Damon's expertise was supposed to be musicology, though some believed this was a cover for a broader influence over Pericles' political policy.
For instance, Damon is said to have been responsible for advising Pericles to institute the policy of paying jurors for their service; this policy was widely criticized, and Damon is said to have been ostracized for it (see the Aristotelian Athenaion Politeia), probably sometime in last third of the 5th century BCE.
Plato invokes Damon many times in the Republic as the musical expert to be deferred to concerning the details of rhythmical education.
The extant texts of the Aristotelian Constitution of the Athenians mention Damonides as an advisor to Pericles.
[1] This seems to be confirmed by ostraka that have been recovered and that bear the name "Damon son of Damonides".