In the film Anatomy of a Fall by French director Justine Triet, which won the 2023 Oscar for Best Original Screenplay, a fatal fall is reconstructed to explore the breakdown of the romantic relationship between the main characters, Sandra Voyter and Samuel Maleski. The movie’s depiction of a breakup is not unusual; worldwide data indicates high rates of marriage failures, with a significant increase towards the end of the last century. In some Western nations, up to 50% of marriages do not last beyond 25 years, leading to the common saying that “half of all marriages end in divorce.” Triet suggests that “it is rare for a relationship to succeed. Most are difficult, and the film delves into that difficulty.” Divorce statistics, however, do not reveal the amount of unhappy relationships. While many marriages might be troubled, some are enduring and appear stronger and more loving than previous ones. This contrast—either widespread failure or notable success—reflects the present situation of marriage in the West, often described as the “all or nothing” marriage.
Research indicates that romantic relationships typically decline over time, with satisfaction generally decreasing. Couples who are successful are those who can halt this decline, maintaining a satisfying level indefinitely. By contrast, many relationships gradually deteriorate to the point where separation seems inevitable. Relationship psychology reveals that love alone is inadequate to keep a couple together—effort is necessary. Relationship expert John Gottman compares this to the second law of thermodynamics, where a marriage or any closed system will deteriorate unless effort is applied. Gottman states, “If you do nothing to improve your marriage, even if you do nothing wrong, it will still worsen over time.” The “all or nothing” concept thus implies that successful relationships demand considerable time and energy. Couples that commit to this will experience high satisfaction, whereas those that do not—like Sandra and Samuel in Triet’s film—are likely to fail.
But why do some couples manage to stop this decline and remain happy? Like Sandra and Samuel, all couples begin in love and desire eternal happiness together. Assuming they are compatible and willing to put in the effort, they create what is sometimes called an “Adam and Eve” relationship—a Biblical symbol of a harmonious, enduring bond. Analyzing this type of relationship using dynamic systems reaffirms the “all or nothing” theory. Dynamic systems are mathematical tools for understanding how a variable changes over time. In romantic relationships, the focus is on the “feeling” of love within the couple. Since effort is necessary to sustain the relationship, it forms a dynamic system controlled by effort: effort influences “feeling,” aiming to preserve it permanently.
Research using this effort-control theory indicates that a successful relationship requires effort beyond the partners’ preferred level, and this effort difference can be hard to sustain over time. As Sandra Voyter states in Triet’s film, relationships can be chaotic, involve individual struggles, joint efforts, or conflicts with one’s partner. The relationship between Samuel and Sandra shares features common to many relationships. Initially, the “feeling” is intense, and both partners believe it will last indefinitely. They are ready to contribute to the relationship’s happiness through personal effort, aware that some external event will likely disrupt this state. Homogamous couples—those sharing similar socioeconomic, cultural, or religious backgrounds—are generally more stable. However, many couples are heterogamous, differing in one or more of these aspects.
Heterogamy can extend beyond personal circumstances and can sometimes be reduced to an imbalance in how each partner converts effort into happiness or “feeling.” This disparity can result in unequal levels of effort in making the relationship successful, which often exceed the efforts both partners wish to exert. This situation occurs in Samuel and Sandra’s relationship; at one point, Samuel points out this imbalance, and Sandra responds that she finds the idea of equal effort depressing. Recent computational models for evaluating the dynamics of effort imbalances in couples help simulate the evolution of happiness in both stable and uncertain environments. These simulations suggest Sandra is correct: equal effort from both partners is not necessary.
In one scene of the film, Sandra and Samuel criticize each other over the efforts made or not made to sustain their relationship, illustrating common negative dynamics in couples where grievances are voiced. The film suggests that Samuel has contributed more effort than Sandra in their relationship. However, our analysis unexpectedly shows that the partner who is more emotionally efficient should exert more effort to sustain the relationship—Samuel appears to be that partner in the film. Our analysis also reveals that during a stressful event, both partners need to increase their effort levels for the relationship to endure, with the more efficient partner needing to increase their effort even more. In the film, Sandra and Samuel face a major misfortune, significantly impacting the narrative. This explains why Samuel feels more stressed than Sandra.
Mathematics predicts an outcome consistent with the film’s narrative: the ongoing overextension of the more emotionally efficient partner—intensified by a prolonged crisis—causes the relationship to break down, leading to Samuel’s downfall in the film.