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Personas and the population

A persona is one simulated person. In Jahan a persona is never invented by a model: it is one real row of a persona dataset, drawn at random. The population is every persona in a study, together with the social network that ties them and the communities found in it. A study has exactly one population, built once and carried through every scenario (ADR 0015).

Where personas come from

The default corpus is MatrAIx Persona 1M1, about a million rows described by up to 1,290 attributes, gathered from several sources:

Source What a row is How its fields were obtained
gss a General Social Survey respondent answered
stackoverflow a Stack Overflow Developer Survey respondent answered
prism a PRISM alignment-study participant answered
real_human_survey a respondent to another human survey answered
wiki a person described on Wikipedia read from text by a model
amazon an Amazon product reviewer read from text by a model
synthetic a generated row invented

The corpus is released for research only (matraix-research-only). It is not in this repository: you download it yourself and accept its terms (ADR 0016). Any other population you have the rights to can be plugged in through the same port.

How much each value is worth: evidence tiers

Sources differ enormously in what their values mean. A survey answer is a measurement; a model's reading of a Wikipedia biography is a claim about a text. Jahan states, for every field of every persona, which kind of value it holds (ADR 0017):

Tier Meaning Example
Measured an instrument recorded it a GSS respondent's age bracket
Extracted a model read it from corpus text, or inferred it from other answers a reviewer's diet, read from their reviews
Calibrated corrected against external human data reserved; nothing produces it yet
Synthesized filled in by a model because the row was sparse a monthly budget, completed for this study

The tiers are ordered strongest to weakest. A tier grades a claim; it never blocks one. But anything judged on several fields is graded by the weakest tier among them, so a pass can never be read as stronger evidence than its weakest input.

Two rules that never bend

  • Demographics and psychographics are never synthesized. A model may fill in an economic, media or decision-rule field; it may never invent someone's age or attitudes for a study.
  • A tier is stated, never inferred. A field with no tier is an error, not a measured value.

Building a population, step by step

flowchart LR
  A["Eligible<br/>(conditioning set present)"] --> B["Sample<br/>(audience quotas)"]
  B --> C{"Gates<br/>(χ², KS)"}
  C -- fail --> X["Refused<br/>no model called"]
  C -- pass --> D["Fill sparse fields<br/>(sampled from a<br/>stated distribution)"]
  D --> E["Social network<br/>+ communities"]

1. Eligibility comes first

The category ontology names a conditioning set: the attributes a persona must carry for its answers to mean anything (for example age, sex and exercise frequency for a protein drink). A row missing any of them is never eligible. This is decided at the index, before sampling, because dropping incomplete rows after sampling quietly skews the population toward the corpus's most complete rows, which are its synthetic ones (ADR 0002).

2. Sampling by audience quota

Each audience gets a quota from its declared share, rounded by largest remainder so the quotas sum exactly to the study size. For 1,500 personas at shares 0.6 / 0.4 the quotas are 900 and 600. Each audience is drawn from its eligible rows with a seeded generator, and a row is drawn at most once even if it fits two audiences.

When too few rows match an audience, the filter is loosened by a fixed ladder, and every step is recorded as a relaxation on the gate report:

  1. widen an ordinal filter by one band;
  2. drop the least relevant filter that is not in the conditioning set;
  3. accept the shortfall, so the achieved mix tells the truth;
  4. fail only if the audience matches nobody at all.

The conditioning set is never a rung: trading it for coverage would undo the reason it exists.

3. Gates: does the draw look like what was asked for?

Before any model is called, every gated attribute of the sample is compared with a reference: what the study's own design implies (each audience's eligible pool, weighted by its share), or, for a study that declares no audiences, the category's measured targets. Gates run only on measured or extracted attributes, never on synthesized ones, since that would be grading an invention.

Categorical attributes: Pearson's χ² test

For an attribute with categories \(i = 1 \dots k\), observed counts \(O_i\) and expected counts \(E_i\) (the reference shares scaled to the sample size):

\[ \chi^2 = \sum_{i=1}^{k} \frac{(O_i - E_i)^2}{E_i}, \qquad \text{df} = k - 1 \]

The p-value is the χ² survival function at that statistic. The gate passes when the p-value is above the significance level \(\alpha = 0.05\).2

Worked example

The reference expects 50% women and 50% men; a draw of 100 personas has 58 and 42.

\[ \chi^2 = \frac{(58-50)^2}{50} + \frac{(42-50)^2}{50} = 1.28 + 1.28 = 2.56, \qquad \text{df} = 1 \]

\(p = 0.110 > 0.05\), so the gate passes: a split this uneven happens about one time in nine by chance alone.

Many attributes at once: Holm's correction

Testing many attributes separately at 0.05 makes a fair sample fail by chance. With \(m\) independent tests the chance that at least one fails is \(1 - 0.95^{m}\): about 30% for 7 attributes and 77% for 29. So the categorical gates of one report are judged as one family with Holm's step-down adjustment3 (ADR 0049). Sort the \(m\) p-values ascending, \(p_{(1)} \le \dots \le p_{(m)}\), then

\[ \tilde p_{(j)} = \max_{l \le j} \; \min\!\big(1,\; (m - l + 1)\, p_{(l)}\big) \]

A gate passes when its adjusted p-value \(\tilde p\) is above \(\alpha\). The level now bounds the chance that a fair sample fails any gate, not each one. Both the raw and adjusted p-values are reported.

Worked example

Three categorical gates return \(p = 0.012,\ 0.040,\ 0.300\).

rank \(j\) raw \(p\) \((m-j+1)\,p\) adjusted \(\tilde p\) verdict at 0.05
1 0.012 3 × 0.012 = 0.036 0.036 fail
2 0.040 2 × 0.040 = 0.080 0.080 pass
3 0.300 1 × 0.300 = 0.300 0.300 pass

Unadjusted, two gates would have failed. After adjustment only the strongest skew does, and the population is still refused, since any failing gate rejects it.

Ordered attributes: Kolmogorov–Smirnov similarity

For an attribute whose bands have an order (rarely < weekly < 3+ a week), the gate compares cumulative shares instead. With \(F_S\) the sample's cumulative distribution over the declared band order and \(F_R\) the reference's:

\[ D = \max_{b} \left| F_S(b) - F_R(b) \right|, \qquad \text{similarity} = 1 - D \]

The gate passes when the similarity is at least 0.80. It is named similarity so the threshold reads the way it means: higher is better.4

Worked example

band reference share sample share \(F_R\) \(F_S\) \(\lvert F_S - F_R\rvert\)
rarely 0.20 0.10 0.20 0.10 0.10
weekly 0.50 0.50 0.70 0.60 0.10
3+ weekly 0.30 0.40 1.00 1.00 0.00

\(D = 0.10\), so the similarity is \(0.90 \ge 0.80\) and the gate passes.

Any failing gate rejects the population, and no model is ever called for a rejected draw. Checking a draw is therefore free. Every threshold above is a recorded study parameter with the engine's default, never an environment variable, so a loosened gate travels with the population that used it.

4. Filling in what the row lacks

Survey rows rarely carry everything a category needs: a GSS respondent was never asked about protein drinks. Where the ontology allows it, a model fills the gap, but never with free text. It is shown the persona's known attributes and the attribute's closed list of values from the corpus, and states a probability for each. The engine then samples the value from that distribution with the population's seeded random stream (ADR 0024). The value is marked synthesized, and the distribution it was drawn from is recorded beside it.

Sampling, not taking the most likely value, matters: if every 30-year-old woman got the single likeliest attitude, everyone with the same demographics would think alike, and the network would look more opinionated than any real population. How widely values may vary is the study's completion temperature \(T\). With stated probabilities \(p_i\):

\[ p_i' = \frac{p_i^{1/T}}{\sum_j p_j^{1/T}} \]

\(T = 1\) samples from what the model stated; \(T < 1\) sharpens toward the likeliest value; \(T > 1\) flattens.

Worked example

The model states \((0.6, 0.3, 0.1)\) for budget-conscious / balanced / premium.

\(T\) distribution sampled from
0.5 (0.783, 0.196, 0.022)
1.0 (0.600, 0.300, 0.100)
2.0 (0.473, 0.334, 0.193)

A distribution that does not cover every value, or does not sum to one, is refused rather than repaired, and the field is left empty. A persona missing a non-conditioning attribute is valid; a persona with an invented vocabulary is not.

Measured: filled-in attitudes are weak

The engine's own holdout found that model-filled attitudes capture relative differences between groups but lose to a plain demographic baseline overall. See Results so far.

5. The social network

Last, personas are tied into a network and its communities are discovered. See The social network.

What the population carries

A built population records the row each persona came from, the requested and achieved audience mix, the source mix, every relaxation, every gate with its threshold and verdict, the tier of every field, the completion distributions, and a hash of all of it. A rebuild against a live model would be a different population (the completions would differ), so a population is built once and carried, never rebuilt.

  1. MatrAIx. MatrAIx Persona 1M (dataset), Hugging Face MatrAIx2026/MatrAIx_Persona_1M, and MatrAIx-Persona-8B, https://github.com/MatrAIx-ai/MatrAIx-Persona-8B. Released under matraix-research-only. ↩

  2. K. Pearson (1900). "On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling." Philosophical Magazine, 50(302), 157–175. ↩

  3. S. Holm (1979). "A simple sequentially rejective multiple test procedure." Scandinavian Journal of Statistics, 6(2), 65–70. ↩

  4. A. Kolmogorov (1933). "Sulla determinazione empirica di una legge di distribuzione." Giornale dell'Istituto Italiano degli Attuari, 4, 83–91; N. Smirnov (1948). "Table for estimating the goodness of fit of empirical distributions." Annals of Mathematical Statistics, 19(2), 279–281. ↩