This work initiates the study of algorithms
for the testing of monotonicity of mechanisms.
Such testing algorithms are useful for
searching dominant strategy mechanisms.
An $\e$-tester for monotonicity
is given a query access to a mechanism,
accepts if monotonicity is satisfied,
and rejects with high probability if more than $\e$-fraction
of the mechanism values must be modified to obtain the property.

The notion of the distance from monotonicity essentially
suggests a notion of distance from truthfulness.
A direct mechanism is $(1-\e)$-truthful if reporting
the true valuation is a dominant strategy for every player $i$
with probability $1-\e$ (assuming $v_{-i}$ are uniformly distributed).
This raises the question of how a local measure of violation,
representing the point of view of the individual player,
relates to the global measure of violation,
representing the point of view of the mechanism designer.