Microblogging, like Twitter and Sina Weibo, has become a popular platform of human expressions, through which users can easily produce content on breaking news, public events, or products. The massive amount of microblogging data is a useful and timely source that carries mass sentiment and opinions on various topics. Existing sentiment analysis approaches often assume that texts are independent and identically distributed (i.i.d.), usually focusing on building a sophisticated feature space to handle noisy and short texts, without taking advantage of the fact that the microblogs are networked data. Inspired by the social sciences findings that sentiment consistency and emotional contagion are observed in social networks, we investigate whether social relations can help sentiment analysis by proposing a Sociological Approach to handling Noisy and short Texts (SANT) for sentiment classification. In particular, we present a mathematical optimization formulation that incorporates the sentiment consistency and emotional contagion theories into the supervised learning process; and utilize sparse learning to tackle noisy texts in microblogging. An empirical study of two real-world Twitter datasets shows the superior performance of our framework in handling noisy and short tweets.