Single peaked preferences
Single-peaked preferences are a class of preference relations. A group of agents is said to have single-peaked preferences over a set of possible outcomes if the outcomes can be ordered along a line such that:
- Each agent has a "best outcome" in the set, and -
- For each agent, outcomes that are further from his or her best outcome are preferred less.
Single-peaked preferences are typical of one-dimensional domains. A typical example is when several consumers have to decide on the amount of public good to purchase. The amount is a one-dimensional variable. Usually, each consumer decides on a certain quantity which is best for him or her, and if the actual quantity is more/less than that ideal quantity, the agent is then less satisfied.
With single-peaked preferences, there is a simple truthful mechanism for selecting an outcome: it is to select the median quantity. See the median voter theorem. It is truthful because the median function satisfies the strong monotonicity property.
The notion was first presented by Duncan Black and later by Kenneth Arrow.