“Brunner and Steelman are ineligible, since they lost in the primary (second and third, respectively). They would lose anyway.”
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I’m not familiar with Missouri election law, but typically the “sore loser” provision only apply to the loser getting on the ballot as an opponent of the person who won their party’s primary - and not as a replacement for the winner.
As to your second sentence, I believe that you are totally wrong. McCaskill would be defeated in a landslide if either Steelman or Brunner (Brunner’s would be a lesser landslide) replaced Akin.