I've had better luck setting up stations based on a song than an artist. I think that the list of determining characteristics is much longer - some 400 or so to pick from. So when I picked J.S. Bach, I got Bach every third song or so, but when I went with Brandenburg Concerto No. 3 in G major, BWV 1048 I get less Bach and far more stuff written in counterpoint, like Telleman, Couperin, and Rameau.
From their site:
We believe that each individual has a unique relationship with music - no one else has tastes exactly like yours. So delivering a great radio experience to each and every listener requires an incredibly broad and deep understanding of music. That's why Pandora is based on the Music Genome Project, the most sophisticated taxonomy of musical information ever collected. It represents over seven years of analysis by our trained team of musicologists, and spans almost a century of music (and soon several centuries!).
Each song in the Music Genome Project is analyzed using up to 400 distinct musical characteristics by a trained music analyst. These attributes capture not only the musical identity of a song, but also the many significant qualities that are relevant to understanding the musical preferences of listeners. The typical music analyst working on the Music Genome Project has a four-year degree in music theory, composition or performance, has passed through a selective screening process and has completed intensive training in the Music Genome's rigorous and precise methodology. To qualify for the work, analysts must have a firm grounding in music theory, including familiarity with a wide range of styles and sounds. All analysis is done on location.
The Music Genome Project's database is built using a methodology that includes the use of precisely defined terminology, a consistent frame of reference, redundant analysis, and ongoing quality control to ensure that data integrity remains reliably high. Pandora does not use machine-listening or other forms of automated data extraction.