We study the voting game with information uncertainty where agents can coordinate in groups. 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. We reveal the surprising equivalence between a strategy profile being a strong equilibrium and leading to the decision favored by the majority (the {\em 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. In our model, 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.

翻译：我们研究了信息不确定情况下的投票博弈，其中代理人可以分组协调。我们证明，策略投票行为对促成“正确”决策具有积极影响，其表现优于常见的非策略行为（如信息投票和诚实投票）。我们的结果为策略投票在做出良好决策方面的价值提供了依据。我们揭示了一个令人惊讶的等价关系：策略配置构成强均衡与引导至多数人偏好的决策（即“知情多数决策”）之间是等价的——随着投票规模趋于无穷，由策略代理人形成的每个ε-强贝叶斯纳什均衡（其中ε收敛于0）以概率趋于1导向知情多数决策。另一方面，我们证明信息投票仅在无偏情形下才能导向知情多数决策，而诚实投票仅在其自身构成均衡时才能导向知情多数决策。在我们的模型中，选民在两个备选方案之间的偏好取决于一个不可直接观测的离散状态变量。每位选民接收到一个与该状态变量相关的私人信号。