  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.
