Monotonicity (mechanism design)

In mechanism design, monotonicity is a property of a social choice function. It is a necessary condition for being able to implement the function using a strategyproof mechanism. Its verbal description is:

In other words:

There is a set ${\displaystyle X}$ of possible outcomes.

There are ${\displaystyle n}$ agents which have different valuations for each outcome. The valuation of agent ${\displaystyle i}$ is represented as a function:

which expresses the value it assigns to each alternative.

The vector of all value-functions is denoted by ${\displaystyle v}$.

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