In specific to the Roman Republic, fraud as you are describing it was not possible because there were no ballots. Instead, elections were by blocks, either by tribes (at first geographic groupings, but this was diluted as more territory was added to the Republic) or by centuries (basically, the economic classes). Each division voted amongst themselves, and a simple majority in each tribe was enough to decide the vote. This was all done in person on the day of the election.

Now, this didn't prevent fraud of another type, which is bribery. If you bribe enough people among those who show up at the election (or during votes at the tribal/centuriate assemblies, which were functionally identical in process) you can swing the vote for that tribe/century to you. While this was technically illegal, it was notoriously under prosecuted. The first law to prevent this, that we know of, was the Lex Baebia in 181 BCE. Numerous other pieces of legislation were passed regarding this, but laws like this often had little teeth in Ancient Rome because the control over the courts for much of its history lay with the Senate, and thus, with people who likely had used some form of bribery or coercion during their rise up the cursus honorum. Indeed, it was not uncommon for people to note with great irony when they were persecuted for corruption that the people persecuting them and judging them were just as guilty.