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Cindy Hyde-Smith, a Republican who was appointed to the Senate this year, faces Mike Espy, a Democrat and former congressman, in a special election runoff on Tuesday after neither candidate won a majority on Election Day. The election was held to fill the seat of Senator Thad Cochran, who retired earlier this year for health reasons. Read more

Although Mississippi is a deeply conservative state, a series of remarks by Ms. Hyde-Smith that were widely condemned as racist and insensitive have led Democrats to believe that they might have a chance to defeat her.

— ALAN BLINDER

Here’s what to watch for.