In some small way I feel like the Supreme Court attempted to answer that in Utah v. Strieff. I think there are valuable lessons in it to consider, not only as regards justice and law but also the nature of the Supreme Court.
It’s no secret why Clarence Thomas wrote the majority opinion: this is a judgment with another chiseling away of rights largely hitting minority communities, and so having him write it offers some legitimacy. Thomas and Sotomayor each had something to share, and it’s an illustrative glimpse at the very plastic concept of justice.
For Thomas (and the majority), this was a technical and procedural question. What should police do? How should they do it? What complications arise, and how do they see them through? It’s a very minutiae-driven analysis about technical aspects of law.
For Sotomayor, justice is not a matter of attempting to tighten the not-quite-snug gears of process. Justice is a matter of aggregates, and the measures of the real world. By her measure (and those of the minority), justice is what is, not what ought to be.
There are advantages to either outlook: technical judgments provide clarity but don’t heavily consider downstream effects, whereas holistic measures avoid things like “separate but equal” but provide only fuzzy guidance for future issues.
Here I’d side with Sotomayor, but it isn’t like I don’t see the merit in what the majority is trying to do. This is why you want a diverse Supreme Court: there isn’t one way to look at these things and there often isn’t one measure of law or justice. There’s an art to all this and that art will necessarily be myopic and damaging if the Court is homogeneous.