He is one of those writers who have/has won the Booker prize.
which is correct: 'has' or 'have'?
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The verb there will apply to the noun which is in its closest proximity. And thus, it'd take 'have'. That is, it'd apply to the 'writers' and not 'he'.
He's one of those writers who have won the Booker prize.
We want to emphasize the group that won the prize. There are quite similar questions here on ELL. One of them is here.