We study the voting game where agents' preferences are endogenously decided by the information they receive, and they can collaborate in a group. We show that strategic voting behaviors have a positive impact on leading to the ``correct'' decision, outperforming the common non-strategic behavior of informative voting and sincere voting. Our results give merit to strategic voting for making good decisions. To this end, we investigate a natural model, where voters' preferences between two alternatives depend on a discrete state variable that is not directly observable. Each voter receives a private signal that is correlated with the state variable. We reveal a surprising equilibrium between a strategy profile being a strong equilibrium and leading to the decision favored by the majority of agents conditioned on them knowing the ground truth (referred to as the informed majority decision): as the size of the vote goes to infinity, every $\varepsilon$-strong Bayes Nash Equilibrium with $\varepsilon$ converging to $0$ formed by strategic agents leads to the informed majority decision with probability converging to $1$. On the other hand, we show that informative voting leads to the informed majority decision only under unbiased instances, and sincere voting leads to the informed majority decision only when it also forms an equilibrium.

翻译：我们研究了投票博弈，其中代理人的偏好由他们接收的信息内生决定，且他们可以在群体中协作。我们证明：战略性投票行为对达成“正确”决策具有积极影响，其表现优于常见的非战略性行为（信息性投票和诚实投票）。我们的结果为战略性投票在制定良好决策方面的价值提供了依据。为此，我们研究了一个自然模型：投票者对两个备选方案的偏好取决于一个不可直接观测的离散状态变量。每位投票者接收到一个与该状态变量相关的私有信号。我们揭示了一个令人惊讶的均衡：一个策略配置既是强均衡，又能引导出以知情多数决策（即代理人在知晓真实情况后所偏好的决策）为特征的结果。当投票规模趋向无穷大时，由战略性代理人形成的任意ε-强贝叶斯纳什均衡（其中ε收敛于0）以概率收敛于1的方式达成知情多数决策。另一方面，我们证明：信息性投票仅在无偏场景下才能达成知情多数决策，而诚实投票仅在其本身构成均衡时才能达成知情多数决策。