  Online social media such as Twitter are widely used for mining public
opinions and sentiments on various issues and topics. The sheer volume of the
data generated and the eager adoption by the online-savvy public are helping to
raise the profile of online media as a convenient source of news and public
opinions on social and political issues as well. Due to the uncontrollable
biases in the population who heavily use the media, however, it is often
difficult to measure how accurately the online sphere reflects the offline
world at large, undermining the usefulness of online media. One way of
identifying and overcoming the online-offline discrepancies is to apply a
common analytical and modeling framework to comparable data sets from online
and offline sources and cross-analyzing the patterns found therein. In this
paper we study the political spectra constructed from Twitter and from
legislators' voting records as an example to demonstrate the potential limits
of online media as the source for accurate public opinion mining.
