This paper provides a new approach for the study of diversification among interdependent investments by all risk averters. Assuming that investors choose mean-variance efficient portfolios, we introduce the concept of weak interdependence based on the magnitudes of a set of regression coefficients. The condition for positive inclusion of an investment in the optimal portfolios of all risk averters is characterized by the concept of weak dependence of the return from this investment on the returns from other investments. In the two-investment case, all risk averters hold a diversified optimal portfolio if and only if the returns on both investments have a common mean and are weakly interdependent. With multiple investments, if the minimum variance portfolio is nonspecialized, then all risk averters hold a common completely diversified optimal portfolio if and only if all of the returns have a common mean and are weakly interdependent.