Aulus Gellius’ Attic Nights, bk.III, XVIII.1-10.

There are many who think that those senators were called ‘pedarii’ who did not express their opinion in words, but agreed with the opinion of others by stepping to there side of the House.
How then? Whenever a decree of the Senate was passed by division, did not all senators vote in that manner?
Also the following explanation of the word is given, which Gavius Bassus has left recorded in his ‘Commentaries’.
For he says that in the time of our forefathers senators who had held a curule magistracy used to ride to the House in a chariot, as a mark of honour; that in that chariot there was a seat on which they sat, which for that reason was called curulis; but that those senators who had not yet held a curule magistracy went on foot to the House: and that therefore the senators who had not yet held the higher magistracies were called ‘pedarii’.

Marcus Varro, however, in the Menippean Satire entitled ‘Hippokuon’ ,says that some knights were called pedarii, and he seems to mean those who, since they had not yet been enrolled in the Senate by the censors, were not indeed senators, but because they had held offices by vote of the people, used to come into the Senate and had the right of voting. In fact, even those who had filled curule magistracies, if they had not yet been added by the censors to the list of senators, were not senators, and as their names came among the last, they were not asked their opinions, but went to a division on the views given by the leading members. That was the meaning of the traditional proclamation, which even to day the consuls, for the sake of following precedent, use in summoning the senators to the House.

The words of the edict are these:
“Senators and those who have the right to express their opinion in the Senate” (Senatores quibusque in senatu sententiam dicere licet)
I have had a line of Laberius copied also, in which that word is used; I read it in a mime entitled ‘Structurae’: “The age-man’s vote is but a tongueless head.”
(Caput sine lingua pedari sententia est.”)
I have observed that some use a barbarous form of this word; for instead of pedarii they say pedanii.