The joint probability of the different parties controlling the president, senate, and house.

[table table-id=1798]

In short, this assumes 100 percent correlation between the outcomes and I think it is a pretty good approximation. If the Republican nominee Donald Trump wins the presidency, the Democrats have almost certainly lost both the senate and house. There would be some gigantic wave that crushed the house and probably took at few marginal senate seats as well. Since the second most likely senate outcome is a 50-50 split, where the presidency literally determines power in the senate, it is hard to imagine a scenario where the Democrats win the senate, but not the presidency. Take a look at the correlation!


Thus, with eight possible outcomes:

President(D),Senate(D),House(D) = Probability of Democratic house

President(R),Senate(D),House(D) = 0

President(D),Senate(R),House(D) =0

President(D),Senate(D),House(R) = Probability of Democratic senate – Probability of Democratic house

President(R),Senate(R),House(D) =0

President(D),Senate(R),House(R) = Probability of Democratic president – Probability of Democratic senate

President(R),Senate(D),House(R) = 0

President(R),Senate(R),House(R) = Probability of Republican president