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We focus on iterative voting systems based on the positional scoring rules plurality, veto, and Borda and study their resistance against shift bribery attacks introduced by Elkind et al. [1] and Kaczmarczyk and Faliszewski [2]. In constructive shift bribery (Elkind et al. [1]), an attacker seeks to make a designated candidate win the election by bribing voters to shift this candidate in their preferences; in destructive shift bribery (Kaczmarczyk and Faliszewski\u00a0[2]), the briber\u2019s goal is to prevent this candidate\u2019s victory. We show that many iterative voting systems are resistant to these types of attack, i.e., the corresponding decision problems are NP-hard. 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