# ML Wiki

## Monotonicity

The monotonicity is a Voting Theory criterion/principle that characterizes voting methods for choosing the winner.

Monotonicity is satisfied when:

• if
• an alternative $x$ rises or does not fall in the individual ordering and
• $x$ was preferred to another alternative $y$ before the change in the individual orderings
• then
• (1) $x$ should still remain at least at the same position
• (2) if $x$ is a winner, it should remain the winner
• (note that (1) $\Rightarrow$ (2))

## Theorems

This principle is used in two important Voting Theory theorems:

## Methods

Methods that respect Monotonicity:

Methods that don't respect Monotonicity