Erik Moberg ã:
A Theory of Democratic Politics


In part 11 I said that a coalition executive cannot have a purely ideological foundation. This, in fact, is a theorem which says that it is impossible to account for the formation of the executive only in terms of a simple a left-right scale, or, in somewhat more technical terms, 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. (For an account for the theoretical context of the theorem see Moberg, 2000.)

In the figure below we see a situation which can be used for proving the theorem. The figure represents a legislature with six political parties, P1-P6, each one with a certain position on the left-right scale and with a certain number of representatives in the assembly with altogether 300 members. Now, we may at first assume that there is no executive at all. If so the decisions taken by the legislature wil be determined by the median voter theorem. This means that that the decisions will become m, which is the ideological position of the party P3 and also the median position.

For proving the theorem 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 the particular figure above. 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. (This, of  course, presupposes that the coalition supporting the executive is connected, but departing from this assumption does hardly add anything of interest.) 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 model.

As a contrast, as mentioned in part 11, it is easy to account for a coalition executive in terms of interests. Thus, the parties belonging to an executive can, for instance, agree to tax those outside the coaltion and share the spoils between themselves.