How do cardinals divine the will of God?

Here is an older 2004 paper from J.T. Toman (pdf):

In modern times, the College of Cardinals have been locked in the Sistine Chapel with the purported aim to divine the Will of God in the election of the Pope. Between 20 and 60 percent of cardinals vote for the same candidate throughout the conclave, depending on the length of the conclave. For those cardinals that change their voting behavior, they are influenced by both the vote counts and the nightly conversations. However, in unifying the cardinals to one winner the dominant force is the observed vote counts.

There is a good summary of the paper here, and another recommended paper here.

For the pointer I thank Adriano.