  It is very common to observe crowds of individuals solving similar problems
with similar information in a largely independent manner. We argue here that
crowds can become "smarter," i.e., more efficient and robust, by partially
following the average opinion. This observation runs counter to the widely
accepted claim that the wisdom of crowds deteriorates with social influence.
The key difference is that individuals are self-interested and hence will
reject feedbacks that do not improve their performance. We propose a
control-theoretic methodology to compute the degree of social influence, i.e.,
the level to which one accepts the population feedback, that optimizes
performance. We conducted an experiment with human subjects ($N = 194$), where
the participants were first asked to solve an optimization problem
independently, i.e., under no social influence. Our theoretical methodology
estimates a $30\%$ degree of social influence to be optimal, resulting in a
$29\%$ improvement in the crowd's performance. We then let the same cohort
solve a new problem and have access to the average opinion. Surprisingly, we
find the average degree of social influence in the cohort to be $32\%$ with a
$29\%$ improvement in performance: In other words, the crowd self-organized
into a near-optimal setting. We believe this new paradigm for making crowds
"smarter" has the potential for making a significant impact on a diverse set of
fields including population health to government planning. We include a case
study to show how a crowd of states can collectively learn the level of
taxation and expenditure that optimizes economic growth.
