Previous studies have shown that Instant-Runoff Voting (IRV) is highly resistant to coalitional manipulation (CM), though the theoretical reasons for this remain unclear. To address this gap, we analyze the susceptibility to CM of three major voting rules-Plurality, Two-Round System, and IRV-within the Perturbed Culture model. Our findings reveal that each rule undergoes a phase transition at a critical value theta\_c of the concentration of preferences: the probability of CM for large electorates converges exponentially fast to 1 below theta\_c and to 0 above theta\_c. We introduce the Super Condorcet Winner (SCW), showing that its presence is a key factor of IRV's resistance to coalitional manipulation, both theoretically and empirically. Notably, we use this notion to prove that for IRV, theta\_c = 0, making it resistant to CM with even minimal preference concentration.

翻译：先前的研究表明，即时复选投票制对联盟操纵具有极强的抵抗力，但其背后的理论原因尚不明确。为填补这一空白，我们在扰动文化模型下分析了三种主要投票规则——多数制、两轮投票制和即时复选投票制——对联盟操纵的敏感性。研究结果表明，每种规则在偏好集中度的临界值 theta\_c 处都会发生相变：对于大规模选民群体，联盟操纵的概率在 theta\_c 以下以指数速度收敛于 1，在 theta\_c 以上则收敛于 0。我们引入了超级孔多塞胜者的概念，并从理论与实证两方面证明其存在是即时复选投票制抵抗联盟操纵的关键因素。特别值得注意的是，我们运用这一概念证明了对于即时复选投票制，theta\_c = 0，这意味着即使存在极微弱的偏好集中度，该制度仍能有效抵抗联盟操纵。