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The paradox of voting implies a situation in which individuals in a society cannot rank their preferences so that the overall society's preference for the public good can be established. In such cases, paired choice majority voting does not give conclusive preference for any public good. This is explained in the next step.

In the below table, Colbert, Fallon, and Kimmel are ranking three public goods (Courthouse, School, and Park) according to their preferences.

The first look at the table does not show any dominant preference for any of the public goods. Thus, you will use paired-choice majority voting in which a first vote is held between any two of the three goods, and then the winner is compared with the left public good to see which one wins.

You will start by taking the pair of Courthouse and School and observing each individual's ranking. The public good, which will have a better ranking, will be preferred. For example, Colbert gives Courthouse a second choice and School a third choice; comparing these two, Colbert prefersCourthouse over School. Similarly, you can find this for others, as done below.

You can see that there is no overall majority for one particular public good. There is only a pairwise majority. For example, the Courthouse is preferred over School, and School is preferred over Park. This should mean that Courthouse should be preferred over Park as well, but this is not the case above. This is the paradox of voting, where ranking preferences can lead to irrational outcomes.