There are plenty of issues where "precise predictions" are available, yet the polarization is as bad as ever, such as drugs, birth control, gun control and taxes.
The fact that statistics exist doesn't mean that "precise predictions exist". It especially doesn't mean that stakeholders in the debate engage in the action of engaging in prediction making.
The prediction expert Philip Tetlock writes in New York Times on the power of precise predictions to counter political polarization. Note the similarity to Robin Hanson's futarchy idea.