This paper investigates how certainty and timing of evidence introduction impact the uptake by policy makers in collective deliberations. Little is known about how researchers should time the introduction of uncertain evidence for policy makers. With a computational model, we simulate how policy makers update their opinions in light of new evidence. We illustrate the use of our model with two examples in which timing and certainty matter for policy making: intelligence analysts scouting potential terrorist activity and food safety inspections of chicken meat. Our computations indicate that evidence should always come early to convince policy makers, no matter how certain it is. Even if the evidence is quite certain, it will not convince all policy makers. This paper also showcases the methodological innovation that agent-based models can bring to the field of science and policy. The model can be endlessly adapted to generate hypotheses and simulate interactions that cannot be empirically tested.