The Taming of the Shrew/WMG

Kate represents Queen Elizabeth I and Bianca represents Queen Mary.
Elizabeth was shrewish, whereas Mary was docile (at least in their personal life).

The play is pro-shrew.
This is a relatively recent theory, or at least recent to be spoken in public, since being pro-shrew back when this play was written meant Getting Crap Past the Radar.

Related theory:

Kate wins.
She's only pretending to be docile in the end.
 * There's been plenty of scholarly debate on this one.