Is 'president' in 'run for president' a bare role NP?

A Student's Introduction to English Grammar says:

A bare role NP is a singular NP that is ‘bare’ in the sense of lacking the determiner which would elsewhere be required, and that denotes some kind of role, office, or position. A PC can have the form of a bare role NP, but an O can’t:

i a. She became [the treasurer]. [NP] = PC

i b. She knew [the treasurer]. [NP] = O

ii a. She became [treasurer]. [NP] = PC

ii b. *She knew [treasurer]. [NP] = O

• In [i] both the [a] and [b] examples are fine because an ordinary NP like the treasurer can be either a PC or an O.

• In [ii], treasurer is a bare role NP, so it is permitted with become, which takes a PC, but not with know, which takes an object.

Where PC stands for 'predicative complement' and O 'object'.

Now, in the following sentence, does [NP] qualify as a bare role NP as defined above?

c. He's running for [president].

If it is a bare role NP, then how about [NP] in the following sentence?

d. The film's competing for [best picture].

While it can be said that president denotes a role/office/position in (c), I don't believe the same can be said about best picture in (d). But these two sentences are strikingly similar in syntax, so if president is a bare role NP in (c), I believe so should best picture be in (d), except it apparently isn't.

So something must have gone awry in this line of analysis. In order to fix this apparent incongruity, we need to say either that (1) president of (c) is not a bare role NP defined above or that (2) there's no such thing as a bare "role" NP in the first place but there's only a bare NP.

Is there any other alternative analysis to (1) and (2)? If not, which of the two analyses is logically correct?

In the sentence "A PC can have the form of a bare role NP, but an O can’t", I think "PC" and "O" are meant to be interpreted as referring specifically to complements of verbs. In your sentence, president is not a complement of the verb: rather, the verb run takes the preposition for as its complement, and the preposition for takes president as its complement. (Perhaps this is arguable; see my answer to "Impinge: transitive or intransitive?" for more information.) The complement of a preposition is sometimes called the "object" of the preposition; they mean the same thing.

I don't think "president" is a predicative complement here. I'm not sure whether for even can take a predicative complement.

I'm also not sure whether president is a bare role NP in "run for president". it's clear that not all singular NPs without an article (a.k.a. "anarthrous NPs") are "bare role NPs". For example, school can be used without an article—either as the complement (object) of a preposition, as in they are at school, or as the complement (direct object) of a verb, as in I don't like school—but school is not a bare role NP. I don't know exactly how "bare role NP" is defined (or whether it even has a rigorous definition), but "run for" can take various kinds of anarthrous complements, and not all of them can be used as predicative complements:

• "He ran for office in 2000" is grammatical, but *"He is office" isn't.
• "He plans to run for reelection" is grammatical, but *"He is relection" isn't.

In the sentence He's running for president, the [bare role NP] is neither a PC nor an O (not a verb O anyway). You have introduced a third sentence pattern.

Let's compare the three. (I am going to use more common, prescriptive grammar terms here for illustration.) . . .

SVC—subject + linking verb + subject complement (PC in your book):

She became the treasurer.

She became [treasurer].

She is the treasurer.

She is [treasurer].

SVO—subject + transitive verb + object (O in your book):

She knew the treasurer.

*She knew [treasurer]. (incorrect)

SVA—subject + intransitive verb + adverb:

She's running for [treasurer].

For treasurer is a prepositional phrase acting as an adverb to modify the verb run. (The PC is the whole PP for treasurer—not the bare role NP alone.)

Now, we can't say She's running for the treasurer without changing the meaning; we must use the bare role NP. But it seems we can say both She's acting as treasurer and She's acting as the treasurer.

I suppose we can blame this on the fact that for has a great many meanings, and the addition of a determiner invokes a different one. Or we can just call run for + bare role NP an idiomatic construction and leave it at that.