LAS VEGAS—In their hunt for delegates who could secure them the Democratic presidential nomination, candidates competing in Saturday’s Nevada caucuses have been looking toward the state’s vast, sparsely populated regions, known locally as The Rurals.

The state party’s caucus rules encourage candidates to leave Las Vegas and its surrounding communities, which are home to a majority of Nevada’s population, to compete for precincts that in some cases hold as few as a dozen voters.

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