March 17, 2018 

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The possibility that the voting preferences of a group of individuals results in an inconsistent, or intransitive, ranking. While consistent, or transitive, ranking of preferences is expected for individuals, such might not occur for groups of voters. If a consumer prefers good A to good B and good B to good C, then it makes logical sense that the consumer also prefers good A to good C. The voting paradox arises because a group of individuals might prefer A to B and B to C, but then prefer C to A, an inconsistent and intransitive ranking of preferences. Other related voting problems identified by the study of public choice includes the median voter principle, logrolling, and voter apathy (due to rational ignorance and rational abstention).
The voting paradox indicates problems that groups of voters might encounter when reaching a mutually satisfactory decision. In particular the ranking among alternative choices facing the group might be inconsistent and intransitive. The group might indicate a preference of option 1 to option 2 and a preference of option 2 to option 3, but then in a seemingly irrational reversal, indicate preference of option 3 to option 1.

This inconsistent ranking is unlikely to occur for an individual. If Duncan Thurly, a well-known hypothetical person, prefers chocolate ice cream to glazed donuts and also prefers glazed donuts to carrot cake, then he undoubtedly also prefers chocolate ice cream to carrot cake.

A committee of three or more people, in contrast, might express a preference for chocolate ice cream to glazed donuts and also glazed donuts to carrot cake, but then indicate a preference of carrot cake to chocolate ice cream.

The problem with this potential voting paradox is that the group of voters might not only fail to reach a decision, but the decision reached need not be efficient.

A Subcommittee of Three

The Voting Paradox
To illustrate the voting paradox, let's work through a simple example. As Chairman of the Shoe Museum Committee, Lance LaLandon has set up a subcommittee to evaluate three spending alternatives -- employee uniforms, parking lot resurfacing, and display cabinets. The three members of the committee assigned to evaluate these alternatives are Roland Nottingham, Geraldine Constance Kennsington, and Hector Hamilton.

The relative ranking of preferences of the three alternatives by the three members is presented in the exhibit at the right. Roland's first choice is the parking lot, his second is display cabinets, and his last is employee uniforms. Geraldine's preference ranking is display cabinets, followed by employee uniforms, then the parking lot. At the top of Hector's ranking is employee uniforms, with the parking lot his second choice, and display cabinets at the bottom of his list.

Putting it to a Vote

Let's see how the subcommittee ranks the three spending alternatives.
  • Parking Lot and Display Cabinets: First, let's see how this subcommittee ranks resurfacing the parking lot versus new display cabinets. Roland prefers the parking lot over the display cabinets. Geraldine prefers display cabinets over the parking lot. The deciding vote is then cast by Hector, who also prefers the parking lot project over buying new display cabinets. As such, the subcommittee ranks the parking lot over the display cabinets by a vote of 2 to 1.

  • Display Cabinets and Employee Uniforms: Now let's compare the subcommittee's relative ranking of new display cabinets versus new uniforms for the employees. Roland prefers the display cabinets over employee uniforms. Geraldine also prefers display cabinets over employee uniforms. Hector is the only member who prefers employee uniforms over display cabinets. As such, the subcommittee ranks the purchase of display cabinets to the purchase of employee uniforms by a vote of 2 to 1.
If the subcommittee prefers the parking lot over display cabinets and display cabinets over employee uniforms, it makes sense to think that it will also prefer the parking lot project over buying new employee uniforms.
  • Parking Lot and Employee Uniforms: Roland prefers the parking lot over employee uniforms. Geraldine, however, prefers employee uniforms over the parking lot. Once again, the deciding vote is cast by Hector. In this case, Hector prefers employee uniforms over the parking lot. The subcommittee ranks the new employee uniforms over resurfacing the parking lot by a vote of 2 to 1.
Even though the subcommittee prefers the parking lot over display cabinets and display cabinets over employee uniforms, it also prefers employee uniforms over the parking lot.

Are these three members crazy? Are they irrational?

Not at all. They are merely exhibiting the voting paradox.

What it Means

What sort of inference can we draw from this little example.
  • Decision Order: First, the order in which decisions are made affects the outcome. If our Shoe Museum Committee has enough funds only for two of the three projects, then the order of the vote, AND ONLY THE ORDER OF THE VOTE, determines which of the three projects will be undertaken. Any two of the three projects can be selected over the third, depending on the order of the vote. As the chairman of the Shoe Museum Committee, Lance can easily obtain whatever result he wants merely by setting the agenda.

  • Efficiency: Second, decisions made by the committee are not necessarily efficient. There is no mechanism to indicate which project provides the greatest satisfaction from available resources. Perhaps resurfacing the parking lot is the most efficiency use of resources. Perhaps it is new display cabinets. Or perhaps it is new employee uniforms. Whichever alternative might be most efficient is irrelevant to whatever choice is ultimately made by the subcommittee.

Other Voting Problems

The voting process might not result in an efficient allocation of resources due to three additional problems -- the median voter principle, logrolling, and rational voter apathy.
  • Median Voter: This voting principle, one that is well known by politicians, is that the median voter determines the outcome of an election. The median voter is the one with an equal number of voters on either side of the vote. As such, the vote cast by THE median voter is the deciding vote. However, this median voter's preference might not generate the best, that is, efficient, result.

  • Logrolling: This is the process in which voters trade votes to ensure the passage of two separate issues neither one of which would receive a majority on its own. This is commonly done in legislative bodies. It's also something that can lead to an inefficient use of resources.

  • Rational Voter Apathy: Voters can be considered apathetic because they rational choose to not be informed (rational ignorance) and not to participate in the process (rational abstention). In each case votes (and nonvoters) undertake actions that maximize utility, but such actions mean their preferences are not adequately included in the political process.


Recommended Citation:

VOTING PARADOX, AmosWEB Encyclonomic WEB*pedia,, AmosWEB LLC, 2000-2018. [Accessed: March 17, 2018].

Check Out These Related Terms...

     | voting problems | logrolling | median voter principle | government failures | rational ignorance | rational abstention | voting rules | special interest groups |

Or For A Little Background...

     | public choice | public choice politics | political game | political views | conservative | liberal | market failures | government functions | public finance | efficiency | public sector | private sector | utility maximization | fifth rule of imperfection | seven economic rules |

And For Further Study...

     | political entrepreneurs | capture theory of regulation | rent seeking | Tiebout hypothesis | principal-agent problem | government bureaucracies |

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