Model 03 · runs in this page · nothing is sent anywhere
Gottman and Murray wrote a marriage as two equations. Here they are, drawn. Then four hundred couples run at once — and the gap between explaining a marriage and predicting one opens up in front of you.
This is a psychoeducational instrument, not a clinical one. It cannot tell you anything about your relationship. What it can do is make a handful of ideas — inertia, threshold, repair, two stable states, base rate — into things you can move with your thumb and watch respond.
In The Mathematics of Marriage (2002), Gottman and Murray modelled a conversation between two partners as a pair of coupled difference equations. Each turn, each partner's emotional tone is: some of where they just were, plus where they sit when left alone, plus whatever the other partner just did to them.
How much of this turn carries into the next. At 0 each turn starts fresh; high inertia is what "we can't drop it" looks like as a number.
Where each partner drifts with no partner in the room. Gottman called this the uninfluenced steady state. It is a parameter, not a personality.
Set both equal and warmth and coldness land with the same weight. Pull the cold side above the warm one and you have built negativity dominance.
How far down the other has to go before the steep slope takes over. Near zero is a hair trigger. Far down is the couple that lets a lot pass — for better and for worse.
Repair fires only when the other has dropped below the threshold — it is a term with a trigger, not general niceness. Damping is the brake on getting carried away upward.
Same couple, same dials. Only where the conversation opens changes.
The famous number attached to this work is a 94% accuracy in sorting couples who divorced from couples who did not (Buehlman, Gottman & Katz 1992 — 52 couples). When independent researchers later asked what that model predicts for a couple you have not already seen the ending of, the positive predictive value came out around 29% (Heyman & Smith Slep 2001).
Nothing dishonest has to happen for that gap to open. Two ordinary things produce it, and both are dials below.
Both rules are calibrated to catch 80% of the separations — the way a screening instrument is set, not by maximising accuracy. (Maximising accuracy was the first version; at a low base rate it degenerated into flagging almost nobody. Noted on the page rather than quietly fixed.)
The base rate. Drag it down and watch the third box fall while the first two barely move. A test can be accurate and still be wrong most times it speaks — that is arithmetic, not a flaw in the researchers.
Prediction only gets the opening. Fitting gets the ending too.
Illness, work, a birth, a move — circumstances that drift after anyone looked. Set this to zero and prediction becomes nearly perfect, because the future stops containing anything the past didn't. Every point above zero is information no early measurement could have held.
Right now every couple has its own dials, drawn at random — the usual assumption: outcomes track stable types.
How much of who-separated is accounted for by the couple's own parameters. Press Couples identical and this goes to nothing — while the two pictures above barely change.
Press Couples identical. Every couple now has exactly the same parameters — no types, no traits, no differences of any kind. The only thing separating them is which random turns they happened to get.
The trajectories still spread. Some still end cold. The histogram still looks bimodal. You can still fit a model that sorts them at high accuracy after the fact — and it will still predict badly going forward. An outcome distribution that looks like types can be produced with no types in it.
This is the move the Zero-Intelligence Market makes about prices: the order in the result came from the structure, not from anything clever inside the agents. Applied here it is a real, testable alternative to the trait story — and it is not a claim that types don't exist. It is the narrower and more useful claim that an outcome spread alone cannot tell you whether they do.
One thing this page must not be allowed to imply. In the no-types setting the PPV lands near 32%, which is close to the 29% Heyman and Smith Slep reported. That is a coincidence of the dial positions, not a reproduction of their result. Nothing here was fitted to any study, no real couple is in this data, and moving any slider moves that number. Treat the resemblance as a prompt to go read the papers, never as a finding.
| It looks like | It is actually |
|---|---|
| A prediction about a relationship | A shape with dials. It has never met anyone. Nothing you type here is measured, scored, stored, or sent. |
| Gottman's model | The published form of it — inertia, baseline, an asymmetric influence function, repair and damping. The constants here are illustrative, not the fitted ones from any study. |
| Evidence about couples | Evidence about the model. A simulation can show a story is coherent and can generate hypotheses. It cannot make a claim about people true. |
| A reason to distrust the research | A reason to read the numbers correctly. The 94% and the 29% are answers to two different questions, and both are honest answers. |
The empirical pattern that survives across models, incidentally, is not any of the origin stories — it is demand/withdraw, one partner pressing while the other pulls back, which meta-analysis puts at around r = .36 with relationship dissatisfaction (Schrodt, Witt & Shimkowski 2014). A useful next test for this lab: do the Gottman-shaped rules, attachment-shaped rules, and NVC-shaped rules all reproduce it? If several different machines generate the one measured pattern, that says something about how much any of the machines can claim.