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Levin is has no idea about what is under discussion. All he observes is that several noblemen appear to be getting excited about supporting the views of their own parties. This fellow Flerov: should he be included in the elections or not? His party says yes, the other party says no.
He finds their agitation distasteful, and calms himself down by hanging back and observing the give and take of the waiters.
By the time it's Levin's turn to cast the ballot, he is confused about what is happening. He lowers his voice and asks Koznyshev what he should do, and is embarrassed when Koznyshev frowns and tells him that it depends on his own individual point of view.
Levin is so embarrassed that, after tossing his ballot somewhere, he winds up in the furthest corner of the room talking to an old marshal of his acquaintance, whom he finds appealing and pitiful.
Meanwhile, the new party proves victorious. They manage to pass the ballot measure 126-98. So now it's on to the real elections.