Agenda Power

Formally, agenda power is the capability of an agenda setter to manipulate the specific order in which N voters will consider J alternatives being offered. Contingent on the particular preferences of the voters, this facilitates indirect control over the outcome of the votes, the alternative(s) actually chosen by the decision process. Agenda power is typically discussed in the context of majority rule and pairwise comparisons. More generally, it refers to the ability to organize legislative business in parliamentary settings.

A (classic) example is as follows. Consider three voters voting on three alternatives x, y, and z. Suppose that voter 1 has preference xP1yP1z, voter 2 has preference zP2xP2y, and voter 3 has preference yP3zP3x (where “P” stands for “strictly prefers to”). This produces a Condorcet paradox: x is majority preferred to y, y is majority preferred to z, and z is majority preferred to x. Suppose now that an individual—say voter 2—has agenda power in that he or she can decide the order in which the alternatives will be considered. By making the first vote between x and y (x wins) and the second vote between x and z (z wins), voter 2 can attain his or her preferred outcome. This example holds, with changes made, for x and y as first preferences too.

Notice that voting cycles are necessary but not sufficient for agenda power. Consider the following example, devised by Peter Ordeshook: suppose that there are N = 3 voters with preferences over J = 8 alternatives denoted a, b, c, d, e, f, g, h given by Table 1. For the preferences described in Table 1, there is a cycle through the alternatives {a, b, c} and a cycle through the alternatives {d, e, f, g, h}, and any alternative from the first set would beat any alternative from the second. So someone with agenda power could obtain a, b, or c, but could not obtain, say, g. Technically, we say that {a, b, c}are in the top cycle.

Agenda power as described exists only when there is no Condorcet winner. A Condorcet winner is an alternative that can beat every other alternative in a pairwise vote. If a Condorcet winner exists, the voting cannot be ordered such that the social preference moves away from it. The almost certain absence of a Condorcet winner in an alternative space of three or more dimensions or in a [Page 12]continuous space (as demonstrated in Richard D. McKelvey's chaos theorem) implies that whoever controls the order of voting can achieve any point in the space as a final voting outcome.

Table 1 Not all cyclical social orders facilitate agenda power

McKelvey's result (like the previous examples) requires that voters vote sincerely, but they might vote in a strategic fashion. If voters know each other's preferences (or at least the majority preference between every pair of alternatives), they can “look down the agenda tree and reason back” to see which alternatives will be paired later in the voting process and decide how to vote at the outset. They can vote strategically to defeat any attempt at agenda manipulation. As an example, suppose that there are two stages to voting: first, on an amendment to a bill, versus the original text of the bill; second, on the bill versus the status quo. The comparison to the status quo in the last stage is actually the method used in the U.S. Congress. Assume that a legislator prefers the amended bill to the unamended bill, and prefers the unamended bill to the status quo. Suppose the legislator is also aware that the amended bill would lose to the status quo, but that the original bill would win against it. Then he or she has a strategic incentive to vote against the amendment when it faces the original bill, but for the original bill when it subsequently faces the status quo. Hence, the legislator does not vote sincerely when considering the amendment.

...