The decision-making process is difficult. As a friend used to say, "the quality of the decision is a function of the quality of the process." In Pirkei Avot 1:8 post, I discussed the primary challenges to objectivity: bias and cynicism. If I am not engaged in either of these , Pirkei Avot 1:9 provides additional wisdom on becoming objective.
Continuing in the language of the legal system, the author of this passage focuses on the role of the "witnesses." In 1:8, the "judge" was referenced in the sense of the decision-making faculty and "litigants" were referenced in the sense of opposing desires. The "witnesses" in 1:9 reference the data points themselves.
The author begins, "be extensive in questioning the witnesses," that is, be as thorough as possible gathering the information available. "In questioning" comes from the Hebrew phrase lachakor, which also has the sense of "for exploring." In other words, there is not a conclusion in mind. The questioning should be open-ended - an exploration in the sense of letting the data points unfold, without arranging or ordering.
Confirming this interpretation is some advice in the second part of passage: "be cautious with your words so that the witnesses do not learn to lie." In order for the "witnesses" to be truthful, they must not be led as a lawyer would lead. It is tempting to connect the data points too early thereby making those data points lie. Be patient; let the data points speak for themselves. (Another good translation for "witnesses" might be "facts." As we all know, "facts" can lie if forced.)