I suppose the Roman Republic wasn't really representative though. At least the people didn't vote for their representatives, even though people voted on their behalf

Except that that's exactly what the people of the Roman state did do, until the Principate. The Republican state was not governed by the senate, the senate was an advisory body composed of former magistrates who advised the current magistrates. Individuals that had held a quaestorship or above were admitted into the senate, where they had pretty much no legal powers in government--indeed, one of the standard ways that Cicero refers to senators is by calling them "private citizens" and all technical terms for senators emphasize the fact that they held no official powers within the state. The senate debated affairs and issued consilia to the magistrates, but the votes and resolutions of the senate held no legal status and their consilia were not laws--the magistrates could and often did ignore the advice of the senate, although usually there were dire consequences for pissing them off, in the form of prosecution. Magistrates, with the exception of a handful of low-ranking magistrates like the military tribunes and extraordinary magistrates (of which the prime example is the dictatorship, although that office ceased to exist after 202--Sulla's dictatorship should really be considered a separate magistracy that just happened to bear the same name) that were senatorially-appointed, were elected by the citizen assemblies. Over and out. The senate had no legal right to interfere with this process, and though it had enormous influence, it nonetheless was legally distinct from the electoral process. Likewise, it was not a legislative body--legislation was proposed by the magistrates, who brought their legislation to the citizen assemblies to have it voted on, and though the senate traditionally reviewed and approved (or disapproved) of proposed bills before they were brought to the assemblies, this was not actually a legal requirement and was several times ignored (most notably by Publius Clodius during the passage of the leges Clodiae early in 58). The Roman citizen body of the Republican state very much did vote for their magistrates, it's sort of the hallmark of the Republic and it's a legal right of Roman citizenship that the Romans valued above just about everything else