Author: IMC

Cooperation is a guiding principle of everyday life. It’s as simple as following the rules of the road when driving or holding a door for a stranger; cooperation is a fundamental aspect of human societies and has long intrigued evolutionary biologists. But how do people reach a consensus on whether, and with whom, to cooperate?

A new study by Taylor Kessinger, a postdoctoral researcher in the Department of Biology, was published in the Proceedings of the National Academy of Sciences and provides valuable insights into community-based social norms by developing evolutionary game theory and mathematical models to mimic the dynamics of reputation-based cooperation in group-structured populations.

“Darwin famously asked: ‘Why would anyone ever be altruistic?’ And it turns out that question has tons of answers,” Kessinger says.

While previous theories have been proposed to explain cooperation (such as kin selection, wherein individuals are more likely to engage in prosocial behaviours with their relatives), in contemporary human societies, people cooperate with members of much larger communities. This leads to a complicated dynamic and interplay between community members, as cooperating with or avoiding certain individuals greatly affects one’s reputation.

“We wanted to understand the driving factors behind the convergence of social norms, especially in a heterogeneous society where different groups might have diverging views on reputations,” says senior author Joshua Plotkin, the Walter H. and Leonore C. Annenberg Professor of the Natural Sciences. “These norms are vital in facilitating cooperation, and yet how they are collectively accepted and evolve remains largely unexplored.”

Kessinger, the paper’s first author and a member of the Plotkin Research Group, explains that traditional models of cooperation have been based on homogeneous societies and straightforward information flow.

“We realized that this isn’t an accurate representation of reality, as societies are multifaceted; different groups disagree, not only about reputations, but also about which norms should govern behaviour,” Kessinger says.

To address this, the researchers developed a model that considers multiple coexisting social norms and studied how these norms might compete as individuals learn from one another and shift group affiliations, and whether this will lead to the convergence upon a shared norm. One of the key findings was the success of a particular social norm called “stern judging.” This norm assigns a bad reputation to individuals who cooperate with those of bad standing, as a punitive means.

“Stern judging came out on top among the norms we evaluated,” Kessinger says. “It was particularly effective in situations where individuals show a preference for interacting within their own group. This norm, emphasizing a sort of vigilant caution, appears to facilitate greater overall cooperation.”

However, the team also found that separating reputation information into independent groups can destabilize cooperation. “It’s a delicate balance,” Kessinger explains. “The more fragmented the information about reputations, the harder it is for cooperation to take root. But we also observed that in-group social interactions can partly counteract this effect.”

Their research paints a complex picture of cooperation. While certain norms promote the behaviour, the social structures of each community significantly influence its success. Stern judging is a robust facilitator of cooperation; however, it does not work in a fractured society without the ability for individuals to share information between groups.

By revealing the factors that influence the emergence of shared social norms, the study offers valuable insights for diverse fields, from sociology to psychology, and economics.

“Our findings have some implications for how to foster cooperation in diverse, multicultural societies,” Plotkin notes. “Whether it’s at a societal level or within smaller groups like neighbourhoods or workplaces, the ability to converge on a shared norm is crucial.”

The researchers also explore potential implications for the evolution of social norms and the number of independent judgment groups a well-functioning society can sustain. “The insights from our research open up new avenues for exploring the complexity of cooperation in society,” says Kessinger.

Looking ahead, the team wants to investigate how well real-world social norms humans use to judge behaviour map onto the abstract theoretical ones they have developed. With this, they believe that researchers will be able to gauge the extent to which individuals in a population adhere to specific social norms, with respect to demographic factors such as culture or age groups.

“There’s so much more to discover about how we come together to agree on norms and, ultimately, how we cooperate,” Kessinger says.

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Credit of the article given to Nathi Magubane, University of Pennsylvania

An international team led by researchers at Nankai University in China and at University of Zagreb in Croatia, along with team at the Institut national de la recherche scientifique (INRS) in Canada, led by Roberto Morandotti has made an important breakthrough in the study of topological phases. Their findings were recently published in Nature Physics.

In the last decade, topological photonics has attracted increasing attention due to the unique prospects to achieve light manipulation with high performance in terms of robustness and stability.

Discoveries in topological photonics have opened the way to the development of a novel generation of photonic devices, such as topological lasers and cavities, featuring topologically protected states that are immune to disorders and defects. The concept of topology in physics is inherited from mathematics, where topology is employed to study geometric properties of an object concerning quantities that are preserved under continuous deformation.

Two objects are topologically identical when the surface of one can be continuously deformed into that of the other one and vice versa, e.g., a coffee cup and a torus are equivalent from a topology viewpoint. In physics, the concept of topology is employed to describe the energy band characteristics, leading to prediction of novel topological states of matter and various topological materials.

Different topological phases (trivial and nontrivial) are distinguished by appropriately introducing quantized topological invariants, which enable establishing a link between the bulk properties and the emergence of the feature at the boundary of these materials, known as the bulk-boundary correspondence. In this regard, the most distinctive feature of a nontrivial topology is the existence of robust topological boundary states protected by specific spatial and/or intrinsic symmetries.

In general, in systems of symmetry-protected topological phase (SPT phase), it is believed that the close relationship between topological boundary states, topological invariants, and one or more overall symmetries is indispensable for maintaining topological protection against perturbations.

As consequence, both topological invariants and topological boundary states are irretrievably affected by any distortion that breaks the underlying symmetry. In this work, the international research team has challenged this traditional common belief, and thus broaden the understanding of SPT boundary states. They found that even if the system no longer has quantized topological invariants and some kinds of global symmetry, the topological boundary states can still exist in the corresponding subspaces, protected by the so-called sub-symmetries.

“Our discovery challenges the common thinking of the symmetry-protected topological phase in topology and renews the correspondence of topological invariant and boundary states,” said Domenico Bongiovanni one of the main investigators, Postdoctoral researcher at INRS-EMT. “Our idea has the potential to explain the topological origin of many unconventional states and can find application in different platforms and physical systems.”

The researchers, by introducing and exploring the concept of sub-symmetry, found that global symmetry in the traditional sense is not completely necessary for the protection of topological boundary states. In this regard, topological boundary states are preserved as long as the symmetries of specific subspaces are satisfied, even when the overall topological invariants no longer exist.

The research team cleverly designed and fabricated photonic lattice structures using a cw-laser writing technique to meet the conditions of different subspace symmetries. The experiments demonstrated a proof of concept with two most typical topological lattices: one-dimensional SSH and two-dimensional Kagome lattices.

In addition, the team innovatively introduced the concept of long-range coupling symmetry into the Kagome lattice model, which resolves the current controversies about the existence and topological protection of higher-order topological states in the Kagome lattice.

This study not only challenges the traditional comprehension of topological states protected by symmetry but also provides new ideas for the research and application of topological states in different physical backgrounds. This impact of this work is expected to further promote the development of topological photonics and its cutting-edge interdisciplinary fields, as well as the research and development of a new generation of topological photonic devices based on sub-symmetry-protected boundary states.

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Credit of the article given to Institut national de la recherche scientifique – INRS

A George Washington University research team has created a novel formula that demonstrates how, why, and when hate speech spreads throughout social media. The researchers put forth a first-principles dynamical theory that explores a new realm of physics in order to represent the shockwave effect created by bigoted content across online communities.

This effect is evident in lightly moderated websites, such as 4Chan, and highly regulated social platforms like Facebook. Furthermore, hate speech ripples through online communities in a pattern that non-hateful content typically does not follow.

The new theory considers recently gained knowledge on the pivotal role of in-built communities in the growth of online extremism. The formula weighs the competing forces of fusion and fission, accounting for the spontaneous emergence of in-built communities through the absorption of other communities and interested individuals (fusion) and the disciplinary measures moderators take against users and groups that violate a given platform’s rules (fission).

Researchers hope the formula can serve as a tool for moderators to project the shockwave-like spread of hateful content and develop methods to delay, divert, and prevent it from spiraling out of control. The novel theory could also be applied beyond social mediaplatforms and online message boards, potentially powering moderation strategies on blockchain platforms, generative AI, and the metaverse.

“This study presents the missing science of how harms thrive online and, hence, how they can be overcome,” Neil Johnson, professor of physics at the George Washington University and co-author of the study, said. “This missing science is a new form of shockwave physics.”

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Credit of the article given to George Washington University

Researchers at the Universidad Carlos III de Madrid (UC3M) and the Universidad Complutense de Madrid (UCM) have discovered a phase shift between chaotic states that can appear in herds of animals and, in particular, in swarms of insects. This advance may help to better understand their behaviour or be applied to the study of the movement of cells or tumors.

A phase shift occurs when the conditions of a system change drastically, for example, when water changes from a liquid to a solid statewhen it freezes. In this research, recently published in the journal Physical Review E, this group of mathematicians has found such a phenomenon in swarms. Related research is also available on the arXiv preprint server.

“The insects in the swarm stay in a limited volume, even if they’re in a park or an open space. To explain this, we assume that there is a harmonic potential, a kind of recuperative force that confines them (like that of a spring that tries to return to its resting position when we stretch or contract it),” explains one of the study’s authors, Luis L. Bonilla, director of UC3M’s Gregorio Millán Barbany Institute.

This confinement of the insects responds to a constant of proportionality between force and displacement. Researchers have found that for low confinement values, the movement of the insects in the swarm is chaotic (their movements change a lot if the initial conditions are changed). In this context, the phase shift occurs when the swarm splits into several swarms that are, however, closely related to each other, because there are insects moving from one to another.

At the critical line between phases of this shift, the distance between two insects in the swarm that are influenced by each other is proportional to the size of the swarm, even if the number of insects in the swarm grows indefinitely. This is called “scale-free chaos” and hasn’t been discovered until now, according to the researchers.

“As the number of insects increases, the critical line moves towards zero confinement. What happens is that the maximum distance between two insects that still feel each other’s influence is proportional to the size of the swarm. It doesn’t matter how many insects we put in it. And that represents an absolute novelty that we have discovered,” explains Bonilla.

Specifically, what these mathematicians predict through numerical simulations is that certain swarms of insects (specifically a class of small flies) have scale-free chaotic behaviour, which translates into certain power laws with exponents similar to those measured in nature. They have also found a simplified mean-field theory that corroborates the scale-free chaos phase shift. “It would be good to look for and find the phase shift between chaotic phases that we predict, either in observations in nature or in controlled laboratory studies,” says another of the authors of the research, UCM mathematician Rafael González Albaladejo, who is also linked to UC3M’s Gregorio Millán Barbany Institute.

The formation of herds is one of the manifestations of so-called “active matter,” made up of something like self-propelled individuals that form a whole, the researchers explain. It can be a swarm of insects, a flock of sheep, a flock of birds, a school of fish, but also bacteria in motion, melanocytes (the cells that distribute pigments in the skin) or artificial systems such as periodically shaken irregular grains or seeds. “Herd formation mechanisms play a role in some of these systems, so the results we have obtained can be linked to biology, to the study of cells, and beyond that, to the study of tumors and other diseases,” adds Albaladejo.

How do so many animals move in unison? These researchers explain that each individual only senses its neighbours and moves accordingly, even though it has no perspective on the movement of the whole herd. And depending on whether they use sight, hearing or the vibrations of the fluid in which they are immersed, the concept of neighbour can change quite a bit.

Sheep moving together see and sense those around them, while birds in a flock see their nearest neighbours, even if they are quite far apart. “Moving accordingly may mean that they move in the same direction as their neighbours (the norm) or they may adopt different strategies depending on the situation. For example, if a crowd is trying to get out of a crowded pen with more than one gate, there are times when not following neighbours is advantageous,” they explain.

It has taken the mathematicians about two years to carry out this research work. Initially, they set out to explain experiments by studying the conventional phase shift between a crowd of insects that fill a space with constant density and become ordered when passing a critical value of the control parameter (e.g., by decreasing the noise). But then they decided to add a harmonic potential to confine the swarm and explore what happens when the attractive force between individuals decreases.

“We discovered many periodic, quasi-periodic and finally chaotic states for a fixed number of insects that we increased. The surprising thing is the transition between chaotic states that we didn’t know or assume existed, and we were able to find the correct arguments and tests to support their existence,” says another of the study’s authors, Ana Carpio, from UCM’s Department of Mathematical Analysis and Applied Mathematics, who points out that there is still a lot to be done based on this work.

“From experimentally seeking confirmation of our predictions and better adapting the model to experimental observations, to carrying out theoretical and mathematical research that goes beyond our numerical simulations,” she concludes.

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Credit of the article given to Carlos III University of Madrid

In the 18th century, the philosopher David Hume observed that induction—inferring the future based on what’s happened in the past—can never be reliable. In 1997, SFI Professor David Wolpert with his colleague Bill Macready made Hume’s observation mathematically precise, showing that it’s impossible for any inference algorithm (such as machine learning or genetic algorithms) to be consistently better than any other for every possible real-world situation.

Over the next decade, the pair proved a series of theorems about this that were dubbed the “no-free-lunch” theorems. These proved that one algorithm could, in fact, be a bit better than another in most circumstances—but only at the cost of being far worse in the remaining circumstances.

These theorems have been extremely controversial since their inception, since they punctured the claims of many researchers that the algorithms they had developed were superior to other algorithms. As part of the controversy, in 2019, the philosopher Gerhard Schulz wrote a book wrestling with the implications of Hume’s and Wolpert’s work.

A special issue of the Journal for General Philosophy of Science published in March 2023 is devoted to Schulz’s book, and includes an article by Wolpert himself, in which he reviews the “no-free-lunch” theorems, pointing out that there are also many “free-lunch” theorems.

He states that the meta-induction algorithms that Schurz advocates as a “solution to Hume’s problem” are simply examples of such a free lunch based on correlations among the generalization errors of induction algorithms. Wolpert concludes that the prior algorithms that Schurz advocates, which is uniform over bit frequencies rather than bit patterns, is contradicted by thousands of experiments in statistical physics and by the great success of the maximum entropy procedure in inductive inference.

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Credit of the article given to Santa Fe Institute

An unsatisfying caveat in a mathematical breakthrough discovery of a single tile shape that can cover a surface without ever creating a repeating pattern has been eradicated. The newly discovered “spectre” shape can cover a surface without repeating and without mirror images.

The pattern on the left side is made up of the “hat” shape, including reflections. The pattern on the right is made up of round-edged “spectre” shapes that repeat infinitely without reflections

David Smith et al

Mathematicians solved a decades-long mystery earlier this year when they discovered a shape that can cover a surface completely without ever creating a repeating pattern. But the breakthrough had come with a caveat: both the shape and its mirror image were required. Now the same team has discovered that a tweaked version of the original shape can complete the task without its mirror.

Simple shapes such as squares and equilateral triangles can tile a surface without gaps in a repeating pattern. Mathematicians have long been interested in a more complex version of tiling, known as aperiodic tiling, which involves using more complex shapes that never form such a repeating pattern.

The most famous aperiodic tiles were created by mathematician Roger Penrose, who in the 1970s discovered that two different shapes could be combined to create an infinite, never-repeating tiling. In March, Chaim Goodman-Strauss at the University of Arkansas and his colleagues found the “hat”, a shape that could technically do it alone, but using a left-handed and right-handed version. This was a slightly unsatisfying solution and left the question of whether a single shape could achieve the same thing with no reflections remaining.

The researchers have now tweaked the equilateral polygon from their previous research to create a new family of shapes called spectres. These shapes allow non-repeating pattern tiling using no reflections at all.

Until now, it wasn’t clear whether such a single shape, known as an einstein (from the German “ein stein” or “one stone”), could even exist. The researchers say in their paper that the previous discovery of the hat was a reminder of how little understood tiling patterns are, and that they were surprised to make another breakthrough so soon.

“Certainly there is no evidence to suggest that the hat (and the continuum of shapes to which it belongs) is somehow unique, and we might therefore hope that a zoo of interesting new monotiles will emerge in its wake,” the researchers write in their new paper. “Nonetheless, we did not expect to find one so close at hand.”

Sarah Hart at Birkbeck, University of London, says the new result is even more impressive than the original finding. “It’s very intellectually satisfying to have a solution that doesn’t need the mirror image because if you actually had real tiles then a tile and its mirror image are not the same,” she says. “With this new tile there are no such caveats.”

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*Credit for article given to Matthew Sparkes*

Consider an auction. You have two types of main protagonists or agents: a seller (or auctioneer) and many potential buyers. There are, of course, certain ground rules. For instance, one objective may be to design the auction in such a way that the person buying the item(s) up for sale is the buyer “who values that good the most.”

But, says Singapore Management University Associate Professor of Economics Takashi Kunimoto, what if you do not know which potential buyer does give the item the highest valuation?

“For example, I want to design a scheme in such a way that they’re willing to tell the truth about their valuation, and I can choose the person who values it the most. So that’s the kind of framework I have in mind to determine who’s going to be a winner, with what probability, and who pays how much.”

Professor Kunimoto, whose research interests include game theory, mechanism design, and macroeconomic theory, has written a paper in conjunction with two other SMU researchers, Professor of Economics Shurojit Chatterji, and Research Fellow Paulo Ramos, titled “Compellingness in Nash Implementation.”

John Nash, who featured in the Russell Crowe movie “A Beautiful Mind,” was awarded the Nobel Prize for Economics in 1994 for his work on the mathematics of game theory. Professor Kunimoto says that, when it comes to a group of agents interacting with each other—whether it be in an auction or in an institution or organization—he has to make a “fundamental assumption about where their interactions will lead,” often referred to as “Nash equilibrium.” (This is when no player can benefit by unilaterally changing their strategy and consequently is “somehow locked in and therefore cannot find anything better.”)

One potential issue with this framework, however, is that there may be many different Nash equilibria. “As a designer I don’t really know which one is going to be played,” says Professor Kunimoto.

This is where Nash implementation comes in. “Can I design a mechanism in such a way that every Nash equilibrium delivers an outcome I want to implement?”

Another Nobel laureate, Eric Maskin, had already established this basic framework, Professor Kunimoto told the Office of Research, but “one issue was omitted in literature. Even though you’re looking at many equilibria, somehow, they only focus on ‘pure strategy’ equilibria so they don’t resort to randomization.” (Pure strategy implies that the player chooses the same strategy each time in a deterministic manner).

This is where the classic example of a penalty shoot-out in football comes in. There is a striker and a goalkeeper. They can go left or right (although, in reality, there are other options). It is, as Professor Kunimoto points out, a zero-sum game. Either the striker scores or does not. “So, my best strategy is the worst strategy for the other. There’s a complete conflict of interest.”

In this zero-sum game, the equilibrium plays entails randomization, implying that the striker does not always try to place the ball in the same part of the net. “But implementing such a randomizing strategy might be quite sophisticated.”

“When I say that with Nash implementation, every Nash equilibrium delivers the right outcome, somehow I implicitly assume they’re going to play some pure strategy which involves no randomization.”

Professor Kunimoto then opts for a mixed strategy approach which does involve randomization and “should be even better” at predicting outcomes. “If that’s the case, maybe I’d better be more careful about how I design the mechanism.”

Of course, the mixed strategy equilibrium could be less likely to be played than the pure strategy equilibrium. If this is the case, one can call such a mixed strategy equilibrium ‘not compelling.” On the contrary, the mixed strategy equilibrium could be more likely to be played than the pure strategy equilibrium. In this case, one can call such a mixed strategy equilibrium ‘compelling.”

But, on the assumption that more than one mixed strategy could be played, “one might be called ‘compelling’ and the other might not.” (In the paper, the researchers call a mixed strategy equilibrium ‘compelling’ if its outcome Pareto—an action resulting in no one losing out although it helps one party—dominates any pure strategy outcome.)

To what extent then does the design of the mechanism need to be modified?

“The question is fundamental and was already addressed in the literature,” says Professor Kunimoto, “but somehow it was overlooked and that’s the context of the question I’m interested in.”

As we have seen, many assumptions are made in understanding the plausibility of both pure and mixed strategy equilibria in Nash implementation. However, isn’t a study of just two participating parties or agents somewhat limited in its focused approach?

“Yes, but we encountered difficulty characterizing how mixed strategy equilibria look like in the mechanism with more than two agents. To avoid some of the technical issues, we decided to confine our attention to the case of two agents.”

“When I design a mechanism, I do not necessarily look at one that works in the real world. To do that, maybe I have to come up with some robustness requirement, which, I hope, leads us to more natural mechanisms.”

“I just hope that finding a more natural mechanism might lead to a mechanism which might work in the real world, and I think my contribution is going to be somehow pushing this agenda towards finding more effective institutions—but it’s still a long way off.”

“Hopefully if we provide the set of guidelines, policymakers and others may find some of the applications useful, although given what I’ve said in the paper, it’s still a long shot.”

As for the paper itself, it has yet to be published and is likely to need some revision.

For instance, in the abstract, the researchers state that they “illustrate the difficulty of extending our result to the case of more than two agents.”

“When we extend our results to environments with three or more agents in a straightforward manner,” the paper concludes, “the class of environments in which compelling implementation is possible becomes very small.”

Professor Kunimoto says, however, they can handle more than two agents as this, he acknowledges, “was a significant limitation in the draft paper. Fortunately, we’re almost able to overcome that deficiency.”

To do that, they are now considering “mini versions of the two-person case, but in many pairs.”

In essence, it all comes down to ‘reverse engineering’ game theory. Instead of trying to make predictions about how the game is going to be played, “we want to go the other way round this,” Professor Kunimoto says.

“Somehow, I really want a particular prediction to be consistent with the objective I want to achieve. I want to design a mechanism, but the outcome is going to be exactly the one I want implemented.”

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Credit of the article given to Stuart Pallister, Singapore Management University

Theoretical string theory in theoretical physics predicts the existence of parallel worlds (mirror symmetry prediction). These two worlds (A-side and B-side) are supposed to differ in terms of the six-dimensional spaces (A and B) hidden in each world.

However, as these spaces are extremely similar and invisible, theoretically, we cannot distinguish them from the world that we live in. Considerable research has been conducted on the properties of space A, and extreme changes (i.e., blowing up) do not occur in it under certain conditions.

However, recently it has been discovered that spaces A and B are transformed in certain ways and their apparently different objects correspond to each other. However, the nature and extent of this transformation are not well understood, and research on the properties of space B has not yet progressed.

In this new study, published in the Asian Journal of Mathematics, researchers mathematically investigated whether the behaviour of space B also has the same properties as that of space A. They transferred a known phenomenon from the A-side to the B-side and proved that blowing up does not occur even in space B under certain conditions.

This achievement provides mathematical proof for one of the previously intuitively expected similarities between the A-side and B-side. Although the researchers made some assumptions to prove this theorem, in the future, they aim to clarify whether the theorem holds even without these assumptions.

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Credit of the article given to University of Tsukuba

Human crowd dynamics are best predicted by a visual neighbourhood model, based on the visual fields of each person in the crowd. Birds flock, fish school, and human crowds, too, move in a collective motion pattern. Understanding human crowd behaviour can be useful for preventing jams, crushes, and stampedes. Mathematical models of collective motion are typically based on characterizing the local interactions between individuals.

One popular approach, called a metric model, is to quantify forces of attraction, repulsion, and velocity alignment for all neighbours within a fixed radius from the focal individual. Alternatively, in a topological model the focal individual might be influenced by a fixed number of near neighbours, regardless of the distance to the focal individual.

For their study published in PNAS Nexus, Trenton Wirth and colleagues asked participants to walk in real and virtual crowds of varying densities, then changed the walking direction of some neighbours to see how the participants responded. The authors found that the data produced was better predicted by the metric model than by the topological model.

But the best model was based on the visual motions of the neighbours the focal individual could see. In dense crowds, near neighbours may partially or completely block the view of more distant neighbours, removing the distant neighbours from the focal pedestrian’s input. Pursuing a visual model promises more realistic simulations of crowd dynamics, according to the authors.

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Credit of the article given to PNAS Nexus

What does artificial intelligence offer that goes beyond traditional statistical models, such as regression analysis, to investigate the behaviour of households, in particular the factors that cause the separation of couples and dissolution of the conjugal bond?

With Bruno Arpino (University of Florence) and Marco Le Moglie (Catholic University of Milan) we have analysed data for over 2,000 German married or cohabiting couples, who were followed for a dozen years on average by the annual GSOEP survey (German Socio-Economic Panel), with more than 900 ending in separation.

By adopting a machine learning approach (specifically, Random Survival Forests) the procedure found on its own the relationship between the various factors contained in the database. In this case it considered more than 40 factors, from age to education level, from health to psychology traits: the mass of raw data was fed to ML, without making precise hypotheses, but simply indicating as event of interest the break-up of the union, and the algorithm indicated the influence of each factor contained in the data. The variables that pose the greatest threat to the stability of a union have been identified with an accuracy of 70% (a predictive ability that outperforms the 50% achieved by traditional regression methods).

Not only was ML able to discover the factors behind the breakup of couples, but it was also able to use this knowledge to predict the end of a union before it happens. This is also because, instead of submitting all the data available to an ad hoc algorithm, half were used to instruct the algorithm itself and the validity of the results was verified with the other half of the dataset.

The results of the analysis are very interesting, above all because the ML methodology is able to weigh the relative importance of various factors in causing the breakup. Factors that had been particularly influential in previous studies have instead lost their relevance here, like unemployment, and the partner’s high level of education and income.

The four major risk factors, that emerged from the study are in descending order: personal satisfaction, the woman’s quantity of paid work, some personality factors and age.

The strongest predictor of separation is personal satisfaction: if both partners are dissatisfied, obviously the couple won’t last. Less obvious is that a strong drop in conjugal stability emerges when the woman is very satisfied with the union but the man much less so, while the reverse effect is less evident. If the woman works many hours outside the home, the risk of separation or divorce is higher, even when the man is more involved in domestic chores (but this result is nothing new and according to the existing literature it depends on the greater agency and independence of working women.

As for personality traits, high extraversion in men (classically linked to a higher infidelity) and low openness in women, less adaptable to the changes brought about by cohabitation, are the traits that more strongly associated with the end of a couple. Also a low level of conscientiousness in both partners (understood as organizational capacity in daily life, and therefore—if low—as disorder and inability to respect commitments) does not help to stay together. But also a too high or too low level of neuroticism can be a problem. This result can be interpreted as the fact that suffering from excessive anxiety, jealousy, guilt, worry or anger clearly complicates the relationship.

This is true above all for women, but, on the other hand, those who don’t feel this type of emotion could lead their partners to read that personality trait as lack of interest (men, in this case). However, no pairing of personalities was determined that is more strongly associated with the breakup of the relationship. Finally, considering age, very young couples tend to be more unstable, but for women stability in relationships intensifies after the age of 40, while this is not the case for men.

ML analysis is not without limitations. In this case a major one is that it refers only to Germany and also has few details on the psychological aspects of the two partners. However, from a methodological point of view, the study demonstrates the great potential of ML techniques in demographic and sociological research in general, highlighting their ability to monitor and analyse a large number of predictive factors, to automatically find linear or non-linear relations, additive or non-additive relations between these factors and the outcome of interest, with greater precision and more robustness of estimates against collinearity than commonly used methods.

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Credit of the article given to Letizia Mencarini, Bocconi University