In this online exercise, we will take a more detailed look at cyclical majorities that are discussed in chapter 2. Differently from the exercises for the other chapters in the book, we will not introduce a dataset here, as chapter 2 focuses on the theoretical model used throughout the book. Nevertheless, we can still think of tasks and questions that you should attempt to answer as you work through the theoretical exercise we present here.

Table 1: General Tasks and Questions

Tasks
When can we consider politics to be unidimensional vs multidimensional?
Under what conditions within a political system is it easier to change policy? When is it harder?
How can we avoid the problem of cyclical majorities and achieve stable policy within a political system?

Starting Point

As we learned in chapter 2, political positions can be depicted in a one- or multidimensional model. Although, or rather because, these models simplify reality, they provide us with a valuable tool to understand political decisions. Figure 1 shows such an arrangement of political positions on two dimensions, the level of public spending on a park and the level of access to it. In this example, we have five actors, A, B, C, D, and E. All of these actors have one distinct position in the two-dimensional model. For example, actor A wants a high level of spending and open access to non-taxpayers. In the following, we assume that the voters will have to make a decision about how to run the park. Thus, we need to understand which compromises have a majority among the five citizens.

Figure 1: Preferences of Actors in a Two-Dimensional Space

Indifference Curves

Which points do the five voters prefer over a status quo policy that is currently in place? We can easily model this spatially. Figure 2 shows an example for two of the actors (actor B and D) and a hypothetical status quo SQ (with moderate spending for the park and limited access to non-taxpayers). Because an actor always prefers policies closer to their ideal point, actor B should prefer any policy that is closer. This is shown using an indifference curve, the circle that is centered at B’s ideal point with a radius equal to the distance between B and the status quo. The actor B is indifferent to the SQ for all points that lie on the circle (because there are equally good policies). Anything inside the circle is preferred by B, shown by the colored area. Similarly, D prefers all points inside the circle around her position. Note that there is some overlap in the circles. Both B and D would prefer policies in this overlapping area, the so called winset of the status quo, and could agree on a policy proposed within this winset if they were the only actors.

Figure 2: Indifference Curves

A First Proposal

Imagine the five voters come together in a town hall meeting. The mayor is part of this group and holds preferences at point D. Assume for now that this town hall meeting is an open forum in which all policy proposals can be voted against each other alternative. That is, no one has gatekeeping or agenda-setting powers, but simply the alternative supported by a majority should prevail.

Suppose now that mayor D speaks first at the meeting and introduces his plan, located at his own position, D. Following this presentation, citizen E comes forward and proposes a new proposal P1. This new proposal is now voted against proposal D. It turns out that P1 is preferred by a coalition of A, B, and E. This is shown in Figure 3, which depicts the areas in the policy space that each citizen prefers over proposal D. Remember that the indifference curves show at which point the actors are indifferent between policy position D and a policy alternative (because it is equidistant from the actors’ respective ideal points). An actor prefers any outcome within her circle (indifference curve) to the status quo. She is indifferent between the status quo and any point along the curve, and she prefers the status quo over any point outside of her indifference curve.

Figure 3: Voting on P1 Versus Proposal D

Counterproposals

P1 has now obtained a majority, but the discussion is not over. Citizen A is not happy with the outcome; she wants a better park, i.e. higher level of spending, but roughly the same level of access. She proposes policy P2, which is voted against P1 (Figure 4). This proposal also obtains a majority, with A, B, and C voting for it. Actors D and E would be worse off under this alternative and oppose the measure.

Figure 4: Voting on P2 Versus P1

It looks like the town has arrived at a solution, but before the meeting is over, mayor D gets to get a final say in the meeting and suggests as a compromise her initial proposal D. It turns out that, compared to P2, C, D, and E all prefer the policy D, reflecting a lower level of spending and more restrictive access to the park (see Figure 5). Thus, the policy has cycled from an initial position to another outcome and then back to the initial proposal.

Figure 5: Voting on D versus P2

Conclusion: Cyclical Majorities

In a particular literature on group decision-making known as “social choice”, this finding that policy outcomes can move around in a policy space with two or more dimensions is known as the chaos theorem, and it was initially described by Richard McKelvey. Formally, the theorem states that in a multidimensional spatial setting, there is no stable policy outcome that beats all other policy alternatives by majority in a pairwise comparison. Whoever controls the sequence of voting, can control the collective choice of the society. Box 2.1 in the book explains the phenomenon of cyclical majorities in more detail.

The finding is disconcerting: it means that if societies need to decide complex issues simultaneously (i.e. in a multidimensional space) and if they use a simple democratic decision rule (i.e. pairwise voting of each alternative against another one by majority), then we actually do not know what this society collectively wants. Any outcome can feasibly be legitimate because it gathers a majority of voters. How do we end up with stable outcomes? This is where the design of political institutions becomes crucial. We can limit the actors who can set the agenda in constitutions (e.g. cabinets or parliamentary parties in parliamentary democracies or the Commission in the European Union). Additionally, political systems can limit the amendment possibilities to the initial proposal, or the rules may insist that any final proposal be compared to the status quo. Finally, the rules could raise the threshold for decision-making from a simple majority to a supermajority (e.g. as in the Council of the European Union). All of these possibilities make stable policy outcomes more likely. If agenda-setting politicians can use their position to pull policies in its preferred direction, then holding such actors to account becomes crucially important. This is why electoral accountability (i.e. the ability to remove governments from office through elections) is important for understanding how democracies work.