Which sentence is correct?

Which sentence is correct?

1. One in 12 people in our neighborhood don’t have a job.

2. One in 12 people in our neighborhood doesn’t have a job.

In my view, while #1 sounds right, #2 appears on paper to be right. Yet I can’t explain why.

So I asked my pal Paul, who said the following:

Two conflicting rules are at play here. Under one rule, the grammatical number is determined strictly by syntax:

“One in 12 people doesn’t.”

Under the other rule (which is called “synesis”), grammatical number is governed by the semantics — the sense:

“One in 12 people don’t.”

So which is better, I asked?

As usual, Paul suggested a rewrite that transcends the problem:

“One in every 12 people in our neighborhood doesn’t have a job.”