  Device independent protocols rely on the violation of Bell inequalities to
certify properties of the resources available. The violation of the
inequalities are meaningless without a few well-known assumptions. One of these
is measurement independence, the property that the source of the states
measured in an inequality is uncorrelated from the measurements selected. Since
this assumption cannot be confirmed, we consider the consequences of relaxing
it and find that the definition chosen is critically important to the observed
behavior. Considering a definition that is a bound on the min-entropy of the
measurement settings, we find lower bounds on the min-entropy of the seed used
to choose the inputs required to deduce any quantum or non-local behavior from
a Bell inequality violation. These bounds are significantly more restrictive
than the ones obtained by endowing the seed with the further structure of a
Santha-Vazirani source. We also outline a procedure for finding tight bounds
and study the set of probabilities that can result from relaxing measurement
dependence.
