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If you're down to say 4 candidates, and one of them is really close to Pariston in votes, he may have no choice but to kill that guy.
Of course Pariston isn't going to attack someone like the Tiger who poses no threat to him in the election. It's like what Chidol says, someone has to come close to Pariston in votes first or Pariston will never stop smiling because he's in a completely safe position. But it's well understood that Pariston is capable of far more than just trash talk and threats. So once someone gets close to him in votes, they'd have to face his counterattack and that's what Chidol is worried about. I don't see Gin being the one who goes out and manipulates the vote to force Pariston to make a move first, since it doesn't even make sense (he has no popularity to manipulate those votes to begin with). He'll definitely play a crucial part in dealing with Pariston's counterattack, but he won't be the one who trigger it.
I don't think killing a contestant would benefit pariston. For one thing, people who are not voting for him do not do so because they mistrust him to begin with. In that regard killing someone who might beat him won't necessarily get him votes. If they mistrust him then by having another contestant "accidentally" killed would result in even more suspicion against him. Pariston is in a position of power, he has a lot to lose meaning that if something like that happens then he will immediately get the suspicion of every hunter against and for him. He has to be extremely careful. Killing a strong candidate is not an option IMO unless he can stage it so overwhelmingly well that not even the most outrageous interpretation of the facts could lead to a shred suspicion against him.