I’m not sure how much the math adds to this analysis, but it adds an air of science to something fairly common-sensical. From Researcher Uses Formulas for Marriage:
John M. Gottman said a 20-year study involving more than 600 married couples shows that by carefully plotting how a husband and wife interact and then reducing those observations to a formula, researchers can tell which marriages will succeed and which are heading for the rocks.
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To gather the data, a team of researchers observed video tapes of couples in interviews by marriage counselors and noted how husbands and wives responded to each other. Gottman said his team found that there basically are three types of stable marriages.The first is a husband and wife who routinely avoids conflict. When a difference of opinion arises, said Gottman, ‘they will never argue. They will listen to the other, but will not try to persuade.’ Such marriages, which he calls the ‘avoiders,’ may be unemotional and distant, but they endure.
A second type is a volatile relationship ‘like two lawyers in a courtroom,’ said Gottman. ‘They can argue at the drop of a hat. They are the Bickersons,’ he said. Such marriages tend to last even though there are frequent and impassioned arguments.
The third type of stable marriage Gottman calls the ‘validating’ couple. They listen to each other, respect the other’s opinion and only occasionally argue. ‘They pick the issues they fight about,’ he said.
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Researchers mathematically chart the marriage interactions by plotting not just what is said, but also how it is said and the body language and facial expression behind it. Emotions such as anger, harshness and hostility get a negative number, while humor and an eagerness to talk lovingly about the partner get a positive rating.
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He said an “escalating negative affect”, or a steep descent on the chart below the neutral point, predicts a couple will divorce within 5.6 years after marriage.