Median mechanism
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A median mechanism is a voting rule that allows people to decide on a value in a one-dimensional domain. Each person votes by writing down his/her ideal value, and the rule selects a single value which is (in the basic mechanism) the median of all votes.
It has been suggested that this article be merged into Median voting rule. (Discuss) Proposed since March 2024. |
The median mechanism can be used, for example, to decide on the size of the country's budget: each person says what the ideal budget size should be, and the chosen size is the median of the declared values. Another possible application is deciding how long the annual school vacation should be: each person says the ideal length in days, and the median is selected. A third example is: deciding what temperature the air-conditioner in an office should be set to. A fourth example is a facility location problem in one dimension.
An important feature of the median mechanism is that it is truthful: if the utility of each voter is higher whenever the chosen value is closer to his ideal value, then an optimal strategy for each voter is to declare his true ideal value, regardless of what other voters say. This is in contrast to other natural mechanisms, such as the average mechanism. With the average mechanism, if the current average is lower than a voter's ideal value, then it may be optimal for the voter to declare a higher value (and vice versa), in order to "pull" the chosen value towards his ideal value. The median mechanism is immune to such manipulations.
Moreover, every mechanism that is truthful and anonymous is a generalized median mechanism - a mechanism that inserts some fixed "society votes" and then selects the median (see below).[1]