Single Peaked Preferences and the Median Voter Theorem

In the last entry on voting paradoxes, I mentioned that things are different if preferences are single peaked.

Let’s look at another scenario. Again, consider a set of policies A,B,C following a sequence from  (A) less to more extreme (C) - maybe tax rates or some level of spending- with (B) being the intermediate policy. Suppose voters rank policies in order of preference/utility as follows:

Voter X:  ABC
Voter Y : CBA
Voter Z : BCA

In this case, no matter what order is undertaken, B always ends up being the law that is enacted. These preferences are single peaked. Each individual has a most preferred choice along the A to C spectrum. If you move away from that choice (in the A-B-C spectrum) they prefer the other choices less.  In the previous example, voter Y did not have single peaked preferences and that is what caused the cycling or order dependent outcomes. With single peaked preferences there is a new problem. With single peaked preferences, the median point of the preference distribution will elicit the most votes. Only those laws or candidates with a centrist twist will get the majority of the votes. Only those voters with centrist views will be happy, and it makes it very difficult for candidates to be elected if they want to bring about major reforms. This phenomenon is referred to as the ‘median voter theorem.’

Both voter cycling (when preferences are not single peaked) and the median voter theorem can have negative implications for majority rule policy adoption. Voters are either governed by irrational ever changing majorities, or they are subjugated by entrenched majorities whose views are maintained by the status quo of median preferences.

References:

Lemieux, Pierre, The Public Choice Revolution. Regulation, Vol. 27, No. 3, pp. 22-29, Fall 2004. Available at SSRN: https://ssrn.com/abstract=604046