Senator Tom Cotton of Arkansas has unexpectedly emerged as a top contender to become Donald J. Trump’s running mate, a signal that the former president is heavily weighing experience and the ability to run a disciplined campaign over other factors. Mr. Cotton’s ascendance comes as Mr. Trump’s leading vice-presidential options have increasingly come into focus, according to three people with direct knowledge of Mr. Trump’s thinking who insisted on anonymity to discuss private meetings. These people said that Mr. Trump’s other current favorites were Gov. Doug Burgum of North Dakota and three of Mr. Cotton’s Senate colleagues: Marco Rubio of Florida, Tim Scott of South Carolina and J.D. Still, the people close to Mr. Trump cautioned that his vice-presidential preferences might change.

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