Those interested in this paper may perhaps also be interested in the book "Towards a Science of States: their Evolution and Properties"
Erik Moberg ©
Ideological politics and Interest
The ideological model
The interest model
The median voter theorem
The theorem of minimal, winning coalitions
The impossibility of purely ideological coalition executives
Ideological Politics and
In modern political theory there are two models, or two
conceptions, of politics, which are quite different. The one is usually
called the spatial model, but it may also be called the ideological model.
The other one does not have a common name, but it may be called the interest
model. The main tool in the former model is a scale, for instance a left-right
scale, which is used for characterizing political opinions and decisions,
and its main result is the median voter theorem. The latter one is rather
of a game-theoretical nature, and a main result is the theorem of minimal,
winning coalitions. These two models deal with very different aspects of
politics, or even very different kinds of politics. Still the differences
are often overlooked and the models are invoked almost simultaneously as
if they are applicable in the same contexts, which creates confusion. Here
I will describe the two models, and in particular the differences between
them. I start with the ideological model.
The ideological model
The basic idea is to describe people's political opinions by placing them at appropriate positions on a scale. Often the scale represents positions from what is commonly understood as extreme left positions, through the middle field of politics, to the extreme right positions. Such a left-right scale is however only one of several possible scales.
Figure 1 can be used for describing the formal properties of the model. It is assumed that the political opinion of any member in the society can be described by a point on the scale. The opinion of the voter V1 is thus represented by the point V1, and the opinion of the voter V2 by the point V2. Obviously V1's opinion is more to the left than V2's opinion. The basic idea behind the scale is however more far-reaching than that. Thus, it is not only assumed that some outside observer, for example a political scientist, can place the voters on the scale, but also that the voters themselves, can place themselves there. This means that all the members of the society understand the scale and its construction in the same way, and place themselves on the same positions as an outside observer would do.
It is furthermore assumed that political proposals, and
candidates for political assignments, can be described by points on the
scale. In the figure the five C may for example be the positions
of five candidates. The position may be thought of as the position a candidate
will support, or fight for, if elected, and is thus not necessarily the
position the candidate holds by herself. Again it is assumed that all concerned
are in agreement about the candidates' positions. Thus all the members
or voters in the society, the candidates themselves, and outside observers,
if there are any, will place the candidates in the same positions.
An additional important assumption usually made is that each member of the society ranks candidates, or other political proposals, lower the farther away, in either direction, they are from his or her own position on the scale. This means, for example, that the voter V1 ranks C2 before C1 and also that the same voter ranks C3 before C4, and C4 before C5. When this assumption is fulfilled it is easy to see that each voter's preferences can be represented by a curve like a mountain with a top at the voter's own position and slopes going steadily downward in both directions from that position. The assumption is therefore often referred to as the single peakedness condition.
According to the assumptions now presented it is not only possible for each member of the society to place her- or himself on the scale in a way that all agree about. The single peakedness condition also means that this same scale is the base for each member's preferences. The statement above that the citizens of the society agree about the construction and the meaning of the scale as such is thus further emphasized. It is only their positions on the scale that make the citizens different. This, it may be argued, is typical for ideological opinions.
An ideological opinion, as I use the concept here, is an opinion about the ideal character or construction of society. Some people with a leftist inclination hold for example that the ideal society has a very large public sector, whereas other with a rightist inclination hold that the ideal society has a very small public sector and a large scope for market transactions. Socialism and liberalism are obvious ideologies in this sense.
This concept of ideology is in good agreement with a definition given by Melvin Hinich and Michael Munger. Their definition (1994, p 11) is this one: "Ideology: an internally consistent set of propositions that makes both proscriptive and prescriptive demands on human behavior. All ideologies have implications for (a) what is ethically good, and (therefore) what is bad; (b) how society's resources should be distributed; and (c) where power appropriately resides."
In particular it may be noted that Hinich and Munger stress
that an ideology is a consistent, or a coherent, set of propositions, and
thus something quite articulated, elaborated and far-reaching. It is therefore
not surprising that words such as Weltanschauung (Downs, 1957, p
109 f) occur in discussions about ideologies. Furthermore Hinich and Munger
emphasize that knowledge about ideologies is widespread and common. Ideologies,
they write (1994, p 5), "are quite different from personal belief systems
or heuristics to guide individual choice. Ideological messages contain
coherent statements of how to choose and what to do. Citizens can, on average,
agree on the content and meaning of these statements, though their evaluation
of the worth of the statements may differ. As a result, ideologies are
the basis for choice in group decisions, and provide the language in which
groups debate and disagree."
In figure 1 only two voters were indicated but obviously the societies, which we are interested in when discussing political opinions, are much greater than that. Usually we are thinking about millions of citizens. When discussing such multitudes of people it is obviously impossible to represent each individual by a single point as in figure 1. In such cases opinions may be represented by a curve as in figure 2. As in the former case the scale may be a left-right scale. The area between any two points, say the marked area between the points A and B, is thought of as proportional to number of people with political positions between A and B. The curve thus gives a description of the political opinions in the society because it tells us how many members of the society there are in the interval between any two possible political positions. This kind of presentation of an opinion is very compact and therefore convenient in many situations. It is, for example, often used for discussing political parties and their strategies, assuming that parties are trying to maximize their votes.
Hitherto we have confined ourselves to opinions or attitudes
which can be represented by a single scale and the model has in that sense
been one-dimensional. Sometimes, however, it may be felt that a
reasonably accurate description of a political situation requires more
than one scale. In addition to a left-right scale it might for example
be appropriate to add some kind of religious scale, or a scale incorporating
attitudes to language or nationality issues, or perhaps both. In such cases
an individual's political position will be represented by a point on each
of the scales, which, of course, is the same as a point on a surface in
the case with two scales, or a point in a three- or multidimensional space
in the cases with three or more scales.1
In these cases we speak about two-, three- and multidimensional spatial
models of political opinions.2
The interest model
People who express ideological opinions thus talk about society in its entirety and its construction, and their concerns are about justice, fairness and effectiveness. People who express interests, as I use the concept here, talk, on the contrary, about their own immediate preferences, such as their own demands, or claims, on resources in society. Interests as such are thus independent of notions about ideal societies, they exist just because people usually want to have more of the goods of this world. This, however, does not preclude that some interests may be supported by some ideologies.
The interest concept is illustrated by table 1.
It is assumed that a society is divided into five subsets called S1-S5.
The subsets are assumed to be of equal size and to cover, together, the
whole society, making each of them contain 20 % of the population. We may
also assume that the subsets are proportionally represented in the legislature,
where decisions are taken by the simple majority rule.
Now, assume that the representatives of the subset S1 make the proposal P1 that all people except the ones in subset S1 shall be taxed, say by 25 monetary units each, and the money shall be transferred to the members of S1, who thus get 100 monetary units each. Assuming that representatives support proposals which are favorable to their own constituencies, and vote against proposals which are unfavorable, this proposal, voted on in isolation, will obviously only get 20 % of the votes in the legislature and is thus rejected.
Let us now continue by assuming that the representatives of the other subsets make similar proposals for their subsets. That gives us the five proposals indicated in the table. Again, each of these proposals, voted on in isolation will obviously be rejected. But if some of the proposals are linked, and thus not voted on in isolation, things may become different. Imagine, for example, that the three proposals P1-P3 are amalgamated into a single proposal. If so that proposal will be supported by 60 % of the legislators in the assembly, and thus it will pass. The result is the transfers shown in the last line in the table. The majority S1-S3 exploits the minority S4-S5.3
The fact that the subsets in the table are rather few
and of the same size, and that their proposals correspond exactly to each
other, is, of course, of no principal importance. The only reason for these
assumptions is the wish for simplicity. In reality things may be much more
complicated. The subsets may be many more, they may be of different sizes,
and their proposals favoring themselves may be of various kinds. Still,
the example illustrates the important idea that a number of minority interests
may sometimes combine to form a decisive constellation, which exploits
the losers in some way, for example by taxing them and sharing the spoils.4
Furthermore, it is clear, that the proposals P1-P5,
although they are simple and straightforward, and easily imaginable in
ordinary politics, cannot be represented by points on simple one-dimensional
scale. This, of course, is a crucial difference between the interest model
and the ideological model.
The median voter theorem
The median voter theorem, in its simplest form, is formulated within the framework of a unidimensional, spatial model. The theorem says that the opinion held by the median voter will become the decision, if the simple majority rule is used. The median voter is the voter having as many voters on her one side of the scale as on her other side. The single peakedness condition, as defined above, is a condition for the truth of the theorem.
The rigorous formulation and proof of the median voter theorem is due to Duncan Black (1948). This result, by the economist Black, has been hailed by the political scientist William Riker (1990, p 178) as "certainly the greatest step forward in political theory in this century". For sure there is a lot of truth in this, but nonetheless the claim is somewhat exaggerated. Black's paper did not come out of the blue. There were predecessors. The most obvious, perhaps, is the economist Harold Hotelling who in 1929 alleged that competing political parties, at least when there are just two of them, tend to take positions very close to each other in the middle of the political spectrum. "The competition for votes", he wrote (1929), "between the Republican and Democratic parties does not lead to a clear drawing of issues, and adoption of two strongly contrasted positions between which the voter may choose. Instead, each party strives to make its platform as much like the other's as possible."
Even political scientists came close to formulating the theorem. Thus Elmer Eric Schattschneider (1942, p 85) claimed that "The second effect of the two-party system is the fact that it produces moderate parties. ... When one stops to consider the amount of thought and energy that has been devoted to the effort to protect people against oppression, it is difficult to imagine anything more important than the tendency of the parties to avoid extreme policies." Furthermore, Schattschneider brings A. Lawrence Lowell, who wrote as early as just around 1900, into his own argument in this way: "A generation ago President Lowell5, writing about English major parties, said that the Liberal and Conservative tended to move toward the political center of gravity, i.e., they tended to be alike. Indeed, the most common criticism made of the American parties is not that they have been tyrannical but that they have been indistinguishable. (There is a strong) tendency of the parties to move toward the middle of the road."
Similarly V. O. Key, Jr., when describing the US political parties in election campaigns in his extensive study Politics, Parties, & Pressure Groups, first published in 1942, stated that (1964, p 220) "Each party leadership must maintain the loyalty of its own standpatters; it must also concern itself with the great blocks of voters uncommitted to either party as well as with those who may be weaned away from the opposition. These influences tend to pull the party leaderships from their contrasting anchorages toward the center. In that process, perhaps most visible in presidential campaigns, the party appeals often sound much alike and thereby contribute to the bewilderment of observers of American politics."
Nine years later Maurice Duverger draw a similar conclusion when discussing the British parties in his great study Political Parties, first published in 1951. "Let us take", he wrote (1964, p 387 f), "a precise example, that of contemporary Britain, neglecting the Liberal party, which is no longer important. Who decides whether the Conservative or the Labour party shall win the election? Not their fanatical partisans who, being unable to cast their vote for any party further to the Right or to the Left, will naturally vote for them whatever they do, but the two or three million moderate Englishmen, politically situated at the Centre, who vote sometimes Conservative, sometimes Labour. To win their votes the Conservative party is forced to attenuate its Conservatism and Labour its Socialism, both of them adopting a calm tone, a reassuring aspect. Both will have to draw up policies clearly aimed at the Centre and therefore profoundly similar. We arrive at the paradoxical situation that the Centre influences the whole of parliamentary life in the very country in which the electoral system prevents the formation of a Centre party." True, Duverger's work appeared three years after Black's essay, but, considering the different cultures of Economics and Political science, it would hardly be surprising if, at that time, Duverger was not aware of Black's contribution.
In the world of the median voter theorem there are thus,
in order to summarize, no redistributions, or transfers, dictated by interest,
and consequently no exploitation. Everything that happens is prescribed
by ideology and the people, by their voting, just choose the ideology.
Furthermore, in remarkable contrast to interest politics, everybody, in
a sense, influences the choice, in spite of the fact that the simple majority
rule, rather than the unanimity rule, is used. Thus any voter who votes,
rather than abstains from voting, or who abstains from voting rather than
votes, or who changes from one side of the median to the other side, affects
the decision. The only change, which does not influence the decision, is
a move from one position to another on the same side of the median.
The theorem of minimal, winning coalitions
William Riker did not only have a very high estimation of the median voter theorem. He is also the father of the other important theorem at issue here, namely the theorem of minimal, winning coalitions. This theorem is as important for interest politics, as the former theorem is for ideological politics. The theorem says (Riker, 1962) that a political coalition tends to be as small as possible, as long as it is winning. To be "winning" here essentially means to be "able to dictate the outcome". If, for instance, we are dealing with a voting assembly, and if the simple majority rule is used, than any decisive constellation, i.e. any constellation with more than 50 % of the votes, is winning.
This conclusion follows from Riker's visualization of politics, in this context, as a zero-sum game. He imagines that the people within the winning coalition will, in essence, exploit those outside the coalition, for instance by taxing them and sharing the spoils. In such a game each individual in the winning constellation gets more the fewer they are, and the more numerous the exploited outsiders are. Hence the attraction of the minimal, winning coalition.
The idea is easily illustrated with the example in table 1 above. Let us assume that the subsets S1-S4 in the table, rather than the subsets S1-S3, form a majority. The result, as is easily checked, will then be that the members of the subsets S1-S4 get 25 monetary units each, and that the members of the exploited set S5 loose 100 units each. The members of the subsets S1-S3 will thus get 25 units less than in the situation originally considered, and consequently they will loose by engaging S4 in the coalition. Although it is quite obvious it may also be stated explicitly that all favors, by the same reasoning, disappear if all subsets unite to support each other in a unanimous decision. In that case the members of each subset wins 100 monetary units, but also have to pay 100 (425) units, and thus the outlays exactly cancel the favors. The important conclusion to be drawn is that exploitation, in the sense discussed, presupposes that some kind of majority rule is used.
The theorem of minimal, winning coalitions belongs to
a tradition in political thinking, which emphasizes the role of interests.
An early representative of this tradition is Wicksell (1896), and in our
days we have, in particular, Buchanan and Tullock (1962). Since they are
aware of the damages which interests may cause, these scholars consider
the unanimity rule as the ideal decision rule. The only reason for abandoning
it is the practical problems which its application encounters. The transaction
costs may for example be too high. The abandoning of the rule in favor
of some kind of majority rule, for instance a qualified majority, is thus
always a compromise. The decision making will be easier, but the price
to be paid is that those outside the deciding majority may be hurt, either
accidentally or intentionally. Buchanan and Tullock talk about external
costs. Riker brings these apprehensions to their logical end, and simultaneously
formulates a piece of theory about real politics. First he says that the
intentional exploitation of the outsiders is maximized when the deciding
coalition is as small as possible, but still decisive. Then he predicts
that exactly for this reason such minimal coalitions will form.
The impossibility of purely ideological coalition executives
The theorem of minimal, winning coalition thus belongs to interest politics, and the median voter theorem to ideological politics. For some people all politics is interest politics, and for some other ones all politics is ideological. These people obviously must settle for their own theorem. For the first ones only the minimum, winning coalition theorem is interesting and valid, and the median voter theorem is just a mental exercise dealing with unreal things. For the other ones it is the other way round. But it need not be that simple. The position taken here is that politics is sometimes dominated by interests, sometimes by ideology, and the problem is to find out when it is the one way or the other. Within such a framework the two theorems do not exclude each other. Rather both can used as valuable, integrated parts of a more comprehensive theory. The one is used for describing and explaining interest politics in cases where that is appropriate, the other one for understanding ideological politics.
As an illustration to this thesis about different spheres of application for the two theories, and their theorems, I will present a result which is of crucial importance for parliamentary systems with coalition executives. Most parliamentary countries with proportional elections are of this type, and some with majority elections as well. The theorem says that it is impossible to account for the formation of the executive within the framework of the spatial model, at least in its one-dimensional version. In a less technical vocabulary this means that it is impossible to account for the formation of the executive only in terms of a simple ideological scale, such as, for instance, a left-right scale.
As an introduction to the proof it may first be noted
that executives, in fact, usually come into existence. This indicates that
it is important for the parties to form an executive rather than to live
in a situation without any executive at all, and it also indicates that
it is important for the parties to become members of the executive rather
than to be left outside. If it were not like that no executive would be
Now, the conditions for the theorem are indicated in figure 3, where we see, as an example, the ideological positions of the six political parties P1-P6, and their number of representatives in a legislature with altogether 300 members.
Within this framework I will now try to account for the formation of an executive, and I will find that that is impossible, which proves the theorem. Let us start by considering a situation without any executive at all. In such a situation the decisions, according to the median voter theorem, would become m. This is the ideological position of the party P3, which holds the median position.
Then we may compare this situation with one in which there is an executive. Clearly, if the executive is to make any difference at all, and thus to be of any interest for its members, its policy must diverge somewhat from m. We may for example think about an executive which has the policy indicated by l, and thus a leftist inclination, and which is supported by the majority composed of P2 and P3.
Now it is easy to see that l is worse than m for P3. P3 is therefore in fact disfavored by belonging to the executive. Therefore, contrary to our assumption, P3 will not be member of the executive or support it. Our assumption that P3 belongs to the executive, since it is advantageous to do so, thus leads to a contradiction. This kind of argument is usually called a reductio ad absurdum. If it is possible to show that an assumption leads to a contradiction, then it is also fair to conclude that the assumption is unreasonable or absurd.
So far I have only dealt with the particular example in
figure 3. Obviously we have to ask if other examples, with other possible
party constellations in the legislature, also lead to contradictions for
the same reasons. The answer is in the affirmative since the examples,
however they are varied, will always have two crucial properties. First,
the executive's policy must always diverge from m since otherwise
the executive would not matter at all and, consequently, it would not be
important to be a member of it. Second, since the constellation supporting
the executive has to be a majority, it necessarily includes the median
member of the assembly.6 Thus, contrary
to our assumptions, the executive will always include at least one party
member for whom the membership is a unfavorable. We are thus entitled to
draw the general conclusion that it is impossible to account for the formation
of the executive within the framework of a simple, one-dimensional ideological
As a contrast it is very easy to account for the benefits of executive membership within the framework of the interest model. A possible mechanism is that the members of the executive engage in logrolling benefiting themselves at the expense of the non-members. As an example we may consider the situation illustrated in table 1 above. Let us assume that S1-S3 are political parties, which form an executive. Furthermore we assume that the proposals P1-P3 constitute the executive's governmental program, which will be implemented during the coming parliamentary period. Obviously that is to the advantage of all the parties in the executive and their supporters, and consequently there is no problem in accounting for the formation of the executive.
If there are only two parties in the legislature, or if
one party has a majority of its own, the argument above about the impossibility
of an ideological explanation does not apply. Consider, for example, the
situation in figure 4. There P2
can easily, by itself, form an executive, which can execute a policy equivalent
position on the ideological scale, and obviously this is to the advantage
for the party. Here it is thus perfectly possible to account for the executive
formation in purely ideological terms.
1 It is because of these spaces that
the model is called the spatial model
2 Even if the idea of multidimensional models is quite simple and straightforward it is important to note that the analysis of optimal strategies, and similar problems, are far more complex than in one-dimensional models and, what is more important, much less conclusive. These kinds of problems are, however, not treated here.
3 The property of this outcome, on which I focus here, is that it is favorable to the majority. It is, however, not an equilibrium outcome.
4 This idea has been elaborated in various ways by different scholars, for example by Anthony Downs (1957, pp 55 f).
5 A. L. Lowell was president of Harvard University.
6 This, of course, presupposes that the coalition supporting the executive is connected. Departing from this assumption does, however, hardly add anything of interest.
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