# Fallacy of the arbitrary threshold?

Prejudices and discrimination against a group of people Y by members of another group X are often justified by assertions that members of Y are more likely than members of X to engage in a particular negatively-viewed behavior, or are more likely to contract and spread a particular disease, or are more likely to bear a particular deficiency in their intellect or ability. Whatever the characteristic is, let's call it C.

Expanding this argument:

• Let the proportion of the members of a group G that bears characteristic C be labeled p(G). In other words, given an arbitrary member of group G, the probability that that member bears C is p(G).
• p(Y) > p(X)
• Therefore, it's reasonable for members of X to treat members of Y badly (shunning them socially, refusing them jobs, denying them equal access to social services, enslaving them, exiling them).

There's an implication here:

• that there exists a threshold probability of bearing characteristic C, p(threshold), such that, for any group G, if p(G) < p(threshold) then that group is entitled to the best treatment while, if p(G) > p(threshold), then it's acceptable to mistreat members of G; and
• p(Y) > p(threshold) > p(X).

The fallacy is that no one in these cases has actually worked out p(threshold). The bigot feels that, as long as p(X) < p(Y), then one can justified. (This is a circular argument.) The bigot won't acknowledge the possibility that p(X) < p(Y) < p(threshold), which would justify inferior treatment of both groups, X and Y; nor the possibility that p(threshold) < p(X) < p(Y), which would demand that both groups be treated as first-class citizens. No, the bigot relies on the fallacious assumption that the acceptability threshold for C lies between its respective prevalence levels among the two groups.

My question is: Is there already a name for this fallacy? I know I used a lot of words to get to this point, but I was trying to figure out a faster way of explaining it to make it clear what I was talking about before I asked my question, and I didn't manage to do that. I've come up with names of my own, like "the fallacy of the self-justifying dividing line", but nothing catchy, and I figured I should find out whether a name already exists.

• I see a flaw in the method: "Therefore, it's reasonable for members of X to treat members of Y badly". These actions themselves are raising p(X), so the method is self-defeating. Aug 19, 2018 at 21:49
• Unless C = "treats members of Y badly" or "treats members of other groups badly", this doesn't follow. C is a specific characteristic that is given as a basis for prejudice or discrimination. Oct 31, 2018 at 20:36
• The bigot can reach the same behavior from logic concerned only with himself and those around him, on a case-by-case basis. "If (by my own biased consideration) that person is more likely to endanger/scare/bother/take-from me than otherwise comparable third parties, I will treat them worse than those third parties." This requires no global threshold, so his argument is not contingent on the logic you are imposing here.
– user9166
Jun 18, 2019 at 22:31