Organizers at the annual conference say about a third out of 1,500 delegates voted in the straw poll. Delegates had to pay to register for the conference and vote in the straw poll.
Cruz promised delegates Saturday to continue his uncompromising approach on Capitol Hill.
Carson did not address delegates before the voting.
Kentucky Sen. Rand Paul, former Arkansas Gov. Mike Huckabee and Texas Gov. Rick Perry trailed Cruz and Carson in the poll.
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