This analogy may not be quite accurate but I think I can get my point across with it.
I was reviewing some obesity statistics:
There is no majority. "Obesity" is the plurality. Is there a specific term for "neither overweight nor obese" as the smallest minority?
I think the trouble here is that it isn't '“Majority” to “plurality.”' In discussing proportions, majority is the counterpart to minority; the whole is divided into two unequal parts, and thus one part is greater than half and the other smaller. If a majority exists, by definition no plurality can exist. At the same time, one can view a plurality as simply the "first among minorities," the largest among various fractions that do not muster 50%.
One would need to employ a phrase to describe a proportion which is neither a majority nor a plurality. The part of the population which is neither overweight nor obese could be the smallest proportion of the population, or the least fraction or the littlest part, or some such formulation.
I think there is a problem with the way you have structured the concept. Plurality, as you use it, is usually defined by most online dictionaries in political terms
the number of votes that a politician or party gets in an election that is more than any other but is less than an absolute majority
It is determined based on two disjunctive characteristics:
The smallest minority is just that - the smallest group. There is not another characteristic that makes it analogous to plurality.
In fact, the term minority itself poses a problem. It is generally defined in the context of two groups
the smaller in number of two groups constituting a whole; specifically: a group having less than the number of votes necessary for control
Further, the term minority can encompass more than one group when there are more than three categories. Which of those (or which combination of those) is of interest depends on the context of the categorization. In social situations, there are often a number of minorities identified based on a variety of characteristics differing from the majority. Further, a number of political or social minorities may coalesce to form a plurality.
You would have to describe what relationship you see between "majority" and "plurality" before you could say what the corresponding word is for "minority".
Normally we say that the opposite of "majority" is "minority", not "plurality". The only way I can see to relate majority and plurality is to say that a majority is the largest group or block and is over 50%, while a plurality is the largest group or block and is under 50%. But to make a similar relationship with "minority" ... what? It's meaningless to talk about a minorities that are over 50% and those that are under 50%. If you're over 50% you're not a minority.
If you're looking for a word that means "the smallest minority", hmm, I don't know any single word for that. If there is one, I don't think it's widely used. I think the simplest thing to do is simply call it "the smallest group".
The answer is, I guess, singularity.
EDIT: I accidentally considered only the title question. Now having read your entire post, it seems to me that your definition of "plurality" (= manyhood, multitude) is not correct. There is no specific term I know of which means "largest group (but not majority)", nor for the opposite (smallest group). So, as far as the terms I know are concerned, you'll have to settle for "largest group"/"largest fraction" and "smallest group"/"smallest faction".
Both the terms majority and minority describes a mass of people in most of the cases. While the term majority describes more number of people, the term minority describes less number of people compared to those in majority. Both these terms cannot be compared to plurality and singularity. however it can be a coincidence if the no. of people in minority are 1.
Original question: "Majority" is to "plurality" as "minority" is to what?"
I had the exact same question, and studying the answers by others, I came to the insight that the correct answer is actually "smallest subset".
First, I think that a better definition of "plurality" is: the largest subset of a kind. In the example of the OP, 3 weight categories are considered, and each category corresponds to a subset of all people. The plurality is the largest of these, hence the obese.
Now, in most definitions I have seen, the definition of "plurality" is defined as the largest minority, where minority is defined as a subset that's less than 1/2 of all elements considered. However, if we just look at all subsets, and one of them turns out to be a majority (hence more than 1/2 of all considered elements), then it is still a plurality with my preferred definition (there isn't an exception to consider). On the other hand, if more than 2 subsets are considered, and we'd ignore the majority, is it useful to talk about a plurality as the largest of the remaining minorities? In that case, if there is a majority, the largest minority can not be more than 1/4 of all the elements considered (please, check). But how is that relevant? This seems futile and rather confusing.
So, I think that the better definition of plurality is simply the largest subset of a kind, as proposed.
Now, let's look again at the analogy
majority : minority = plurality : unknown.
Consider first that if there are only 2 subsets, they're either both equal in size, and there is no majority, nor a minority (since the definition of majority is that it ought to be more than 1/2, and a minority ought to be less than 1/2). But if there is a majority, there is certainly a minority (the rest), and the plurality equals the majority.
In fact, we saw earlier that the majority, if it exists, always equals the plurality, not just in the case of 2 subsets.
Consider next that if there are more than 2 subsets, then considering majority vs. minority, we're considering at most 1 subset vs. at least 2 subsets. This is an asymmetrical situation. In particular, there can be only at most 1 majority, but there will be more than 1 minority. However, since there are more than 1 minority (and if there is no majority), then looking at the largest minority makes sense and that is the most common situation.
In this case, we can still talk about the smallest minority, which is simply the smallest subset; but it is nonsensical to talk about the smallest majority (you don't need a second term to describe the same unique thing, majority).
Let's translate the analogy to
"subset > 1/2 of elements" : "largest subset" = "subset < 1/2 of elements" : unknown.
We want to solve for unknown. My proposed candidate is "smallest subset". Let's see how this fits.
First, in case of 2 subsets, we see that the relationship on the left expresses the identity, if there is a majority. But if there isn't a majority (both subsets are equal), then we also know that the largest subset equals the smallest subset. In both cases, we can thus write the valid analogy:
"subset > 1/2 of all elements" : "largest subset" = "subset < 1/2 of all elements" : "smallest subset".
Second, in case that there are more than 2 subsets, we need to reconsider the meaning of the analogy expressed.
a.) If there is a majority (unique), then the largest subset is equal to the majority. b.) If there is no majority, then all subsets are minorities, and the largest subset equals the largest minority.
Let's see how we can translate this into the right side terms, mutatis mutandis:
a.) If there is a minority (not unique), and then the smallest subset is equal to a minority. b.) If there is no minority, then TRUE, and whatever.
Note. The b.) leg is seemingly collapsing here. However, if there are more than 2 subsets, it is impossible for there not to be a minority. Namely, in this case, all subsets should be at least 1/2 of all elements (no minority), but with at least 3 sets, this can't be true (unless the subsets are overlapping, but we are implicitly assuming they don't). This means that the b.) leg is TRUE by default (and I just asserted that with "TRUE", but copied the format of the earlier b.) leg for the case of 2 subsets. Consider the definition of an if-then assertion! In particular, the statement "if A then B" is true if A is not true, such as here.
In particular, in the analogy we can use for whatever = "the smallest subset equals the EMPTY set" (this is untrue, but that doesn't matter; it fits the analogy!)
So, surprisingly, for more than 2 subsets, the analogy can include the b.) legs as well! The a.) legs would work with = "smallest subset", if we ignore the slight asymmetry between majority and minority.
Hence, the best candidate for unknown equals "smallest subset", yielding the analogy
majority : minority = plurality : smallest subset.
I don't think anybody so far understands the question (either that or I don't).
I think what the OP is asking is, what is the word for a minority that is not the largest minority (not a plurality). He wants a word that makes clear that the minority of which he speaks (if he could find the word for it) is not the plurality. Example: Say the demographics of a state are: 45% Caucasian, 25% African-American, 20% Asian, 10% Native American. The word "minority" applies to all groups. Is there a word that only applies to the non-plurality minorities? A word that makes clear that this particular minority is not a plurality? A word that you can use to describe all of those minorities except Caucasians (which are a plurality).
I don't know of such a word, but I'd like to.
