The plural of person is not people, it is persons. That being said, however, it is not common to use persons except in certain cases. One case is your example, when specifying a particular number of persons. You could say "Starter for 4 persons" or "Starter for 4 people", although in the context of a restaurant menu, it would (in my opinion) be slightly less awkward-sounding to use persons rather than people. The word people is more of a collective. You would never say "The persons of the United Kingdom" but always "The people of the United Kingdom" when speaking collectively. But if being severely formal, you might say about a distinct group of people who hail from the UK: "All United Kingdom persons must check in with their consulate upon arrival." It would be awkward-sounding to use people in that sentence.
From Collins World English Dictionary (cited on Reference.com)
person (ˈpɜːs ə n) — n , pl persons
- an individual human being
- the body of a human being, sometimes including his or her clothing: guns hidden on his person
- a grammatical category into which pronouns and forms of verbs are subdivided depending on whether they refer to the speaker, the person
addressed, or some other individual, thing, etc
- a human being or a corporation recognized in law as having certain rights and obligations
- (philosophy) a being characterized by consciousness, rationality, and a moral sense, and traditionally thought of as consisting of both
a body and a mind or soul
- (archaic) a character or role; guise
- in person - (a) actually present: the author will be there in person ; (b) without the help or intervention of others
Usage "People" is the word usually used to refer to more than one individual: there were a hundred people at the reception. "Persons"
is rarely used, except in official English: several persons were
interviewed