Fallacy of the arbitrary threshold?

Question

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.

Answer 1

The argument of the beard or sorites fallacy may be relevant. Here is how Bo Bennett describes it:

When one argues that no useful distinction can be made between two extremes, just because there is no definable moment or point on the spectrum where the two extremes meet. The name comes from the heap paradox in philosophy, using a man’s beard as an example. At what point does a man go from clean-shaven to having a beard?

The OP presents a situation where a "bigot" claims that there is a useful characteristic allowing one to discriminate between groups X and Y, but "no one in these cases has actually worked out" where the dividing line is between an acceptable and unacceptable amount of the characteristic.

Claiming that there is no distinction because there is no threshold when an opponent claims there is a useful distinction may itself be an example of the argument of the beard. Perhaps what one needs to do to further the argument on both sides is to present empirical data on the prevalence of the characteristic in groups X and Y.

Furthermore, one should be careful about characterizing the opponent as a "bigot". This may lead to a claim, or even perception in a critically influential audience listening to the argument, that one cannot defend one's position without using the ad hominem fallacy.

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Bennett, B. Argument of the Beard. Retrieved on June 17, 2019 from Logically Fallacious at https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/58/Argument-of-the-Beard.