University of Aarhus

1. Introduction

When studying coalition behavior one can choose between different, though related, aspects: coalition formation (the end product), bargaining in the process of coalition formation, the actual distribution of payoffs in a completed coalition, and coalition maintenance.¹ In this analysis we shall deal with coalition formation. The primary purpose is to detect some general features of coalition formation in the 20th century's Denmark, the term coalition referring to the parliamentary basis of governments. In a broader perspective the conclusions arrived at might contribute to the general understanding of coalition formation, especially with regard to coalitions of political parties in multi-party systems.

By way of introduction it ought to be stressed that a highly relevant characteristic of Danish parliamentary democracy is the existence of several political parties,2 which, of course, makes majority formation more complex than in two-party systems. Since the adoption of parliamentarism in 1901 at least four parties of varying size have been represented at any moment. Further, since 1932 the number has never been less than six.₃ Now, it is obvious that not only the number of parties but also their relative strength condition the possibilities of government formation. The concept of fractionalization developed by Douglas W. Rae 4 combines these two aspects into a single notion. Fractionalization of parliamentary systems (F_p) is defined as the probability of paired disagreement with respect to party, i. e. the chance that any two members of parliament belong to different parties:

where Si is any party's share of the seats. The Fp-values would seem to be useful
for obtaining a general survey of the fundamental conditions of majority formation

in Denmark. Therefore, the computed values after each Folketing election since 1901 are graphed in fig. 1. In order to simplify comparisons two dotted lines denote the Fp-value in a two-party system with a 6CMK3 split of seats, and in a five-party system with an equal distribution of seats.

Compared with a pure two-party system, in which 0.0 <Fp <^ 0.5, the Danish party system is characterized by a high degree of fractionalization. Since 1915 the Fpvalue has varied within the interval of 0.70 to 0.78 with an average of 0.73, which also indicates a certain stability. Particularly, stability is revealed in the inter-war period. In the first decade of the century the picture is less unequivocal. The Fpvalue, very low in 1901 (0.52), successively increases to 0.77 in 1909, whereupon it drops to 0.63 in the following year. In fact, Denmark was ruled by a one-party government which commanded exactly half of the votes in the periods 1906-1909 and 1910-13. Since 1906 at least two parties have always been required to form a majority in the Folketing.

In the following sections we shall try to find the patterns of coalition formation
on the foundations thus presented. First it is discussed whether the size principle of
William H. Riker 5 is applicable to the coalitions formed.

2. The Size Principle and Danish Government Coalitions

The size principle reads as follows: "In social situations similar to n-person, zero-sum
games with side-payments, participants create coalitions just as large as they believe

will ensure winning and no larger".6 If information is perfect, only minimum winning coalitions occur. The testing of such a hypothesis in real world situations involves very difficult problems. As E. W. Kelley points out: even if the specified conditions actually occur, they probably never occur alone. "... it is quite possible that Riker's hypothesis is a true generalization, but we will never observe a real world situation in which only his initial conditions are relevant; hence there may be no real-world situation in which the hypothesis can be precisely tested".⁷ It might be said, however, that if the size principle is relevant to our purpose, then the coalitions actually observed must conform to the prediction, i.e. they must be of minimum size, perfect information assumed. Whether that is the case we shall see after having clarified some preliminary questions.

Preliminary Problems

First, an operationalization of the concept of a winning coalition is required. It is obvious that majority governments represent winning coalitions. But in Denmark minority governments have been quite as common (1909-1918, 1920-29, 1945-57, 1964-68). These minority governments, however, can be divided into two categories. Some of them were based on a more or less permanent cooperation and understanding with specific parties outside the government, and some were not.⁸ Put in another way, the distinguishing feature is the existence or non-existence of "support" parties. I.e. in certain periods minority governments are based on a parliamentary majority obtained from the combined votes of the governing party and the supporting party, or parties. As a rule, this relation of support is conditioned by policy concessions to the support party by the governing party. This does not necessarily mean that minority governing parties and their support parties adopt the same attitude in any legislative question. It means that the support party furnishes the votes required on occasions crucial for the government to stay in office. But, of course, in one way or another a support party will find it advantageous to maintain a minority government. If that should not be the case, it can dissolve the support relation, as actually happened in 1926, 1929, 1947, and partially in 1967.⁹ Now, the point to be made is that it seems reasonable to classify minority governing parties and their support parties as winning coalitions, despite the fact that the intensity of cooperation varies considerably within different support relations. Thus extending the meaning of "the end product of coalition formation" a list of all Danish winning coalitions since 1901 is given in Table I.

It must be admitted that this classification is not wholly satisfactory, due to the regrettable absence of detailed and systematic studies of the relations between governments and support parties. Future research on the peculiarities of Danish interparty relationships may point out that our distinction between minority governments with and without support to form a majority is an oversimplification. However, the only study relevant at present tends to support the classification made. Mogens N. Pedersen 10 has constructed an "index of distance", measuring the "distance" between

parties as their tendency towards heterogenous voting in the final division on government bills in the Folketing. The index value is 0 if the parties voted completely uniformly during a session, and 100 if they took diametrically opposed stands on the bills. Table I shows four winning coalitions in the period 1945-66, viz. two majority governments (1957-60, 1960-64) and two winning coalitions held together by means of support relations (1945^7, 1953-57). Mogens N. Pedersen's index values show,¹¹ as we should expect, that parties in the majority governments voted practically uniformly.

Further, there was a marked difference in the votes cast by support parties
and other non-governmental parties. The index values relevant to the L+R+G
coalition 1945-47 were:

Thus the votes of the Conservatives and the Radicals differ only slightly from the votes of the governing party. The figures do not show the extent to which the two parties have abstained from voting, which is not entirely irrelevant, as, under certain circumstances, abstaining can be interpreted as passive support to a government. Nor do the figures show the diverging votes. At any rate, however, diverging votes have only been given if they had no parliamentary consequences.

The corresponding figures for the period 1953-57 are as follows:

Also this indicates that the parties of the winning coalition voted highly uniformly. Considering the fact that the Radicals did not support the government's defence policy and that this field had no influence on the continuance in office of the government owing to the concordant attitudes of the three major parties (SD, L, C) towards this question, the uniformity of the attitudes of the Social Democrats and the Radicals was in a certain sense much more pronounced. On the basis of information from the Folketingsårbog for the years in question we have calculated the following distance index values, the defence legislation not considered:

In evaluating the relevance of Mogens Pedersen's index values to government-support party relations it must be noted that: firstly, the votes on bills are only one of the means of the parties to demonstrate their opinion of the governments; secondly, Mogens Pedersen's investigation also indicates that the distances were minimal, in 1950-53 between the Liberals + Conservatives and the Social Democrats, and in 1965-66 among the Social Democrats, the Radicals, and the Liberals, i.e. exactly in periods when no winning coalition could be identified. This indicates a distinction between attitudes towards formation of government and attitudes towards bills. In

Denmark most of the government bills are adopted unanimously or in "broad agreement" ¹² Charles R. Adrian and Charles Press¹³ have suggested that often in coalition formation "responsibility costs" tend to produce large majorities with a view to dilute responsibility and to avoid raising of questions about the legitimacy or wisdom of decisions. Maybe similar reasons in part explain large majorities in Danish law-making. Further, many bills of a rather technical nature are not likely to arouse political controversy.¹⁴ But it should be strongly emphasized that government formation and government maintenance are primarily not problems of legislation. They are problems of securing a power position from which to govern, and this problem is certainly refers to one of competition. If a government is formed which, for reasons later to be commented on, does not represent a winning coalition directly or indirectly by means of support, then the problem becomes one of securing support for bills and other measures from case to case. In this situation the position of the government is extremely weak, farreaching concessions to various opposing parties being necessary for the government to stay in office.ls

The second preliminary question concerns the perfect information assumed in Riker's model, though not in the size principle. If the information possessed by the players is imperfect, this may lead them to create coalitions larger than the actually minimum winning size, due to a rational attempt to ensure that they win rather than 105e.16 In Denmark government majorities are formed by parties none of which since 1906 has had a parliamentary majority by itself. These parties, or proto-coalitioris in the terminology of Riker, are characterized by a very high degree of cohesion ¹⁷ particularly with respect to government formation. This implies that every participant has complete and perfect informationlB about any other, hence they can aim at creating exactly minimum winning coalitions.

The third question is related to the second. Regarding the assumption that protocoalitions are indissoluble, Riker states that in a dynamic world it is absurd.l9 But, as a matter of fact, it is the only meaningful one concerning government formation in Denmark. It is the rule rather than the exception. Acceptance of the assumption raises a theoretical question: which coalitions are then minimum winning coalitions? A minimum winning coalition is defined as one which is rendered blocking or losing by the subtraction of any member.2o Does "member" refer to party (proto-coalition) or to individual persons with the assumption made here? Further: is the winning coalition with fewest seats minimal if, with a given distribution of seats in the Folketing, no minimum winning coalition is possible on purely arithmetical grounds? Or is a winning coalition to be termed minimal if it is rendered losing or blocking with the subtraction of any party? Before answering this important question, we shall take a look at the consequences of both interpretations.

We shall now concentrate on the size of the winning coalitions listed in table I,
postponing questions about why, sometimes, no permanent winning coalition is established.

Predicted and Actually Formed Winning Coalitions

At the outset, two occasions of grand majorities call for special treatment. Theoretically the existence of overwhelming majorities should be incompatible with the size principle. In the years of 1901-05 the Reform-Liberal Party held about 2/s of the seats in the Folketing, and during the German occupation of Denmark 1940-45 and its immediate aftermath all-party governments controlled nearly all the votes. These occurrences, however, do not contradict the size principle. The grand majority of the Reform-Liberals was acquired before their take-over of government, indeed before the principle of the supremacy of the Folketing was acknowledged. As William Riker argues,²¹ evidence about the size principle is obtained if leaders of grand coalitions or overwhelming majorities, formed by reason of some accidental circumstances, consciously behave in some way to minimize their coalitions. Since we cannot pursue a historical analysis the reader must be content with the assertion that this was precisely what happened around 1904/05. Led by J. G. Christensen, the Reform Party expelled a number of members, later known as Radicals, the remaining majority constituting the smallest possible winning coalition (1905-06) and forming a majority government with J. G. Christensen as prime minister.

During the German occupation of Denmark all-party governments were in office. Of course, due to external pressures and other extraordinary circumstances, the operation of the size principle could not be presumed. On the other hand it is striking evidence that a new government formed immediately after the Liberation in May, 1945 and representing a "coalition of the whole" could hardly be held together for half a year. Differences of opinion prevailed on practically every major issue, and the government was described by ministers as a debating society! Not surprisingly, therefore, the coalition was dissolved. It was replaced by a Liberal minority government relying on support from the Conservatives and the Radicals, the combined votes of the three parties amounting to exactly a minimal majority. Thus it seems safe to conclude that the events of 1901-05 and 1945 are in accordance with the prediction of the size principle.

The instances of grand majorities put aside, what about the size of the other winning
coalitions? These are listed in Table 11, which also shows the votes required to
form a majority and the difference between coalition size and minimum majority.

From Table II it appears that in four of the election periods minimum winning coalitions occured, the majorities being 1—9 larger than necessary in the other election periods. Considering the total membership of the Folketing these majorities were not very large; however, the information condition being fulfilled one should expect only minimum winning coalitions. But, as was underlined above, the parliamentary parties as a rule must be regarded as indissoluble. Therefore it could be suggested that the actually formed winning coalitions were those with the smallest possible number of members under given distributions of the total number of seats.

Before answering the question, a special restriction on the admissible winning
coalition should be introduced. This limitation is designed to exclude from potential
winning coalitions some small parties, which did not wish to be in a coalition and/or

were not accepted as coalition partners at any moment by any of the four "old" parties (Liberals, Social Democrats, Radicals, Conservatives). Thus the following parties are ignored: The Trade Party (Erhvervspartiet), the Communists, the Agrarians (Frie Folkeparti = Bondepartiet) and the National Socialists.

Now we can decide whether the winning coalitions listed in table II were the smallest possible. Calculations made from data given in the appendix show that all but four were so, the exceptions being: 1920 III: the smallest was Social Democrats + Conservatives (75), 1957: the smallest was Liberals + Conservatives + Socialists (89), and 1968: the smallest possible was Social Democrats + Radicals (90).

Before stating some conclusions to be drawn from the investigation in this section a special problem shall be commented on. As may be known, the Danish legislature until 1953 was bicameral. Though only a majority in the Folketing was required to form a government, the value of winning coalitions was of course greater if they commanded a majority in both houses (Folketing and Landsting), since agreement between the houses was a condition for adoption of bills. Therefore, it hypothetically might be assumed that the non-minimality of winning coalitions formed is ascribable to a desire to have a "law-making majority". However, there is no evidence that this desire has been effective. In fact, most of the winning coalitions listed in table II before 1953 did not command a majority in both houses.22 And as will be seen later on, the patterns of coalition formation prior to 1953 do not differ from those after 1953.

The general conclusion seems to be that without modifications the size principle ;~;~

not particularly relevant to government coalition formation in Denmark. This does not mean that the size principle has been disproved, because, as stated in the beginning of this section, one cannot be sure that the antecedent conditions of the prediction actually occur without other relevant factors intervening. Especially we note that the existence of parties with a very high degree of cohesion does not fit well with the assumptions of Riker's model. Further, several instances of minority governments without permanent support from other parties strongly indicate that other factors than the desire to "win the game" are at work.

Lastly, however, perhaps the most important result of our analysis remains to be explicitly presented. As will be recalled the question of how to interpret the concept of a minimum winning coalition was posed above. When, as; we have seen, highly cohesive parties are the real actors, it seems logical to define a minimum winning coalition as one which is made non-winning by the subtraction of any party. Using this definition it at once becomes quite clear that all the actually formed winning coalitions were minimal.23

We shall utilize this conclusion in the next section.

3. The General Limits of Coalition Formation

In this section we shall elaborate on the general results arrived at in the foregoing section with a view to narrow down the number of possible winning coalitions in Denmark. If we succeed in doing this, we shall also be able to formulate more specific predictions of future winning coalitions, i.e. predictions regarding the composition of future majority governments and regarding parties cooperating in support relations maintaining a minority government.

First Limitation

What emerges from section 2 in short is, firstly that only minimum winning coalitions occur (defining a minimum winning coalition as one which is rendered nonwinning if any party left the coalition). Secondly, that only certain parties, whatever the reasons may be, have participated in winning coalitions, viz.: Liberals, Radicals, Social Democrats, Conservatives, the Justice Party (single taxers), and Socialists. We shall restrict our analysis to these parties with two further modifications: The Justice Party is ignored at all times before 1957 on the grounds that prior to 1957 it was generally regarded as a party unsuited to participate in government coalitions, i.e. not "koalitionsfähig".24 Similarly the Socialists are ignored in 1960 and 1964 on the grounds that they were not accepted by any of the said parties prior to 1966.

From this point of departure it is possible to formulate a first limitation with
respect to the number of possible winning coalitions: Only minimum winning coalitions
made up of the parties mentioned occur. While the number of possible winning

coalitions, of course, is large, the number within this limit is 2, 3, or 4, as can
be seen from Table 111.

Discussing party strength in relation to coalition formation it appears that the sheer number of seats is not a good measure. Therefore in Table 111 a measure of party strength with respect to coalition formation is also given. "Winning probability" (WP) of party N is defined as the chance that N will belong to the actually formed minimal winning coalition, assuming full freedom of combination.²⁵ Considering the winning probabilities in Table 111 some interesting features appear. Firstly, sometimes a party cannot at all, with a given distribution of seats, become a member of any possible minimal winning coalition (Conservatives 1913, 1915, 1918; Radicals 1920111, 1926, 1950, 19531, 1964, 1966; Socialists 1968). Secondly, parties with a very different number of seats often equally frequently are found in potential winning coalitions (e.g. 1957: Liberals (46) and Radicals (14). Thirdly, only in 16 instances of 25 has the largest party had more possibilities than other parties to enter into minimum winning coalitions, though, on the other hand, its position is never inferior to that of the other parties. Fourthly, the largest party is sometimes what could be called essential, i.e. no minimum winning coalition can be formed without that party (WP = 1). Finally the WP of especially the small parties fluctuates greatly, and unlike that of the large parties it may be of the value 0.

Second Limitation

Though the first limitation thus to a certain extent reduces the number of possible

winning coalitions, it still permits the existence of 2-4 possibilities. Therefore, our problem is how further to restrict the number of possibilities. Now, it is a common experience that in multi-party systems some parties generally are more likely to cooperate than others, or as Gunnar Sjöblom writes: "The relations between the parties in a specific party system can be highly varied and can sometimes change rapidly. However, they usually follow definite patterns."26 A method of characterizing the relations between parties is to grade them on a right-left-scale using one criterion or another, e.g. attitude to the degree of state intervention in the economy, the desired degree of change in the society, or the degree of political measures demanded in order to produce an income equalization.²⁷ At any rate the four "old" Danish parties in the first two decades, or so, of this century can be ordered thus: SD, R, L, G, indicating the relative positions of the parties regarding the major issues of constitutional reform, defence policy, and economic and social policy in general28 though the party intervals29 varied in the three areas. The problem of ordering the parties with respect to general policy questions in the subsequent fifty years appears much more difficult. Poul Meyer argues that a classification of the parties can only be made using several factors not necessarily operating in the same direction for the same party.³⁰ Probably no single policy criterion exists to rank the parties on a right-left scale in order to signify the possible relations of governmental cooperation between parties.

In this situation, however, our point is that, whatever the reasons and underlying considerations may be, it is an undeniable fact that in Denmark distinct patterns of party relations exist as far as government formation and support are concerned. Though hardly one combination of major parties is found which at one time or another has not been considered or negotiated by the actors, it can be seen, nevertheless, looking at the winning coalitions formed (tables II and III) that any party has only cooperated with certain other parties. Stated more precisely: only winning coalitions which have been formed according to the sequence of parties in fig. 2. occur (In 1957 the Justice Party in a way placed between SD and R):

This sequence never was broken, i.e. a winning coalition has never been formed
which was not made up of parties placed at the side of each other, or formed in the
way of two parties flanking a third in the sequence.

Consequently, as our second limitation of winning coalitions we state the following:
Only winning coalitions formed according to the sequence of parties in fig.
2 occur.

It should be kept in mind that the sequence in fig. 2 is established from observation of coalition behavior of the parties mentioned. We think that, for example, differences in standpoints on important questions in some significant way are related to the sequence, and that the voters' images of parties to a certain degree correspond to the sequence. But these interesting questions are not dealt with here.³¹

Combining the two limitations our general conclusion is that only minimum winning
coalitions formed according to the sequence of parties occur. Using both limitations,
the number of possibilities after the elections 1906-68 is shown in Table IV.

From Table IV it appears that there have often been two possibilities - but never

more - for a minimum winning coalition in accordance with the party sequence (1906-1918, 1924, 1929, 1932, 1957, 1968), sometimes one (1920, 1926, 1935-1947, 195311, 1960, 1966) and sometimes none at all (1950, 19531, 1964). Except for the potential L+R+C coalition in 1947 it is a fact that in all cases with only one possibility, this possibility was utilized. In 1947 the Liberal government's attitude towards the South Slesvig question32 was not acceptable to the Radicals. Therefore the L + R + C coalition could not be continued, and a minority government without permanent support had to result. As will be seen from the table, a winning coalition is not necessarily realized even if two possibilities exist (1909, 1910). Especially divergent attitudes in constitutional matters and a traditional antagonism between the Liberals and the Conservatives (Right) probably prevented, at that time, a cooperation between these parties33 just like a Liberal-Radical cooperation was impossible owing to divergent standpoints, especially concerning defence matters and for personal and other reasons, cf. p. 36. It is significant that since 1913 a winning coalition has always been established if it was possible, with the exception mentioned above concerning 1947.

4. Bargaining Strength in Coalition Formation

In section 3 we said that a party's number of seats was not a particularly good measure in evaluating the chance that the party would be a member of the winning coalition formed. Instead we proposed the notion of winning probability, defined under the assumption of full freedom of combination. As also was seen in section 3 this assumption is not a realistic one. Therefore, it is now abandoned. Our purpose is to define a measure of party strength with respect to coalition formation in the light of the experience obtained from our analysis.

Similar to the winning probability above, we can define party strength with respect to coalition formation under both limitations formulated in section 3: Bargaining strength of party N is the chance that N will belong to the minimum winning coalition actually formed according to the party sequence. The difference between bargaining strength and winning probability of party N, of course, is the particular strength that N obtains, or loses, due to its position in the party sequence. To designate this differential strength we shall introduce the notion of a position value. Consequently, the following conceptual relationship exists:

bargaining strength -f- winning probability = position value or,

winning probability + position value = bargaining strength.
In Table V these values are listed.

From the Table it can be seen that at least one of the "extreme" parties always has a negative position value, i. e. less possibilities to enter into a minimum winning coalition if its position in the party sequence is considered than if this sequence is not taken into account. For instance, until 1966 the Social Democrats never gained strength from their position, but very frequently they lost. On the other hand one

or more of the "center" parties always have a positive position value in so far as a winning coalition can be established at all within the given limitations. Apart from 1920 the Radicals have never had a negative position value, and most often it was positive. It is notable that the bargaining strength was zero for all parties in 1950, 19531, and 1964, which means that minority governments without permanent support were established. It is also remarkable that, although the Radicals have been the smallest of the four "old" parties after 1920, they have most often had maximum bargaining strength (1913, 1915, 1918, 1924, 1929, 1932, 1935, 1939, 1945, 1947, 195311, 1957, 1960, 1968), i.e. that in all these cases a permanent majority could not be established without this party's participation.

In order to enable a general treatment of the possibilities of various parties to form a winning coalition we now proceed to establish some precisely defined categories. The classification is made with the purpose of placing parties on a discontinuous scale running from maximum to minimum degree of advantage in the initial situation of coalition formation.³⁴ Furthermore, the categories of the classification are exclusively defined, in the sense that all relevant situations are accounted for. We propose the following six categories, of which the first refers to a coalition rather than a party:

5. A weak party is a party which cannot become a member of any possible minimum winning coalition formed according to the sequence, though it can participate in minimum winning coalitions not respecting the sequence (BS = 0; 0 < WP < 1). 6. A losing party is defined as a party which cannot at all become a member of any minimum winning coalition (BS = 0; WP = 0).

Using these definitions the parties are classified in Table VI, columns 2 to 6 indicating
declining degree of advantage.

Primarily, Table VI is intended to give a clear and yet varied picture of the parties' relative strength and mutual coalition possibilities from 1906 to 1968. The distribution of seats (appendix p. 53) and the consequent degrees of fractionalization (fig. 1) give only little information in this respect. On the contrary the definitions forming the basis of table VI are sensitive even to small variations in the distribution of seats. Of course, the categories of the Table do not exhaust the topics of strength and behavior of the parties - especially as far as the legislation process is concerned, where non-minimal majorities often occur, and where the party sequence is not always relevant. However, these categories will probably be suitable as the basis of a

further analysis of given parliamentary situations. Perhaps it ought to be emphasized that even if they form part of all potential minimum winning coalitions, the essential parties are not necessarily "strong" in other ways. After the election in 1935 the Social Democratic Party has often been essential; in 1950, 19531, and 1964, however, no permanent minimum government majority could be established at all in accordance with the party sequence. This means that after these elections the WP of the Social Democrats was one, whereas the BS was zero. On the contrary also the BS was one in 1935, 1939, and 1953 II for the Social Democrats and in 1906 and 1910 for the (Reform-)Liberals. Therefore, the column "essential party" is placed in the "weak half" of the Table.

Among other things, Table VI illustrates how the Liberals, favourized, partly favourized, or belonging to the optimal winning coalition since 1906 became a weak party³⁵ in 1935 (like the Conservatives). This situation has remained unaltered except for the periods after the elections in 1945, 1947 (cf. the weakness of the Social Democrats), 1957, and 1968.

The concepts offered might also add some precision to common Danish political language in certain respects. For example, the Radical Party is often mentioned as the holder of the balance in Danish politics.36 Similarly, stating that the most important function of minor parties in multi-party systems is majority building in which a small party might "tip the scale", Poul Meyer comments that "thus this applies especially to the Danish Radical Party which has been of crucial importance for formation of governments in Denmark since 1913 and which has maintained this position after its entry among the small parties".37 Kenneth E. Miller gives the following characterization:

Although usually fourth in strength among Danish parties, in five of the nine Folketing elections since World War 11, it has been pushed into fifth place by another party. Yet the Radicals have occupied a key position in Danish political life. "For almost at all the time the party has been in existence, the Folketing chamber's equator has run through the Radical group; it determined on which side the political majority or the possibility for a Government, sometimes even the only possibility for political discussion, should be formed" (Svend Thorsen). Its strength has often been sufficient to determine which other parties might take office, either alone or perhaps in coalition with the Radicals. Today it is still ardently courted by other parties desiring to form a Government.³⁸

These observations about the key position and special influence of the Radicals can now be compared with Table VI. Initially, we may point out that when a party is able to "tip the scale", it must mean that in principle the party can throw its number of seats into both scales, i.e. it forms part of two possible minimum winning coalitions, and thus in our terminology it is a favoured party. As Table VI clearly shows the Radical Party has often been favoured (1913, 1915, 1918, 1924, 1929, 1932, 1957, and 1968). Further, in 1935, 1939, 1945, 1947, 195311, and 1960 it was a member of the optimal winning coalition, and in 1906-10 it was partly favoured. But it also ought to be underlined that in six instances the Radicals have been a losing party (1920111, 1926, 1950, 19531, 1964, and 1966); however, this does of course not mean that the party had no political influence, especially not after the

elections in 1950, 19531, and 1964, when the BS of the other parties was also 0.
But after the elections in 1920, 1926, and 1966 the influence of the party was much
reduced.

Concluding this section we state, employing the terminology introduced, that besides
optimal winning coalitions only winning coalitions made up of favoured or
partially favoured parties occur.

5. Some Problems of Theory

In the previous sections we arrived at certain general conclusions. These results, however, were obtained ad hoc, so to speak. I.e. they are not verifications of inferences analytically derived from some basic assumptions. Therefore, the question arises: What theory may explain our results? For the moment we hesitate to present an elaborated theory of coalition formation in Denmark. In this final section only some very provisional comments shall be made on a selection of problems involved in theorizing about this subject.

Many questions come up at once: Why are only minimum winning coalitions established? Why do these coalitions conform with a certain party sequence? Why is exactly one definite minimum winning coalition established where two possibilities exist? Why did the Justice Party appear as a government partner in 1957 and the Socialists as support party in 1966, but not previously? Why is it sometimes impossible to identify any winning coalition at all, even if it should be possible according to the general behavior observed? Why are support parties such a frequently occurring phenomenon?

Especially in recent Swedish literature on party behavior in multi-party systems³⁹ it is stressed that behavior is determined by at least two general considerations involving the value system of a party and the desire to attain parliamentary influence or control of government, respectively. In our unpretentious attempt to establish a certain order in the mentioned variety of complex problems, we will start from Gunnar Sjoblom's reflections. Sjoblom's definition of the general goal of a party reads: "The party itself shall make the authoritative decisions in accordance with its evaluation system". This formulation covers four so-called - often mutually conflicting — "basic goals": 1. programme realization; 2. vote maximization; 3. maximization of parliamentary influence; 4. party cohesion.4o No doubt this description is also adequate for Danish party politics,41 though at present one cannot decide how far investigations following the paths proposed by Sjöblom can guide us.⁴²

In this connection especially the third basic goal is of interest. Direct parliamentary influence can be obtained when a party alone or together with other parties forms a majority government or it can be obtained in the case of minority government when the party chooses to remain outside the government but together with it forms majority voting coalitions.⁴³ Further, Sjöblom observes that a party can aim at maximizing its parliamentary influence in the short term,i.e. within the framework

of the election period, or even for each of the questions that are continually coming
up for parliamentary consideration, or in the long term, i.e. after a new parliamentary
election.44

Sjoblom's leading idea is now that when choosing whether or not to enter into a coalition a party must weigh the possible "yields" against the possible "costs", yields meaning the effects that suggest a higher degree of goal attainment with regard to one or more of the four basic goals, costs referring to the opposite.45

When, as we have seen, only minimum winning coalitions are formed in Denmark, this might be interpreted quite abstractly in the way that the positive difference between anticipated yields and costs for participants in such coalitions, ceteris parihus, is always greater than for participants in non-minimal winning coalitions. The notion of ceteris paribus is extremely important in this connection. We do not simply state that every minimum winning coalition is of greater value to the partcipants than every non-minimal winning coalition. Our argument is that any minimum winning coalition is of greater value than a non-minimal coalition composed of the same parties plus one or more parties. Though it probably is very difficult to calculate the values of potential winning coalitions we find it highly plausible that always in Danish government coalition formation the following inequality is valid:

value of minimum winning coalition PI ... Pn > value of PI ... Pn +1.

Therefore, we conclude that parties of minimum winning coalitions generally have
better possibilities for mutual cooperation than parties of non-minimal winning coalitions.

However, these cooperation possibilities are limited by the party sequence. It may be noted that Sjöblom enumerates several factors to be taken into account before a party decides to enter into a coalition. But he also adds that the analysis is simplified by certain "role expectations" concerning a party, more or less independent of its actual standpoints: "... concepts concerning a party's relative position in relation to other parties should normally be an important component in such "party images". These concepts have been assumed to be relatively determined, and they will therefore act as a restraining factor for a party when appraising innovations, for instance when entering into a new coalition."⁴⁶ We agree with Sjöblom that these party images play the most important role in connection with government coalitions, as normally the parties need not to the same extent take them into account at voting coalitions.⁴⁷

Then the party sequence, previously ascertained and deriving from the beginning of the century, probably appears to a great extent as a normative idea in the minds of party-actors and voters. Several observations intimate that this hypothesis is justified. For instance, in the history of the Social Democratic Party the following statement is made about the negative result of the negotiations on a Social Democratic cooperation at the end of the twenties: "This issue is hardly to be regretted ... a cooperation with the Conservative Party would have been felt as unnatural and could only have been a May fly".48 Similarly, in 1950 the leader of the Liberals refused to participate in a coalition government proposed to be formed of Social Democrats, Radicals, and Liberals because this coalition would be "unnati>ral"

although according to the radical negotiator he had no essential objections to a government program proposed to him.49 Thus, the party sequence probably involves that certain potential party combinations are never seriously considered. Even if the realization of for instance Social Democratic-Conservative or Social Democratic cooperation might present some advantages for both parties in the short term, it is quite probable that these short-termed advantages more than outweighed by anticipated long-term costs, especially in the form of defection of voters who have voted according to "party images", which are highly determined by the previous behavior of the parties. Pronounced deviations from a party's behavior may, of course, be utilized by competing parties for propaganda purposes.

Even if these remarks may be accepted as an initial tentative explanation of the parties' coalition behavior, it might seem difficult to explain why for example in 1968 the Radicals chose the Liberals and the Conservatives as coalition partners and not the Social Democrats. For a long time a direct and fixed cooperation between Radicals and Conservatives was considered as impossible, cf. note 47. However, a concrete analysis of the political conditions during the immediately preceding election period may clarify the Radicals' choice. The intimate cooperation in this period between the Social Democrats and the Socialists was interpreted by the Radicals as a Social Democratic distancing from the Radical Party and an approaching towards the Socialists. Previously the Social Democrats only cooperated with the party "to the right". These occurrences may be understood as an indication of the relevance of operating with one party sequence, the distance between the various parties being varying during time in spite of unchanged sequence. Such a view also fits better than for example Riker's "maximization of payoffs" aspect to the time before 1953 when the governments were not established with a special view to the possibilities of legislation majority, cf. p. 37.

The cooperation between the Social Democrats and the Socialists 1966-68 is a good example of rapprochement between two parties when a possibility to establish a majority exists. Before 1966 these two parties together had no majority, and the Social Democrats took a hard, deprecatory attitude to the "splinter party". However, when the possibility occurred after the election in 1966, the two parties entered into an intimate cooperation.⁵⁰ Something similar was in evidence in 1957 when the Justice Party was accepted in a majority government together with the Social Democrats and the Radicals.

Sometimes, as stated in Table I, no definite winning coalitions can be identified, i.e. no majority government or minority government with permanent support to form a majority. There have been three instances (cf. p. 43 f) where a winning coalition could not be established according to the party sequence. By the explanatory remarks just made these occurrences to some extent are explained. And there have also been three instances with existing possibilities within the established limits, but where various, briefly intimated circumstances prevented a fixed cooperation. Generally the following reasoning can be made: A party's primary goal is not to form a government, but as mentioned: "The party itself shall make the authoritative decisions in accordance with its evaluation system". To hold power is in itself an efficient means

to influence decisions. However, a party can also do this when it is outside government. Especially the latter occurs in case of weak minority governments. (In this connection it may be mentioned that till 1936 the Liberals and the Conservatives held the majority in the Landsting, which meant that at least one of these parties had secured its influence on legislation beforehand during the Social Democratic majority government. Thus, this situation is very similar to the one just mentioned). Therefore, we conclude that governmental coalition formation must be viewed against the background of other possible means of influence than control of government as a power position. This also applies when, with a view to the possibility of future greater influence, a party abstains from committing itself to a fixed cooperation.

Penally it can be said about the phenomenon of support parties that in essential fields the parties in question may disagree with the governing party. Thus the Radicals 1953-57 and the Socialists 1966-68 disagreed with the government on foreign and defence policies. Under such circumstances the establishment of a support relation can be strategically advantageous for both parties. Partly, the support party can avoid sharing the responsibility for every decision made, just as, in some fields, the governing party preserves a certain freedom of action in relation to third parties, and partly, both parties can attain advantages in common fields. Since Denmark's accession to the NATO, foreign and defence policies have been handled in concert by Social Democrats, Liberals, and Conservatives. Therefore, these problems were not involved in the divergencies among the parties mentioned, whereas at first the Radicals and later especially the Socialists opposed the pursued policy although they supported Social Democratic governments.

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NOTES

1 E. W. Kelley, "Techniques of Studying Coalition Formation", Midwest Journal of Political Science, vol. XII, No. l, (Febr. 1968), p. 62.

2 For a general introduction to Danish politics, see for example Kenneth E. Miller, Government and Politics in Denmark, Boston: Houghton Mifflin Company, 1968 (with a selected bibliography).

3 In the appendix the composition of the Danish Folketing 1901-1968 is shown.

4 Douglas W. Rae, The Political Consequences of Electoral Laws, New Haven and London: Yale University Press, 1967, pp. 53-58, 62.

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5 William H. Riker, The Theory of Political Coalitions, New »Haven and London: Yale University 1962.

6 Riker, oö.cit., p. 47.

7 Kellev. ob.cit.. D. 66.

8 Cf. Erik Rasmussen, "Parlamentarismens typologi i svensk teori og dansk politik. Nogle hovedpunkter". Statens almindelige Videnskabsfond. Årsberetning 1956/57. København, 1958, pp. 23-26.

9 Elections to the Folketing was called in all four situations with a change of government as the eventual result.

10 Mogens N. Pedersen, "Partiernes holdning ved vedtagelsen af regeringens lovforslag 1945-66", Historie, Jyske Samlinger, ny række VII, 3, 1967, pp. 404-435. See also Mogens N. Pedersen, "Gonensus and Conflict in the Danish Folketing 1945—66", Scandinavian Political vol.143-166.

11 Historie, pp. 418f., cf. Scandinavian Political Studies, vol. 2. p. 153.

12 Scandinavian Political Studies, vol. 2, p. 149.

13 Charles R. Adrian and Charles Press, "Decision Costs in Coalition Formation", The American Political Science Review, vol. LXII. No. 2. Tune. 1968, pp. 558f.

14 Further possible reasons for the large majorities are given by Mogens N. Pedersen, Scandinavian Political Studies, vol. 2, pp. 150f., 160f.

15 To a certain extent this may explain the finding of Mogens Pedersen (Scandinavian Political Studies, vol. 2, p. 154) that the Social Democratic Party in opposition 1950—53 never voted against the government bills in the final divisions.

16 47f.

17 Gf. Mogens N. Pedersen, Scandinavian Political Studies, vol. 2. PP. 146-148

18 Riker. oto.cit.. D. 78.

19 Rikor- o* fif r-, 1 3Q

20 Riker, op.cit., p. 40.

21 Riker, op.cit., especially pp. 54—66.

22 Cf. the following list of winning coalitions prior to 1953 with and without a "law-making majority": Year of -..,. • /-, „.. Law-Making _, . Winning Coalition „ . . ° Election Majority 1906 Reform-Liberals + Moderate-Liberals — 1913 Radicals + Social Democrats — 1915 Radicals + Social Democrats — 1918 Radicals + Social Democrats — 19201 Liberals + Conservatives + 192011 Liberals + Conservatives + 1920111 Liberals + Conservatives + 1924 Social Democrats + Radicals 5-1926 Liberals + Conservatives + 1929 Social Democrats + Radicals — 1932 Social Democrats + Radicals — 1935 Social Democrats + Radicals — 1939 Social Democrats + Radicals + 1945 Liberals + Conservatives + Radicals +

23 Michael Leiserson has suggested a "bargaining proposition" ("Factions and Coalitions in One-Party Japan: An Interpretation basedon the Theory of Games", The American Political Science Review, vol. LXII, No. 3, Sept. 1968, p. 775) stating that as the number of actors increases there is a tendency for each actor to prefer to form a minimum winning coalition with as few member actors as possible. Applied to the Danish winning coalitions mentioned the proposition would predict that as few parties as possible formed a winning coalition. However, it is easy to realize that the prediction is wrong in 1945, 1957, and 1968, because, numerically, more than two parties never have been necessary to make up a majority.

24 In 1960 the Justice Party was brushed aside at the polls.

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25 This assumption is unrealistic and will be abandoned later on. Nevertheless, it is at present analytically necessary to our reasoning.

26 Gunnar Sjöblom, Party Strategies in a Multiparty System, Lund Political Studies 7, Lund, 1968, p. 158.

27 Ibid., pp. 158f. with references. R. M. Maciver, The Modern State, Oxford University Press, 1955, pp. 406-416.

28 Cf. Erik Rasmussen, Velfærdsstaten på Vej 1913-1939, (John Danstrup og Hal Koch. eds., Danmarks Historie, vol. XIII, København 1965), p. 22.

29 Cf. Sjöblom, op. cit., p. 159.

30 Poul PolitiskeKøbenhavn:Nordisk159-170.

31 Some sufferestions in this resoect are made in the final section.

32 Cf. e.g. Kenneth E. Miller, op. cit., p. 49. Defeated on this issue in 1947 the Liberal government had called elections to the Folketing.

33 Cf. e.g. Kenneth E. Miller, op. cit., pp. 35f.

34 The classification in part was inspired from the reasoning of Riker (op. cit., chapter 6), who tries to specify situations in which proto-coalitions possess some bargaining advantage.

35 The Liberals only lost 5 seats, while the Conservatives gained 3. The F_p-value remained unchanged.

36 N.Scandinavian Politicalvol. 11.p. 155.

37 Poul Meyer, op. dt., p. 100.

38 Kenneth E. Miller, op. cit., p. 83.

39 Björn Molin, Tjänstepensionsfrågan. En studie i svensk partipolitik (The Supplementary Pensions Question: A Study in Swedish Party Politics), Göteborg, 1965; summarized in Scandinavian Political Studies, vol. l, 1966, pp. 45-58. Gunnar Sjöblom, "Analysis of Party Behaviour", Scandinavian Political Studies, vol. 11, 1967, pp. 203-222. Sjöblom, Party Strategies in a Multiparty System.

40 Sjöblom, Party Strategies in a Multiparty System, pp. 73f.

41 Cf. Erik Rasmussen, Komparativ Politik, 11, København, 1969, chapter 10, 6.

42 One should be aware that Sjöblom in his book presents a "scheme of analysis", the primary purpose of which is systematically to pose relevant questions, not to solve them. In Scandinavian Political Studies, vol. 11, p. 217, Sjöblom defines a scheme of analysis as follows: "A scheme of analysis implies a codification and classification of questions, terms used, and choice of aspects - such aspects as in the connection studied may be assumed to have an explanatory function. The scheme of analysis lays down more or less the points of suspension for an analysis, but does not constitute as such an explanation of the phenomena it is intended to study. It lays down the factors the analyst regards as necessary for an explanation but says nothing about the relations between these factors in the concrete case. It must, of course, leave the question open if the factors are sufficient".

43 Sjöblom, op. cit., pp. 81, 255.

44 Ibid. p. 255. The relevance of such a distinction has also been underlined by Erik Rasmussen, Komparativ Politik, I, København, 1968, pp. 250f.

45 Sjöblom, op. cit., pp. 266-272<. Adrian and Press, op. cit., rejecting the model of Riker, state that once the formal rules indicate the size of coalition minimally necessary, the size and makeup of the coalition is theoretically determined by an algebraic summation of the decision costs involved for participants, and incorporating a variety of economic and psychological factors. The decision costs treated are: (1) information costs, (2) responsibility costs, (3) intergame costs, (4) costs of division of payoffs, (5) dissonance costs, (6) inertia costs, (7) time costs, and (8) persuasion costs. Thus they present a scheme of analysis for the empirical study of coalition formation. But we do not think that all of their concepts are particularly useful to our special purpose, though, for instance, the concept of dissonance costs seems relevant. Dissonance costs are "the costs of conflict and disagreement within the winning coalition that result from the fact that no two persons arenever in perfect agreement with one another and, therefore, the larger the group, the more internal discord that group vail experience . . . Whenever controlling coalitions seek to minimize their size, their behaviour may be motivated not necessarily so much by a concern for maximizing individual payoffs from the coalition as by a desire to minimize decision costs of dissonance within the controlling group", (op. cit., p. 560). The notion of inertia costs involved in changing existing coalition patterns, too, might prove useful (ibid. p. 561).

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46 Sjöblom, op. cit., pp. 271f.

47 Ibid. p. 272. For example, Bertel Dahlgaard, when a leader of the Radicals, once said: ". .. we should like to negotiate impartially and amicably in the daily work ... However, we do not consider it natural for us to bring conservative ministers into the world . . ." (Folketingstidende 1953/54, col. 108).

48 Oluf Bertholt et. alt., En bygning vi rejser, 11, København 1955, p. 142.

49 Folketingstidende 1950/51, col. 767. Bertel Dahlgaard, Kamp og Samarbejde, København, 1964, pp. 109f.

50 See, e.g. Miller, op. cit., pp. 115f.