I would amend the OP to say that policy should be arbitrated, not by scientists, but by scientific principles.
Rather than voting directly on policy right away, votes should be held on the desired outcome of policy. Based on the priorities of the representatives elected to Congress, a hierarchy of weighted priorities should be determined. This would numerically represent how important GDP growth is to Americans compared to how important climate change is to Americans, and how important reducing abortions is to Americans and how important reduced taxes are to Americans, etc. Each desired outcome would be weighted on a scale of 0-1 according to how much support each was given in the vote.
Much more can be agreed on with regard to outcomes than with regard to methods. No one is going to vote that they desire more gun violence as an outcome. No one is going to vote that they desire a higher rate of abortion as an outcome. No one is going to vote that they want less freedom as an outcome, etc...
After a weighted hierarchy of desired outcomes is determined, the methodology for evaluating and modeling those metrics would be debated in the broadest way possible, so that the methodology would be applied across all issues, and not cherry-picked from one issue to the next.
After both the hierarchy of outcomes and the methodology have passed both the house and the Senate, and been signed by the President. The agreed-on methodology would be applied in modeling each issue in a blind study, where all of the data is symbolically represented so that the people modeling the projected outcomes don't know whether a given variable represents gun deaths or stock prices.
The model that generates the highest overall projected outcome with the highest chance of success becomes the new policy. As new data comes in, the policy would be continuously revised based on applying the new data to the agreed-on methodology, until a new hierarchy of outcomes and a new methodology are voted on.