Single peaked preferences
Restriction on preferences in social choice / From Wikipedia, the free encyclopedia
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Single-peaked preferences are a class of preference relations. A group has single-peaked preferences over a set of 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, which is to select the median quantity; this results in the median voter theorem.[citation needed] It is truthful because the median function satisfies the strong monotonicity property.
The notion was first presented by Duncan Black[1] and later by Kenneth Arrow.[2]