluctuations, centripetal and centrifugal movements of parties.29 Thus, it is

relevant to ask what pattern of change in behavioral relations emerges when we
follow the behavior over a span of time.3o

By utilizing data from two different arenas, the final divisions in the law-making process, and the divisions which finish the debates on 'agenda motions',³¹ we are able to compare the behavior of parties in two very different situations, that of law-making and that of controlling the government. Our purpose is to see to what extent the behavioral patterns are similar or different in those two situations.

3. The Data

Two types of data are utilized in this analysis. First, we have collected a set of data relating to the legislative process proper, viz. the reported results from all final divisions on government bills in the period 1945-1968. The very few private member's bills which are voted in the Folketing have been omitted, as have of course all bills which did not reach the third and final reading. The total number of bills for which we have information, amounts to 2,802, the average annual number of passed bills thus being 128.32

For every single division we have information about the declared stand of every participating party. As party cohesion is very high, it is always possible to identify the party vote as either a vote jor the bill proposed by the government, a vote against, or as an abstaining vote.

Secondly, we have collected a set of data relating to divisions on 'agenda motions'. These motions may be put forward at almost any moment during a debate in the Folketing. If voted favorably, they often have the effect of closing the debate (depending on their wording), but if they express a lack of confidence, they may cause the resignation of the government. Most of these motions originate in debates on interpellations or in important legislative debates.

Compared with the former set of data, the latter is considerably smaller. Only 204 divisions are reported in the period 1945-1968, and only 82 of the motions were passed. These figures indicate, that this set of data differs from the first set in one important respect, namely that these motions were initiated by many different parties and ad hoc coalitions of parties. For every single division we have the same kind of information as for the legislative divisions.

This considerable amount of information has been condensed by means of an
index of distance (ID) into 16 data matrices. The procedure, in brief, runs as
follows:33

Pairwise comparisons of behavior are made for every pair of parties in every single parliamentary session. In these comparisons the tendency to heterogeneous voting is registered. Two parties vote similarly, when they take the same position in the division; they vote differently, when the first party takes one of the three possible stands, and the other party takes one of the two alternative stands. Thus, three possible types of different voting are taken into consideration, the yes-no

variant, the yes-abstain variant, and the no-abstain variant. In the next step in the procedure we have summated over governmental periods the raw values obtained through the pairwise comparisons, and this gives us 8 raw-data matrices for each of the two types of data. These matrices have finally been standardized for differences in the number of reported divisions during government periods.

The result is 2 X 8 matrices, containing a summary description in terms of dissimilarities of the voting patterns in successive postwar periods. As the number of represented parties has usually been 6, the matrix will most of the time have 6 X (6-l)/ =15 ce115.34 Thus, the kind of matrix we end up with has the form of Table 11.

Utilization of roll call or similar data always calls for a cautious evaluation of data, measuring instrument, and findings. As research data roll calls have several shortcomings, the most important being that the stand of the individual or, in our case, the party, is the result of numerous influences which we are not able to separate. An inferential interpretation of roll calls in terms of motives, purposes, etc. is most dangerous. Our index of distance measures the tendency towards heterogeneous voting and is not utilized in this paper as an indicator of other phenomena. As long as the focus of our research is the overall structure of the space, and not the underlying dimensions, we are legitimized to use the index without qualifications, but it ought to be stated that as soon as one moves beyond pure description, the problem of validity becomes an almost insurmountable barrier.³⁵

A description of the overall structure of the voting patterns requires a set of data, which encompasses all divisions of a given type. A sample, random or weighted, will not be sufficient. It has to be noted in passing, however, that we are well aware of the fact that the voting patterns differ considerably from one policy area to another. This observation opens possibilities for the creation of a more differentiated picture, but we shall deliberately avoid the temptations to proceed in this direction here and now.

The last methodological problem, which deserves some comment, is our interpretation of the abstaining votes. While we have treated the yes and no positions as an unambiguous dichotomy, we have decided to interpret the abstaining vote as a middle position. It is evident that parties themselves will sometimes interpret abstain

as a positive and sometimes as a negative vote, but as no guidelines exist for a differentiation of this type of votes, we have preferred to treat them as a kind of neutral 'in-between' behavior, or as indicating 'partial agreement'.36 Future research may take this problem into consideration, e.g. by operating with three different interpretations in order to gauge the effect of this choice on the findings.

3. Graphical Representation

Our earlier studies have revealed that the data in the matrices are highly structured and that the voting patterns have changed considerably over time. But even the closest inspection of the data-matrices cannot bring us far beyond the negative finding that the parties cannot be represented meaningfully in a unidimensional space. The relations within and between clusters of parties are far too complex and fluid over time to be caught in a verbal presentation. In order to get a more thorough understanding, it is necessary to process the data one step further.

In the last few years, a whole family of computer techniques has been dedicated to the purpose of creating spatial models, which are isomorphic to correlation matrices.37 From all kinds of coefficients of similarity within pairs of objects, the objects being variables, categories, individuals, groups, ideas, physical objects, etc., it is possible to determine a Euclidean space, in which the distances between the represented objects will reproduce a high percentage of the information in the datamatrix.

Our objects are political parties, and our index of distance produces coefficients of dissimilarity. Thus it might be appropriate to process the data by means of a technique, which is based upon the same kind of logic as the above-mentioned computer techniques.

The method is so simple that it does not even require high-school geometry. We began by plotting the two parties whose matrix value was the largest as fixpoints in a two-dimensional space. The geometrical distance between the fixpoints was made equivalent to the ID-value. If, for the moment, we call these two parties and their corresponding points P and Q, the spatial location of the remaining parties was found at the intersections of circles drawn with P and Q as centers, and with IDvalues of pairs comprising P and Q as radii. As the two sets of circles around P and Q will in most cases produce two sets of intersections, we had to choose between alternative locations of the parties.38 That solution was chosen, which would minimize the summed squared deviations of geometrical distance from matrix ID.

By this procedure a spatial representation of the matrix was obtained, in which all distances to and from P and Q are reproduced equivalent to the ID-values. We have thus deliberately decided to concentrate all errors of transformation in the remaining distances, which of necessity are among the smallest. By way of example, the spatial representation of the matrix for government bills 1960-64 in Table II started out with the plotting of F and U as fixpoints, and all errors of transformation

were, as a result of this decision, concentrated in the distances between the
coinciding A-B, C, and D.

The last step in the procedure consisted in the drawing of a system of coordinates in order to ease comparisons of the configurations. The origin was placed in point A (Social Democrats), abscissa always running through point D (Liberals). We strongly emphasize that these coordinates are drawn arbitrarily; they do not represent vectors, factors, or dimensions, but are intended only as a means of simplifying comparisons. The same end is supposed to be served by a (semi)circle in each configuration, indicating the unit of measurement. The resulting 16 diagrams are shown in Fig. 1.

Before embarking upon the analysis of the graphed configurations, one has to know something about their 'goodness of fit', i.e. how well the interpoint distances in the configuration of points match the corresponding ID-values of the matrix. Obviously, the method employed here can only yield perfect results if two-dimensionality prevails in our data (or, of course, when only three points exist). In all other cases, the configurations will distort or misrepresent the 'true' interparty distances to a greater or lesser degree.

Generally speaking, we can state that our two-dimensional graphical solutions

have the property whereby the interpoint geometrical distances reproduce the ranking of the ID-matrix values as well as ID-values without too formidable distortions. This can be seen from Table 111, which shows for each government period 1) the rank order correlation between the ranking of the original data and the ranking of the computed geometrical distances; 2) a measure of the 'degree of distortion' of the exact ID-values as defined in the table.

Although the fit between the spatial models and the matrix values was satisfying in most cases, parts of the data were nevertheless analyzed by means of an alternative method, the Guttman-Lingoes Smallest Space Analysis (G-L SSA-1), because we wanted to see to what extent two different methods would give equivalent transformations ³⁹ We specified runs for two-dimensional solutions, using data from the periods 1953-57 and 1960-64. The rationale for selecting these two periods is that the highest degree of distortion and the lowest rank-order correlation were obtained for the 1953-57 data, while the 1960-64 data produced a perfect rank ordering and only a minor degree of distortion, the two periods thus representing extremes with regard to the fit between matrix and graph.

The two methods cannot be expected to produce truly comparable spatial models. The graphical method described above aims at combining simplicity with minimization of deviations from the matrix values; the Smallest Space Analysis aims at recovering the rank ordering in the data, given a specified number of dimensions, and, in the terms of the inventors of the method, this means minimization of the 'stress'.4o

In a perfect Smallest Space solution 'stress' is zero, i.e. there exists a perfect monotone relationship between the dissimilarity values and the computed interpoint distances in the model. As indicated in Fig. 2 this perfect solution was obtained in all four cases. The simple method did produce perfect rankings for the 1960-64 data, but not for the 1953-57 data. However, our graphical interpoint distances correlated better with the original ID-values than did the distances in the Guttman space.41

All of this was not unexpected, bearing in mind that the two methods were designed to stress different aspects of the transformation. The important thing is that the overall structure of the party space looks pretty much the same, regardless of the method used. Abstracting from the arbitrary coordinates in Fig. 1, there does exist a basic structural similarity in the two sets of configurations.

On the other hand, the differences between the graphs of the 1953-57 data serve to emphasize the obvious limitations of the methods in general, and the simple method in particular. Reliable two-dimensional solutions can be expected only when the data fit a two-dimensional model. If this is not the case, both methods will tend to produce more or less arbitrary results. But while the Smallest Space Analysis can be extended to other multidimensional solutions, which may give better transformations, this is not the case with the simple method. This means that the principal heuristic value of the simple method is that it allows for a first quick inspection of the data in order to find out whether a given set of data has or has not a two-dimensional structure.

5. Findings

The most conspicuous result of the analysis is that it confirms our suspicion that a unidimensional spatial model does not fit the data. This conclusion holds true for all governmental periods since 1945 and for both types of parliamentary behavior. In some periods, such as 1945-47 and 1966-68, the party space comes relatively close to unidimensionality, but in other periods, most notably 1953-57, not even the two-dimensional model fits the data.

A comparison of the party spaces in Fig. 1 further gives rise to the conclusion that the overall tendency to heterogeneous behavior is far more pronounced in the divisions over agenda motions than in the legislative divisions proper. While unanimity or 'broad agreement' between the major parties is the rule in the latter case, most divisions in the former split the votes of the parties. This difference in magnitude of party distances tends to demonstrate that party conflict is pre-eminently to be found in the agenda-motion-type division. An important thing to note is, however, that this difference between the two behavior patterns is more a difference of degree than a substantial difference. An inspection of the spaces clearly reveals that the structure

of the spaces is fairly similar within each of the consecutive periods. This is even more noteworthy as the two types of divisions are related to differences with respect to initiating parties. While, by definition, government bills originate from parties in government, agenda motions are, in the majority of cases, put forward by opposition parties, especially by the 'new' and small ones. Furthermore, one could also argue that disagreement concerning bills in the most general sense is understated by using government bills only, since a number of private member's bills are put forward by opposition parties in every session, but hardly ever reaching the final stage in the decision-making process. If one could account for the amount of disagreement involved here (which is not possible as the vast majority of private members' bills are simply 'buried' in committees) the 'gap' between the two sets of distances would presumably shrink somewhat. Finally, one should keep in mind that the number of agenda motion divisions is relatively small, which means that a few divisions involving disagreement carry heavy weight and may thus inflate the distances in some cases.

A common feature of the two sets, regardless of time, is the difference as regards internal consistency of the voting behavior between the four 'old' parties (A, B, C, D) on one side, and the small 'new' parties on the other. The 'old' parties tend to be consistent in their behavior vis-å-vis each other in the two types of divisions. When a major party changes its position in the party space from one period to the next, this change will tend to appear on both arenas of parliamentary behavior. In contrast, there is less consistency in the behavior of the 'new' parties. While the small workers' party, be it the Communists (K) or the Socialists (F), with a few exceptions behave more like the Social Democrats than like the two 'bourgeois' parties, Liberals and Conservatives, and while the declared 'right wing' party, the Independents (U), was always closer to the 'bourgeois' parties than to the Social Democrats, the positions and the distances are nevertheless changing considerably from arena to arena, and from period to period.

The violator par excellence of the consistent pattern is, however, the Justice Party (E), which in graphical terms was circling around in the party space throughout its post-war existence. There was neither consistency from period to period, nor from arena to arena. This party has sometimes been described in Danish political debate as a 'right wing' party, and sometimes as a party in the middle of the spectrum. Sometimes the party saw itself as truly progressive. Our graphs tell in behavioral terms why it was difficult to catch the party in the running and put a label on it!

Another characteristic property of the changing party space is that it is possible to identify two clusters of 'old' parties in most of the post-war period, especially between 1953 and 1966. Conservatives and Liberals make up one cluster, Social Democrats and Radical Liberals the other. Thus, the description of the Danish party system as a 'two-bloc system'⁴² gets some support from this analysis, but the fluctuations are nevertheless so dominant a feature that a cautious use of this concept for descriptive or analytical purposes has to be recommended.

Between 1966 and 1968 a major re-orientation took place in Danish politics. In

1966 a Social Democratic minority government obtained a working majority in the Folketing through close and institutionalized collaboration with the Socialist People's party. An increasing hostility between Social Democrats and Radical Liberals was a major result of this new alliance, and in 1968 the Radical Liberals consequently interpreted a massive electoral victory as a mandate from the voters to begin governmental collaboration with the Conservatives and the Liberals, thus ending a period of mutual distrust that had lasted for decades. The graphs for the period 1966-68 demonstrate that the voting behavior of the Radical Liberals changed during these years. We have presented the ID-values for governmental bills in Table IV in order to refine this picture. The changing values bring out the gradual but complete reversal of behavior of the Radical party.

Amidst the fluctuations, the main impression of an inspection of the 16 graphs is, nevertheless, that the structure of the party space is rather stable. In almost all cases a profound difference can be found between the behavior of the 'old' parties on one hand, and the 'new' parties on the other, and between the 'new' parties themselves. This pattern disappeared only between 1957 and 1960, when the longtime opposition party, the Justice Party, entered a coalition government, but is was re-established in 1960-64, when two new parties, the Socialist People's party and the Independents, took the places in the party space that had hitherto been occupied by the Communists and the Justice Party. This major reshuffle of the party system had surprisingly enough no immediate effects on the structure of the party space.

Stability despite changes and fluctuations thus seems to be a major characteristic
of the Danish party system in the post-war period.43

6. Conclusions

In section 2 we set as our goal to demonstrate that the Danish party system does not lend itself to a description in the simple and familiar 'left-right' terminology. In order to arrive at a more realistic model, we developed a simple geometrical method, by means of which we were able to transform a set of data from parliamentary divisions into graphical representations of the party space. As was shown the results of these transformations gave support to our initial expectation, which was that, with

regard to the data at hand, the Danish party space is at least two-dimensional. We were further able to spell out in some details a few of the characteristics of this party space, as it emerged from two different parliamentary arenas and as it changed over time.

As is often the case in social science research, we end up with more questions than we started out with. Our description of the Danish party space is only to be seen as a partial and imperfect snapshot of a complex reality. Because each of the questions might inspire future research in Danish politics, let us put some of them on paper.

We could first of all ask for a genetical explanation of the party space we have been able to map out. A lot can be learned from the writing of Danish historians, since several of them have, more or less explicitly, treated modern Danish politics in terms of the changing relations among parties. Nevertheless, an examination of the voting patterns back in time would be worth-while, not least as a kind of test of some of the prevailing hypotheses and allegations. This task is relatively simple, although some difficulties are in store because of the changes in the extent to which the party votes are registered.

Next, an interesting topic would be to break down the data, according to the policy area. We are aware of the possibility that the two-dimensional space we have found may easily be interpreted as the result of a few, more or less unidimensional, orderings of the parties on some significant issues.

In order to give more adequate answers to the question about what factors account for the relatively stable and uniform voting pattern, a whole array of methods can be called in. Our method was not designed so as to reveal the underlying dimensions or coordinates. A look at the 16 graphs in Fig. 1 gives many reasons for expecting that closer scrutiny will demonstrate the existence of a fairly strong 'left-right' ordering of the parties, regardless of policy area, but until a more complete Smallest Space Analysis or a factor analysis have been applied to the data, all attempts to assign coordinates to the space will be guesswork.

Beyond the questions we have put so far come three sets of much more difficult problems, all of them related to the concept of party space. One set has to do with the existence of various different party spaces at a given time.⁴⁴ We should first of all like to know, to what extent our findings match with the party spaces that might be obtained from inferential analysis of policy statements etc., and to what extent they match the perceived party spaces which an analysis of interview data might bring forward. The search for this kind of party space can be pursued at many different levels, among voters, party members, party activists, legislators, and leaders. Each level will require modifications as regards the basic methodology. The important things to note are that we have no reasons a priori to expect these party spaces to be identical, and that these types of data are conditio sine qua non for further work.

When party spaces of one kind or another are looked upon over time, another set of questions becomes essential. It is possible to imagine changes in the position of the parties in every single party space mentioned above, without these changes being due to changes in inter-party relations. The system of coordinates may

change, both in the minds of the voters and the leaders. New issues may come up for processing in the legislature and may create new configurations of parties, when votes are counted. The saliency of dimensions may be different at the various levels, and may as well change over time. Stability and consistency are not properties we are allowed to assume, but properties that may or may not be revealed through empirical analysis over time.

When some of these data are at hand, it will be possible to proceed to the even more important set of questions which has to do with the consequences for the functioning of the political system of the observable pattern. What are, e.g., the consequences of the cleavage between the 'old' and the 'new' parties? What would we expect the short-term and long-term consequences to be for the party system and the political system as a whole, if a discrepancy exists or emerges between the observed party space and the various perceived party spaces, especially the party space that exists in the mincl of the Danish voter? By these questions we are brought right to the problem of political representation and the dynamics of the party system. Although there is a long way between questions and answers at this point, it is nevertheless the possibility of payoff by a move in this direction that makes it worth-while to study the Danish party space.

To conclude, it is easy to understand why unidimensional thinking has been prevailing in the studies of interparty relations in Denmark. In contrast to many other multiparty systems, the Danish has neither been formed around, nor is it maintained by, profound ideological, religious, or ethnic cleavages, which might be thought of as ordering dimensions. Our analysis has indicated that multidimensionality is nevertheless highly probable. The consequences for future research of this finding are limited on the one hand, but quite demanding on the other. The consequences are limited, because most of the research done so far may easily be translated to the more realistic multidimensional language. After all, it does not require much extra effort to speak about distances in a multidimensional space instead of distances on a unidimensional line. Much more demanding in this respect is the requirement that the various aspects of the concepts of party distance and party space become analytically separated, and that future research maintains this distinction.

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NOTES

1 R. M. Maciver, The Modern State, Oxford University Press, 1926, p. 406.

2 An EconomicNew Y0rk:&1957.

Anthony Downs, Theory of Democracy, Harper Row, 3 Donald E. Stokes, 'Spatial Models of Party Competition', The American Political Science Review, vol. 57, 1963, pp. 368-377.

4 E.g. Robert A. Dahl, ed., Political Oppositions in Western Democracies, New Haven and London: Yale University Press, 1966, p. 373. Gunnar Sjöblom, Party Strategies in a Multiparty System, Lund Political Studies 7, Lund, 1968, pp. 167 f.

5 Their name is legion. For example in his 'Party Systems and Patterns of Government in Western Democracies', Canadian Journal of Political Science, vol. I, 1968, pp. 180-203, J. Blondel argues that it is necessary to take into account the place of parties within the ideological spectrum, but he fails to provide criteria justifying the locations made.

6 E.g. Robert R. Alford, Party and Society, London: John Murray, 1964, pp. 11-18.

7 See for instance Hans Daalder, 'Cabinets and Party Systems in Ten Smaller European Democracies', Paper (R.G.AI) to IPSA Round Table, Torino, September 1969.

8 J. A. Laponce, 'Note on the Use of the Left-Right Dimension', Comparative Political Studies, vol. 2, no. 4, January 1970, pp. 481-502.

9 Poul Meyer, Politiske Partier, København: Nyt Nordisk Forlag, 1965, pp. 159-170.

10 Despite this categorical denial of the possibility of using the unidimensional concepts, they are nevertheless utilized without hesitation by the same author in other context, see, e.g., Poul Meyer, op. cit., pp. 111-113 and pp. 120-124.

11 Erik Rasmussen, Komparativ Politik, I, København: Gyldendal, 1968, pp. 237 f.

12 This point is discussed in Kenneth Janda, A Conceptual Framework for the Comparative Analysis of Political Parties, Sage Professional Papers in Comparative Politics, vol. 01—002, Beverly Hills, Calif., 1970, p. 88.

13 Matthews and Protho, 'The Concept of Party Image and Its Importance for the Southern Electorate', in Jennings and Zeigler, eds., The Electoral Process, Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1966, pp. 139-174.

14 Philip E. Converse, 'The Problem of Party Distances in Models of Voting Change', in M. K. Jennings and L. H. Zeigler, op. cit., pp. 175-207. Bo Särlvik, 'Voting Behavior in Shifting Election Winds', Scandinavian Political Studies, vol. 5, 1970, pp. 262-276.

15 See Poul Meyer, 'Regeringsdannelsens teknik', Økonomi og Politik, 1967, pp. 284-307, and Poul Meyer, Politiske Partier, pp. 171-186.

16 Arend Lijphart has convincingly argued that consociational democracies are characterized by ideological polarization at the mass level and a high degree of pragmaticism and moderation

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at the top level (The Politics of Accomodation, University of California Press, 1968, especially chapters VII-VIII). This may to a certain extent also be characteristic of centripetal democracies like Denmark, cf. also Arend Lijphart, 'Typologies of Democratic Systems' in A. Lijphart, ed., Politics in Europe, Englewood Cliffs, New Jersey: Prentice-Hall, Inc., pp. 46-80.

17 Cf. the passage following the quotation given above (note 11): 'The fact that the Radical-Liberal party in 1968, contrary to previous occasions, preferred to form a majority government with Conservatives and Liberals rather than with the Social-Democrats thus expresses - regardless of motives to that - that the party now perceived the distance to these partners as smaller than to the previous partner'. Erik Rasmussen, op. cit., p. 238.

18 Hans Jørgen Nielsen, 'Forskelle mellem politiske partier?', Økonomi og Politik, 1969, nr. 2, pp. 156-164.

19 Olavi Borg, 'Basic Dimensions of Finnish Party Ideologies: A Factor Analytical Study', Scandinavian Political Studies, vol. 1, 1966, pp. 94-117.

20 Philip E. Converse in Jennings and Zeigler, op. cit., p. 176. Butler and Stokes in their recent study of British electoral behavior asked questions concerning policy attitudes, party orderings, and recognition of left and right, but found almost nothing to support the classical left-right model. See David Butler and Donald Stokes, Political Change in Britain, London: MacMillan, 1969, Chapter 9: 'Patterns in Political Attitudes'.

21 Bo Särlvik, 'Partibyten som mått på avstånd och dimensioner i partisystemet', Sociologisk Forskning, vol. 5, 1968, pp. 35-80. — See also his "Voting Behavior in Shifting 'Election Winds' ", Scandinavian Political Studies, vol. 5, 1970, pp. 241-283.

22 John C. Wahlke, Heinz Eulau, William Buchanan, and Leßoy C. Ferguson, The Legislative System, New York: John Wiley and Sons, Ins., 1962, pp. 372-375.

23 Allan Kornberg, Canadian Legislative Behavior, New York: Holt, Rinehart, and Winston, 1967, pp. 121-126.

24 Cf. Lee F. Anderson, Meredith W. Watts, Jr., Allen R. Wilcox, Legislative Roll-Call Analysis, Evanston: Northwestern University Press, 1966, pp. 77 f.

25 However, in The Netherlands a survey among parliamentarians has been conducted by Hans Daalder and others. Respondents were asked to put a number of parties in sequence of preference and the resulting rankings are to be handled by 'smallest-space' analysis. A Swedish member of parliament study 1969, directed by Bo Särlvik, also contained a ranking question.

26 Among the few examples of this type of analysis are two papers by Mogens N. Pedersen ('Consensus and Conflict in the Danish Folketing 1945—65', Scandinavian Political Studies, vol. 2, 1967, pp. 143-166, and 'Partiernes holdning ved vedtagelsen af regeringens lovforslag', Historie, vol. VII, 3, 1967, pp. 404-435), but in those papers the aim was not explicitly a discussion of party distances and dimensionality.

27 One of the present authors strongly felt the need for such a measure in a study of Danish coalition patterns (Erik Damgaard, 'The Parliamentary Basis of Danish Governments: The Patterns of Coalition Formation', Scandinavian Political Studies, vol. 4, 1969, pp. 30—57, especially p. 42). The results obtained warranted the hypothesis that some underlying leftright dimension was reflected in the actually observed coalition formations. — See also Klaus Törnudd, 'Composition of Cabinets in Finland 1917-1968', Scandinavian Political Studies, vol. 4, 1969, pp. 58-70.

28 In a recent major contribution to coalition theory several authors are wrestling the 'ideological distance' problem, see, e.g., Abraham De Swaan, 'An Empirical Model of Coalition Formation as an N-Person Game of Policy Distance Minimization', and E. W. Kelley, 'Utility Theory and Political Coalitions: Problems of Operationalization', in Sven Groennings, E. W. Kelley, Michael Leiserson, eds., The Study of Coalition Behavior, New York: Holt, Rinehart and Winston, 1970, pp. 424-444, and pp. 466-480. - A simple measure of ideological distance (presupposing a left-right ordering of legislative parties) is suggested by Risto Sänkiaho, 'Voting Strength in the Finnish Parliament 1951—1966', Scandinavian Political Studies., vol. 5, 1970, pp. 119-128. It is obtained 'by placing the parties with their number of seats in ideological order from left to right and determining the distance between the middle points of segments obtained in this manner'. Ibid., p. 126.

29 Giovanni Sartori, 'European Political Parties: The Case of Polarized Pluralism', in Joseph La Palombara and Myron Weiner, eds., Political Parties and Political Development, Princeton University Press, 1967, pp. 137-176.

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30 This was a central question in previous papers by one of the authors (see note 26), although the restricted focus was the changing relations between governing parties and the opposition parties.

31 'Agenda motion' (motiveret dagsorden) is a special device in Danish parliamentary practice, which can be utilized during most kinds of debate. Essentially it is a means whereby the Folketing articulates its opinion or demands, especially vis-a-vis the government and including motions of censure.

32 Only the first session in the parliamentary year 1967/68 is included (prior to the general elections in January 1968, which led to a change of government). This explains that the average number of passed government bills is a bit smaller than one might expect.

33 The formal definition of the Index of Distance is to be found in Mogens N. Pedersen, 'Consensus and Conflict in the Danish Folketing 1945-66', Scandinavian Political Studies, vol. 2, 1967, pp. 164 f.

34 A small short-lived party, Liberalt Centrum (1966-68), has been left out of our analysis as have the representative of Slesvigsk Party (German minority party with only one member 1953—1964), the 2 representatives from Greenland, and a few members who detached themselves from their party during the period.

35 For a discussion of these problems, see e.g., Lee F. Anderson et. al., op. cit., chapter 2, and Duncan Macßae Jr., Dimensions of Congressional Voting, Berkeley, 1958, pp. 300-308.

36 This is also the position of Arend Lijphart, whose index of agreement is conceptually equivalent to the index of distance. See his 'The Analysis of Bloc Voting in the General Assembly: A Critique and a Proposal' in The American Political Science Review, 57, 1963, pp. 902-917.

37 See e.g., J. C. Lingoes, Behavioral Science, 1963.

38 If a unidimensional spatial model fitted the matrix data only one set of intersections would be found.

39 James C. Lingoes, 'An IBM-7090 Program for Guttman-Lingoes Smallest Space Analysis', Behavioral Science, vol. 10, 1965, pp. 183 ff. - We are indebted to professor Henry Valen and mag. art. Jan Hovden, University of Oslo, for making this part of the analysis possible.

40 J. B. Kruskal, 'Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis', Psychometria, vol. 29, 1964, pp. 1-27. See also Duncan Macßae, Jr., Issues and Parties in Legislative Voting, New York, 1970, pp. 75-86.

41 The calculations are not shown here.

42 See Erik Rasmussen, op. cit., and Poul Meyer, op. cit.

43 Cf. the older and partly outdated discussion of the government-opposition relations to be found in Mogens N. Pedersen, Scandinavian Political Studies, vol. 2, 1967, pp. 143-166.

44 To the following see e.g., Donald Stokes, op. cit. and Philip Converse, op. cit.