I'm reading The Punic Wars by Adrian Goldsworthy, and he strongly suggests that consular Roman elections were not determined by a true majority of Roman citizens. This conflicts somewhat with my understanding garnered from Mike Duncan's The History of Rome. Perhaps my confusion is based on ambiguity about the number of Roman residents who were actually citizens.
So: Were consuls selected by a true majority of Roman citizens? Did wealth or influence somehow permit an influential citizen to directly "stuff the ballot boxes" by means apart from the well-established patronage system?
Oh no, not at all. The Roman election system was...interesting, and completely different from anything in practice today. While reading this, remember that at its core, the Republican Roman system was a government designed for a city-state. The system itself worked, but with Rome expanding as it was, things got...complicated.
So let's look into consular elections. I haven't listened to Mike Duncan, so if you'd like to discuss him, you'd just have to clarify exactly what he said :) However, the Roman consuls were elected by the Comitia Centuriata, or the "Century Assembly." The Assembly was organized into different "centuries" - like the military, "Century" was just a term, unrelated to the size of the unit. There were centuries of thousands and thousands, and there were centuries who only had a handful of men. Each century had the equivalent of 1 vote. Discussion on the elected candidates was forbidden when voting time came around, and they basically just nominated the people they liked for consul - typically chosen from the men who ran for the office. Scipio Aemelianus is a bit of an anomaly there - we're just not sure exactly how much canvassing he did pre-election (Answer: Probably a LOT).
There were 193 different centuries, which were further classified into five different "tiers." The tiers were based off of wealth and the votes were slanted straight towards that wealthy class. The "First Class" had 80/193 centuries, II-IV had 20 each (60/193, total is up to 140), the "Fifth Class" had 30/170 (bringing the total to 170), and the last 23 were "specialty centuries." Only one of those centuries was for the landless, while the equites (the richest of the rich) had 18. If you do the math, that means the wealthy had 98/193 votes - enough to elect whoever they chose. To tip the scales even further, voting order was also based on wealth. So you'd have the equites vote first, the First Class vote second, the Second Class vote third, etc. As soon as a majority was reached, no more votes were cast, and the vote often didn't go beyond the First Class.
The consuls (and praetors) were basically selected by the will of the wealthy, who were in the top few percentage points of society.
Did that answer your question? :)