  For a compact surface $S = S_{g,n}$ with $3g + n \geq 4$, we introduce a
family of unitary representations of the mapping class group Mod($S$) based on
the space of measured foliations. For this family of representations, we show
that none of them has almost invariant vectors. As one application, we obtain
an inequality concerning the action of Mod($S$) on the Teichm\"{u}ller space of
$S$. Moreover, using the same method plus recent results about weak
equivalence, we also give a classification, up to weak equivalence, for the
unitary quasi-representations with respect to geometrical subgroups.
