This is a working instrument, not an illustration. It takes the structural parameters that Richard Talbert established for the senate as a corporate body and that Andrew Lintott established for provincial administration, holds them apart from anything they do not say, and lets you assemble a picture of the spectrum of office-holders alive in any single year between AD 1 and AD 235 — how many men stood at each grade, how old they were, how fast they were moving, and who had put them there.
Every parameter in this model carries one of these. They are visible everywhere: on the establishment table, in the tooltips, in the apparatus.
For any year, the number of posts of each kind. This layer is almost entirely tier A and B: Talbert gives the counts and the dates at which they changed. It answers how many places existed. It says nothing about who filled them.
Twenty men enter at about 25 each year and are aged forward through a mortality schedule calibrated so that mean further life at 25 is thirty years — Talbert's own demographic requirement for holding the senate at 600. They compete for the establishment of Layer 1 under the seniority and age rules Talbert sets out. The output is a population: grades, ages, career velocities, and the share of each entry cohort that ever reached the consulship.
Talbert states a demographic requirement and never names a life table. The Talent pool view supplies the six published alternatives — Coale–Demeny West at three levels in both sexes, and Frier's reconstruction of Ulpian's annuity table — and runs the whole model under each. The spread between them is not error; it is the range the demographic literature genuinely leaves open, and it turns out to straddle Talbert's six hundred rather than confirm it.
Each post is classified by who filled it: the emperor directly, the lot, or election in the senate under imperial veto. This is where Lintott does the work Talbert cannot — legati appointed "at will without any legal restrictions", proconsuls "selected by lot ... normally expected to serve a single year".
Ten propositions the two books jointly support or complicate, each stated so that the model can be made to bear on it, and each paired with the evidence that would falsify it. These are the point of the exercise: the numbers exist to make the arguments testable.
"This minor difficulty aside, therefore, to maintain total membership at 600 it would be necessary for twenty entrants annually aged around 25 to have an average life expectancy of 30 years. Demographically speaking, that is apparently a plausible expectation."
Everything demographic in this model hangs on that sentence. Twenty entrants a year at twenty-five, thirty further years of life on average, and the arithmetic closes at six hundred. The cohort engine implements exactly this and nothing more; it then reports what else follows from it, including one consequence Talbert did not draw and one place where his own two figures pull against each other.
Pick a year. The model reports the establishment — the number of posts of each grade that existed that year — and then the population the cohort engine puts into them.
Everyone alive in a given year who has already held office — the accumulated governing cadre, not the men holding magistracies that year. This is the view the two books make possible but neither performs: Talbert supplies the intake and the establishment, and states the demographic condition his figures require; the published Roman life tables supply the mortality he leaves open. Put together, they give a pool with a knowable shape and a genuinely uncertain size.
Talbert gives ages, not durations, and he gives them for three kinds of man. This view reconstructs the timetable from those ages and the statutory rules, then shows what the cohort engine actually produces when twenty men a year compete for a fixed establishment.
A synthetic senatorial population, aged year by year through the establishment. This is the most heavily modelled part of the instrument and the least evidential: read it as a consequence-generator for Talbert's own assumptions, not as a reconstruction of what happened.
Who put a man in a post. This is the axis on which the two books are complementary rather than overlapping: Talbert traces the magistracies and the lot, Lintott the governorships and the emperor's unrestricted power over his own legates.
Ten propositions, five quantitative and five qualitative. Each is stated so that it could be wrong, each names the evidence in Talbert or Lintott that bears on it, and each names what would falsify it. Quantitative hypotheses can be exercised against the model directly; the controls that matter are named.
Every parameter, every citation, and — as importantly — an explicit register of what the two books do not contain.