Academic journal article Atlantic Economic Journal

Why No Cycles

Academic journal article Atlantic Economic Journal

Why No Cycles

Article excerpt


This article explains the absence of cycles in regular governmental voting procedures. Most acts of Congress and other legislative bodies are the result of the negotiation carried on in private. As a result of this negotiation, the bill would be impossible to beat by any ordinary alternative. (JEL D0, D5, D9)


Condorcet first discovered the cyclical voting possibility and thus it has been known since before he had his difficulty with Robespierre that there may be no choice that can get a majority over all of the others. This can lead to cycling or, if a reintroduction of alternatives is forbidden, an outcome which is an accidental result of the order in which the proposals are taken up.

I do not want to repeat the proofs here, but the fact remains that although mathematically all of this looks very sound, there do not seem to be many real life examples. Riker thought he had found one at one point, but most people do not agree that he did. In any event, the votes that he dealt with did not actually cycle. He thought that clever politicians had used a potential cycle to stymie an outcome of which they disapproved. Eventually, there was a successful maneuver by their opponents and they lost. To the best of my knowledge, this is the only case in which anybody has claimed that they found a cycle in the real world.

The other possible outcome of intransitivity, an outcome dependent upon the order of the voting would be hard to detect. For reasons to be discussed below, this is probably rare.

This does not mean that voting outcomes are unchanged over time. Not long ago, Congress enacted a law that would provide nursing care for people who are seriously ill, and the cost fell mostly on upper income people. This was a fairly uniformly popular bill when it was passed, but immediately upon being passed, it met a storm of criticism, mainly from upper income retirees. As a result, Congress repealed it with great speed. This is one of the rare cases of quick repeal, but it was not cyclical.

Potential cycles would seem to be very common. Stockman [1986] discusses several times "opening the federal 'soup kitchen'." This is negotiation in the last hours before a vote to get people "off the fence." He goes on to say:

"At this point democracy becomes not a discussion of the ideals of Jefferson, or the vision of Madison. It becomes a $200,000 feasibility study of a water project, the appointment of a regional director of the Farmer-Home Administration of Western Montana, etc." [1986, p. 221].

Once the bill has been passed, it would seem clear that another bill in which the $200,000 feasibility study of the water project is deleted, but is otherwise identical to the one passed, would get 434 votes to 1 (see Table 1). This in turn would be beaten by a simple repeal of the basic bill so the cycle could start again. This does not happen, and much of the rest of this study will be devoted to explaining why not. [2]

It should be noted that this kind of particular item for one legislator is not confined to the U.S. Mr. Major lost his formal majority in the House of Commons when a longtime conservative back-bencher surrendered the whip because the government had not provided a 24-hour emergency room for his constituency.

It seems likely that most acts of the U.S. Congress, and for that matter the British Parliament, are susceptible to this problem. There almost always are some special provisions that have been put in to acquire a few marginal votes. Deleting them, taken by itself, would get a majority. Such cycles are not observed in any modern legislative body.

It can be said that a great many people think that the Rules of Order are such that the bill does not run through cycles because the proposal once beaten cannot be reintroduced. Looking at proceedings in any legislature, it is rare that something that was once beaten gets back on the agenda, but is it not the Rules of Order that prevent it. …

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