I would guess that Mantineia's reputation comes from this story in Herodotus:
"Their late calamities now induced the Cyrenaeans to send to Delphi and inquire of the god what form of government they had best set up to secure themselves prosperity. The Pythoness answered by recommending them to fetch an arbitrator from Mantinea in Arcadia.
"Accordingly they sent; and the Mantineans gave them a man named Demonax, a person of high repute among the citizens; who, on his arrival at Cyrene, having first made himself acquainted with all the circumstances, proceeded to enrol the people in three tribes. One he made to consist of the Theraeans and their vassals; another of the Peloponnesians and Cretans; and a third of the various islanders.
"Besides this, he deprived the king Battus of his former privileges, only reserving for him certain sacred lands and offices; while, with respect to the powers which had hitherto been exercised by the king, he gave them all into the hands of the people. "
Later references to Mantineia, for example during the Peloponessian War, don't seem to say anything in particular about its government; but the Oracle's recommendation of Mantineia as the place to go for political wisdom could have boosted their reputation for quite a while.
The suggested reforms also would have been an early step towards democracy. I seem to recall seeing references to Demonax giving them a constitution at the same time; but I'm not sure if that is based on another source or just someone's interpretation of this one.
Anyway, this story is from Book IV of Herodotus' Histories, which is available here (it's got the whole thing on one very long page, and this passage is about three quarters of the way down - you'll want to search for Demonax. Anyone who knows of a better organized online source, feel free to replace the link).