There isn't. Actually this is one of the most hotly debated questions in the study of Roman society. Especially in recent years there have been a number of scholars raising the question, which was often treated without much concern in the 20th Century, and coming to completely different conclusions. The question as it's understood now has its roots in Syme--earlier scholars examined the degree to which the Republic was democratic, but Syme's argument is the basis for the modern camp that holds that the Republic had the trappings of a democracy but was ultimately an oligarchy, and a relatively narrow one at that. Syme believed, though, that this was true of all ancient governments, arguing that in fact all governments are, when you boil everything else away, essentially just oligarchies. People like Brunt and Gelzer took it essentially for granted that the Republic was, though it maintained a pretense of popular democratic institutions, firmly in the control of the aristocracy, although Brunt was very interested in the idea of the people's exercising more political influence in the late Republic, through legal means or otherwise. More recently scholars like Fergus Millar and Henrik Mouritsen have appeared on the scene. Millar argues that the Republic, and particularly the late Republic, was fundamentally a democracy and that the aristocracy did not have much of a hold on the voting body at all. Instead of more or less obediently following the behests of the senatorial class and acting as extensions of aristocratic legislative squabbles the citizen body as far as Millar sees it exercised more political independence than they're given credit for, until by the late Republic they were basically totally able to assert their political influence at the expense of the senatorial class. Others who are more familiar with Millar may comment more, but he runs into some issues--Millar's not really able to explain the fact that the late Republic, which he considers to be the high-point of the democracy, was simultaneously the most corrupt period of the Roman state, and that in many ways the political power of the citizen body was being abused by all kinds of people rather than originating organically from the desires of the people themselves. He also has a problem with fitting the power of senatorial oratory, an issue that Morstein-Marx deals with--no matter how democratic the institutions of the Republic were, the power of oratory in influencing the voting body was extremely important, and there are a number of ways in which we can interpret the real influence of oratory. Mouritsen sort of pokes holes in both camps. He pretty definitively points out that patronage, while important, cannot reasonably have been as binding as it often has been thought (to step back to myself for a moment, I read an article by Ray Laurence a while back which argued that literally every person in the city was a client to somebody and that every member of the Republican city was a member of a collegium. There's an absurd idea if I ever heard one), thereby challenging the idea that the senatorial class basically mustered the citizen body through clientage as essentially personal political retinues of their own. But Mouritsen also challenges Millar's idea of the Republic as essentially democratic in nature--he points out that no matter how democratic the state was in name in practice our sources indicate that the people simply did not express their desires through legal channels, and that the assemblies simply did not have much real power. Mouritsen's very interested (which makes him pretty useful for my purposes) in the distinction between the idealized populus Romanus as some sort of monolithic entity and the socio-economic realities of the urban and rural poor, who often simply could not afford to take time off from their daily struggle for survival to participate in political activities. He's also got a discussion somewhere about how many voters various public spaces could actually hold--I'm not totally sure I buy this line of thought, but Mouritsen at least argues that it's vastly smaller than the massive public participation that Millar sees, and I think I'd agree with his ultimate point that elections, although theoretically representative of an enormous body, were really quite restricted to those who were able to come and who wanted to come, which Mouritsen thinks was really pretty small. I'll stop there before my own opinions start popping up--I'm generally inclined to agree with Mouritsen on most points--but you get the idea, that it's a question without a whole lot of straightforward answers and a lot of argument. Probably all of the people that I've mentioned are wrong--it's an awfully complicated question, one that doesn't lend itself well to simplification. But that's the gist of it, that classicists have no consensus on this point at all, except that pretty much everyone agrees that no matter how democratic it was for however many people, there was still more political liberty in the Republic than under the emperors.