Thanks for throwing this back to me, giving me a chance to correct my mistake. Here goes:
On their own, "a majority" is typically plural and "the majority" is typically singular.
Of this year's graduating class, a majority will attend college. (plural)
The majority rules. (singular)
However, when "majority" is followed by a modifier, usually of the form "of things," that rule of thumb does not apply. That was my mistake above.
Here are the correct sentences:
The majority of students are smart.
A majority of students are smart.
The majority of physics students are smart.
A majority of physics students are smart.
{In other words, "a" or "the" doesn’t matter in this case. The verb should match the plural "students."}
A majority of railway commuters read or listen to music while traveling.
The majority of railway commuters read or listen to music while traveling.
{Plural verbs to match plural "commuters."}
I'll quote myself here:
The majority of students is smart.
The majority of physics students is smart.
(Those sound weird to me, frankly. I prefer "The student majority is smart" but since "student majority" is the same thing as "majority of students," the above is correct.)
The fact that it sounded weird should have been a clue! Notice that my ear told me that the only way to use a singular verb is to rearrange so that "the (student) majority" was not followed by an "of" prepositional phrase! That's the only way you can rely on the rule that "the majority" is singular.
One exception: "the majority" may require a plural verb even when not followed by an "of things" IF an "of things" is implied earlier in the sentence.
The customers of Ye Olde Ice Cream Shoppe have voted, and the majority prefer waffle cones.
(It is implied that "the majority
of customers prefer...."
In summary:
a majority" by itself-->plural
"the majority" by itself--> usually singular, unless an "of things" modifier is implied earlier in the sentence.
""the/a majority of things"-->plural, like the things