Why do scientists reach an agreement on new experimental methods when there are conflicts of interest about the evidence they yield? I argue that debiasing methods play a crucial role in this consensus, providing a warrant about the impartiality of the outcome regarding the preferences of different parties involved in the experiment. From a contractarian perspective, I contend that an epistemic pre-requisite for scientists to agree on an experimental method is that it be neutral regarding their competing interests. I present two medical experiments (on smallpox inoculation and mesmerism) in which debiasing procedures such as blinding and data tabulation provided warrants of impartiality that allowed people to agree on an experimental design even if they disagreed on the outcome.