The Geometry of Relationships

When two friends fall out, one stops answering the phone. When two countries fall out, one recalls its ambassador “for consultations,” a polite diplomatic way of saying “we are unhappy with you.” The tools differ, but the logic is the same: show displeasure, avoid violence, and leave a door open for coming back.

The resemblance is not a coincidence. Trust, violence, withdrawal, reconciliation and rivalry exist between people and between countries alike. This essay offers one lens for looking at both. It won’t predict what a particular couple or country will do. Instead, it gives you six questions that make any relationship easier to read:

1. Where does the relationship stand?
2. How does each side see it?
3. What moves it?
4. Who are the two sides?
5. What surrounds it?
6. How does it change over time?

Each of the first six sections takes one question. Along the way we put rough numbers on things, such as a scale from 0 to 10, because numbers make comparisons easy to see. Treat them as a way of thinking, not as measurements. After that, we put the pieces together in one picture and look at eight familiar patterns, from a couple’s argument to an arms race, that the lens helps explain.

1Where does the relationship stand?

Psychologists have a well-known way of describing personality, the “Big Five” traits.¹ Relationships have no equally accepted model, but several studies have found overlapping dimensions.² Combining them gives seven. Think of each as a scale from 0 (low) to 10 (high):

1. Warmth: from hostility to friendship
2. Aligned interests: is one side’s gain also the other’s?
3. Power balance: who has the upper hand?
4. Interdependence: how tied together are their fates?
5. Trust: can each count on the other’s behaviour?
6. Formality: does it run on contracts, or on custom and feeling?
7. Stability: how settled is the relationship?

Each dimension shows up in both worlds:

The seven dimensions are independent of one another. Two friends can share high warmth and opposed interests, for example when both apply for the same job. Two rival countries can have little warmth and a lot of economic interdependence. That independence is what lets the lens say more than “good” or “bad.”

A handy way to see all seven at once is a radar chart. Each spoke is one dimension, and the further out a point sits, the higher the value. Join the points and every relationship gets a shape.

2How does each side see it?

A relationship has two pictures, not one: my picture of it and yours. Many arguments start from the gap between those pictures rather than from the relationship itself. The political scientist Robert Jervis showed that wars, too, have often started this way, with one side misreading the other’s intentions.³

We call the distance between the two pictures the perception gap. It works differently for different dimensions. Warmth and trust exist only in each side’s mind. Interests, power, interdependence and formality also have a real value that can be checked, through trade figures, treaties or military strength, and either side’s picture can drift away from it.

3What moves it?

The picture does not stay still. The same loop repeats again and again: each side reads the other’s latest behaviour, its picture of the relationship shifts a little, it chooses what to do next, and that choice becomes the other side’s input. Each side reads through the filter of its own personality, which section 4 describes.

Behaviours fall into six families. Each family pushes the relationship in its own direction, and each has a version between people and a version between countries:

Behaviours also differ in how ambiguous they are. A silence can be read as tiredness or as indifference. That ambiguity is where personality comes in: it decides which reading wins.

4Who are the two sides?

Two people in the same situation do not behave the same way. The lens gives every actor a personality, but it does not measure a person and a country with the same ruler.

For an individual, five traits. Two come from the Big Five: agreeableness, and threat sensitivity, which psychologists call neuroticism. Two come from attachment theory, which studies how people handle closeness and distance in close relationships.⁴ The fifth, drive for power, comes from research on motivation.⁵

For a group, such as a team, a company or a country, six traits. Two come from international relations: strategic culture, a country’s settled habits about when force is acceptable,⁶ and its stance toward the existing order, whether it wants to keep things as they are or change them.⁷

The last trait connects the two tables. The more concentrated decision-making is, the more a group behaves like its leader. Scholars still debate how much individual leaders shape history, but they broadly agree that leaders matter more where power sits with a few people.⁸

5What surrounds it?

No relationship lives alone. Each pair sits inside a wider network, and several things around it shape what happens between the two sides:

• A third party can bring them together as a mediator, make betrayal costly as a guarantor, or unite them as a shared enemy.
• A referee, a higher authority such as a court or a police force, makes violence expensive. Between countries there is usually no such referee; international relations scholars call this condition anarchy.⁹
• Audiences watch each side: voters, colleagues, family. They make backing down and compromise more expensive, because giving in looks like weakness to the people watching.¹⁰
• Mechanisms attached to the relationship itself make behaviour clearer or betrayal costlier: verification, collateral, or a direct hotline like the one set up between Moscow and Washington in 1963.¹¹
• External shocks, such as a crisis, a disaster or a new common threat, hit the relationship from outside.

6How does it change over time?

A relationship moves in steps, one turn of the loop at a time, and a few rules shape how those steps add up.

Trust is built slowly and lost quickly. Many small good acts raise it a little at a time; one betrayal can undo most of that in a single step. Researchers call this the asymmetry principle: trust is easier to destroy than to create.¹² Repair is possible, but slower than the damage, and it often leaves a scar. The relationship climbs back, but not all the way.

When nothing happens, a relationship does not reset. It drifts a little and then settles, keeping part of what came before. Old friends who have not met in years still keep some of their warmth, and an old betrayal can colour a relationship long after it happened.

Over time, these steps add up to stability. A long history with few swings makes a relationship hard to shake, for better or for worse, and it tends to come to rest in one of a few states. The political theorist Alexander Wendt describes three such states between countries: enemies, rivals and friends.¹³ Relationships between people settle in similar ways.

7The whole model in one picture

Here are all the pieces together: the network everyone lives in, the two sides of one relationship, the behaviours that pass between them, and the patterns that come out of that back-and-forth.

8Eight patterns the lens reveals

A good lens makes familiar things easier to see. The eight patterns below appear between people and between countries, and each one follows from the pieces above.

1. The escalation spiral

Two threat-sensitive sides with no referee read each other’s ambiguous moves as hostile, answer with a little hostility, and each answer becomes the other’s next input. International relations scholars call this the security dilemma: arming for defence looks like a threat to the neighbour, who arms in turn.¹⁴ At home, it is the argument that starts with one ambiguous sentence and lasts for hours.

2. Trust takes the stairs and leaves by the lift

Section 6 described how trust is lost faster than it is built. Research on couples puts a rough number on it. The psychologist John Gottman found that in stable marriages, even during disagreements, positive interactions outnumber negative ones by about five to one.¹⁵ In other words, one harsh moment takes about five good ones to balance.

3. Pursue and withdraw

When one partner is anxious and fears distance, and the other is avoidant and flees closeness, every step one takes toward the other pushes the other back. Couples researchers call this the demand–withdraw pattern.¹⁶ Such a pair rarely becomes either enemies or close friends. They hover in the middle, and because the anxious partner reads distance as coldness, their two pictures of the same relationship drift apart.

4. Withdrawal only works on someone who needs you

Giving someone the cold shoulder works only if they depend on you. Studies of economic sanctions point the same way: sanctions work best against allies and trading partners of the country imposing them.¹⁷ And withdrawing from someone who does not care about you only widens the distance.

5. The blind spot of the upper hand

The stronger side tends to see less of the imbalance. A manager may believe the relationship with an employee is equal and friendly while the employee feels otherwise. Experiments support part of this picture: people put in a position of power become less likely to take other people’s point of view.¹⁸ An unequal relationship therefore tends to carry a lasting gap in trust. The weaker side has more to lose, so it trusts less, even when both sides behave in a friendly way.

6. Three resting states

As section 6 described, relationships tend to settle as enemies, rivals or friends. Moving from one state to another takes a big push, not a few nudges. After the Second World War, France and Germany placed their coal and steel industries, the raw materials of war, under a shared authority.¹⁹ They changed the structure of their relationship, not just its mood.

7. The enemy of my enemy

When a third party enters, triangles tend toward balance. The psychologist Fritz Heider called this balance theory: the enemy of my enemy is my friend.²⁰ The alliance between the United States and the Soviet Union against Nazi Germany is a classic example, and so is its collapse once the shared enemy was gone.

A third party can play the other roles described in section 5 as well. In Muzafer Sherif’s well-known Robbers Cave experiment, two groups of boys at a summer camp became enemies, and made peace only when they faced problems neither group could solve alone.²¹

8. A face-saving way out

Section 5 described how audiences make backing down expensive. During the Cuban Missile Crisis in 1962, part of the deal that ended it, the removal of American missiles from Turkey, was kept secret for years, so that neither side had to give way in front of its audience.²²

9Try the lens yourself

Pick any relationship: a friendship, a team at work, two companies, two countries in the news. Then ask:

1. On the seven dimensions, which are high and which are low? Sketch the shape.
2. Would the other side draw the same shape? Where would the two pictures differ most?
3. Which behaviours have been moving it lately, and in which direction?
4. What in each side’s personality makes it read things a certain way?
5. Who else is involved, who is watching, and is there a referee?
6. Which resting state is it in, and what would it take to move it?

The second question is often the hardest to answer honestly, and often the most useful.

10What the lens doesn’t show

This lens is a map, not the territory. The numbers in this essay are illustrations, not measurements. Seven dimensions are not everything a relationship is: love, identity and culture are more complicated than a handful of numbers. And people are not countries. Countries have no referee above them, and their decisions pass through bureaucracies and domestic politics.

Still, when the same few pieces explain both a couple’s argument and an arms race, both a quiet withdrawal and a recalled ambassador, they have captured something real about relationships.

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Notes

1. The Big Five (openness, conscientiousness, extraversion, agreeableness, neuroticism) is the most widely used model of personality. See McCrae, R. R. & John, O. P. (1992), “An introduction to the five-factor model and its applications,” Journal of Personality 60(2), 175–215. ↩
2. Wish, M., Deutsch, M. & Kaplan, S. J. (1976), “Perceived dimensions of interpersonal relations,” Journal of Personality and Social Psychology 33(4), 409–420. They found four dimensions: cooperative vs competitive, equal vs unequal, intense vs superficial, and socioemotional vs task-oriented. The seven dimensions in this essay are our own combination. ↩
3. Jervis, R. (1976), Perception and Misperception in International Politics, Princeton University Press. ↩
4. Attachment theory began with John Bowlby (Attachment and Loss, 1969) and Mary Ainsworth. Its application to adult relationships, including the anxious and avoidant styles, comes from Hazan, C. & Shaver, P. (1987), “Romantic love conceptualized as an attachment process,” Journal of Personality and Social Psychology 52(3), 511–524. ↩
5. McClelland, D. C. (1975), Power: The Inner Experience, Irvington. ↩
6. The term was introduced by Jack Snyder (1977), The Soviet Strategic Culture: Implications for Limited Nuclear Operations, RAND Corporation, R-2154-AF. ↩
7. On status-quo and revisionist states, see Schweller, R. L. (1994), “Bandwagoning for profit,” International Security 19(1), 72–107. ↩
8. Byman, D. L. & Pollack, K. M. (2001), “Let us now praise great men: bringing the statesman back in,” International Security 25(4), 107–146. ↩
9. Waltz, K. N. (1979), Theory of International Politics, Addison-Wesley. ↩
10. Fearon, J. D. (1994), “Domestic political audiences and the escalation of international disputes,” American Political Science Review 88(3), 577–592. See also Putnam, R. D. (1988), “Diplomacy and domestic politics: the logic of two-level games,” International Organization 42(3), 427–460. ↩
11. The United States and the Soviet Union agreed to set up a direct communications link in June 1963, after the Cuban Missile Crisis showed how slowly messages could travel in an emergency. The link went into service on 30 August 1963. ↩
12. Slovic, P. (1993), “Perceived risk, trust, and democracy,” Risk Analysis 13(6), 675–682. ↩
13. Wendt, A. (1999), Social Theory of International Politics, Cambridge University Press. Wendt calls the three “cultures of anarchy”: Hobbesian (enemies), Lockean (rivals) and Kantian (friends). ↩
14. Herz, J. H. (1950), “Idealist internationalism and the security dilemma,” World Politics 2(2), 157–180; Jervis, R. (1978), “Cooperation under the security dilemma,” World Politics 30(2), 167–214. ↩
15. Gottman, J. M. (1994), What Predicts Divorce? The Relationship Between Marital Processes and Marital Outcomes, Lawrence Erlbaum. ↩
16. Christensen, A. & Heavey, C. L. (1990), “Gender and social structure in the demand/withdraw pattern of marital conflict,” Journal of Personality and Social Psychology 59(1), 73–81. ↩
17. Hufbauer, G. C., Schott, J. J., Elliott, K. A. & Oegg, B. (2007), Economic Sanctions Reconsidered, 3rd ed., Peterson Institute for International Economics. ↩
18. Galinsky, A. D., Magee, J. C., Inesi, M. E. & Gruenfeld, D. H. (2006), “Power and perspectives not taken,” Psychological Science 17(12), 1068–1074. ↩
19. The plan was announced in the Schuman Declaration of 9 May 1950 and put into effect by the Treaty of Paris, signed on 18 April 1951, which created the European Coal and Steel Community. The declaration proposed placing French and German coal and steel production under a common High Authority. ↩
20. Heider, F. (1946), “Attitudes and cognitive organization,” Journal of Psychology 21, 107–112. ↩
21. Sherif, M., Harvey, O. J., White, B. J., Hood, W. R. & Sherif, C. W. (1961), Intergroup Conflict and Cooperation: The Robbers Cave Experiment, University of Oklahoma. The experiment took place in 1954. ↩
22. Bernstein, B. J. (1980), “The Cuban Missile Crisis: trading the Jupiters in Turkey?”, Political Science Quarterly 95(1), 97–125. The trade was confirmed publicly only in the late 1980s. ↩