Brett Kavanaugh versus Christine Blasey Ford is a classic rashomon: As things stand now, it is not possible for anyone outside of the principals to know what the truth is. If no new information emerges, then whose side you take is most likely to be determined by your priors.
So if you can’t figure out a course of action based on truth or falsity, maybe game theory can help.
Before we begin, we have to identify the goods that the two players—in this case we’ll generalize them as liberals and conservatives—care about. We could fairly say that liberals goals for the game go something like this: Deny Kavanaugh the seat; get the least conservative justice possible; force people to take sexual assault claims seriously; not destroy public respect for the institution of the Supreme Court.
And we could say that the conservative goals are: Seat Kavanaugh; get the most conservative justice possible; deny incentives to bad actors who might be tempted to make false claims about future nominees; not destroy public respect for the institution of the Supreme Court.