https://www.unrv.com/empire/roman-population.php
https://en.m.wikipedia.org/wiki/Demography_of_the_Roman_Empire
I know its wikipedia, but it is one of the better articles, fairly well sourced and thorough.
https://www.princeton.edu/~pswpc/pdfs/scheidel/070706.pdf
This one is a pretty dense overview of the current debate on the topic, I’ve only skimmed it.
Ultimately, most of these sources do discuss the population of Italy in a fair amount of detail, so they’re pretty useful.
I still don’t have a solid number on just how many socii there were, but the that paper from Princeton does mention that Medieval Italy had 161 cities of decent size, so we can use that at least for a ballpark estimate. Hardly perfect, and it likely includes the Po Valley (Cisalpine Gaul) and possibly Sicily. So, whatever the figure is, its likely to be reasonably small than that. That also includes Rome (-1 there), and there’s likely some outlying suburbs that wouldn’t need to be counted either.
So, if we assume that this concerted effort through an alt-Lex Sempronia to enfranchise the whole of Italy starts in 133 BC, proceeds relatively steadily, and proceeds at a rate of 2 cities per year, then all of the Socii will be upgraded at least to Latins by 53 BC, and full citizenship by AD 27. Again, this is all very roughly estimated.
That seems very reasonable to me, and I think once the political system adapts in, say, a generation, the pace might pick up.
Haha I also used wikipedia in my sources, no sweat. That's actually where I got the 7 million figure for the population of Italy. I've skimmed your sources, and they all seem to place the Italian citizen population somewhere in the 4-10 million range, depending on how you count (some counts include women as citizens, some don't). I read the Princeton study that you linked and it offers a few competing claims, although the study ultimately comes to the conclusion that it is really impossible to tell from the few primary sources we have. However, if we take the "high count" offered by Tenney Frank in his research (as provided by the Princeton study), we arrive at a total of 4 million adult male citizens in 28 BCE. From what we know about mortality rates and Roman slavery we can estimate that the total free population (i.e. including women and children) was roughly 10-12 million, and at the time of the census there could have been anywhere from 2-5 million slaves. So if we assume this highest estimate is accurate, we have to next determine what percentage of that free population is eligible for military service by the time of 133 BCE. If we subtract just 1 million to account for population growth between 133 and 28 BCE, then there are roughly 9-10 million free adult males in Italy in 133 BCE. Furthermore, if we assume that the military levies reported by Polybius are equal in proportion to population at the time of the 2nd Punic War (which is a dubious assumption as the levies on the socii were likely higher than that of Roman citizens), then the ratio of Roman citizens to Latins to Socii is very roughly 3:1:8.
From here on out, all population counts only include free adult males.
If we take the total population of Italy, reserve roughly 500K for the city of Rome itself, and take the average population density and urbanization rate coupled with the number of significant cities (I'll use an estimate slightly lower than yours to account for Cisalpine Gaul and the relatively early POD) at the time of 133 BCE, then we arrive with a total urban population of 2.8 million, or around 20,000 inhabitants per city (given around 145 cities). To go forward, I am making three more assumptions. Firstly, I will assume that the free male population of Rome is made up entirely of Roman citizens; secondly I will assume that Roman citizens outside of Rome live in cities at rates similar to all other Italians (given an urbanization rate of 30%). Third and lastly, I will assume that the cities of Roman Italy follow a log-normal distribution (with each successive city having a population of 1/(n+1) in proportion to the largest city, Rome (most countries today follow this distribution of population). Given the 3:1:8 ratio stated earlier, that means that there are a total of 2.5 million Roman citizens, 800K Latins, and 6.5 million socii of which 500,000 citizens (excluding those in Rome), 240,000 Latins, and 1.8 million socii live in cities. Taking the 3:1:8 ratio again, and assuming that all cities have a homogenous population, then there are 36 Roman colonies, 12 Latin colonies, and 97 cities belonging to the socii. If the lex Sempronia takes effect in 133 BCE, then all of the cities with Latin rights in that year will be citizens by 126 BCE, and the new Latin population will be comprised entirely of former socii. However, assuming the log-normal distribution of citizen population, and assuming that any consul will prefer to give citizenship to the largest city available (in order to win the most favor with the new citizens), then 80% of the former socii living in cities (or around 25% of the total socii population) will be citizens within 10 years after 126 BCE. By this new threshold year of 116 BCE, there will be a total of 4.8 million Roman citizens (with 2.5 million living in cities around Italy), 600,00 Latins, and 5 million socii. The vast majority of the remaining Latins and socii will live in the countryside, since all the large cities in Italy will have been given citizenship by this point, probably incentivizing even more Latins and socii to move to the large cities in the years before they are given citizenship.
The movement of Italians into cities will probably be offset by the spread of poor Romans to the countryside in redistributed land. The 500,000-strong population of Rome was probably at least 90% poor, with around 100-200,000 living on bread subsidies. So assuming a distribution of 100,000 citizens onto small farms (which is probably extremely high, the actual number would likely be much lower), this means that the citizen population with enough wealth to be recruited into the legions would be roughly equal to the sum of around half of the citizen population given land by the lex Sempronia plus ten percent of all citizens living in urban areas plus some fraction of the total agrarian citizen population as well as an equal number of socii. This means at least 50,000 given land by the lex Sempronia plus 250,000 citizens living in cities and anywhere between 25-100,000 additional agrarian recruits for a total of around 300-400,000 potential legionaries with at least as many socii.
Looks like this may be possible folks, assuming that the senate and populares cooperate for the period 133-108 BCE leading up to the Jugurthine and Cimbrian Wars.