A Mathematical Study of the Mexican Drug Cartels

The ongoing havoc wrought by the Mexican drug cartels provides Mexico with an ongoing problem. How can the cartels be defeated?

A recent study approaches the problem mathematically and offers a solution . It’s an interesting study and worth consideration.

There is a report on the study in an article on ZME Science entitled The Math Behind Why Mexico’s Cartel War is a Never-Ending Nightmare. The article also includes a video.

Here’s an explanation from the article: “The study, authored by researchers Rafael Prieto-Curiel, Gian Maria Campedelli, and Alejandro Hope, used a decade’s worth of data on homicides, arrests, and cartel interactions in Mexico. The findings are sobering. Mexican cartels now boast an estimated 175,000 members, making them the fifth largest employer in Mexico, right between the grocery chain Oxxo and telecoms company América Móvil. [See here.]

This study looks at the recruitment factor: “Cartels lose members constantly through conflict with rivals and arrests by the state. Yet they replenish their ranks at an alarming rate, recruiting at least 350 people every week. This relentless cycle of violence is self-sustaining. It’s a sobering conclusion that needs to be taken to heart by the authorities: increasing arrests does not reduce violence. Instead, it might make things worse.

Four Factors Contributing to the Size of Cartel. Source:Science magazine

The cartels are growing. “Despite setbacks, the researchers found that cartels continue to grow. They estimate that between 2012 and 2022, cartel membership rose by 60,000 members.”

One of the three researchers, Rafael Prieto-Curiel, a former police officer in Mexico City, is currently a mathematician at the Complexity Science Hub, a research center in Vienna, Austria.

Rafael Prieto-Curiel, interviewed by ZME Science in Berlin. Source: ZME Science

Here’s what Prieto-Curiel said in an interview with ZME Science: “We try to understand with a system of equations how cartels change in size and how they manage to prevail as an institution despite the number of losses that they have through either killing or arrests. Given the data that we actually have, like the number of homicides and arrests in the country, we can understand the inside of the cartels in Mexico. And that’s what we did.”

The article discusses the problem and the research: “Cartels have an uncanny ability to adapt. When authorities crack down on one group, others move in to seize territory, recruit new foot soldiers, and expand their networks. Taking into account publicly available data and cartel dynamics, the researchers crafted a series of equations that can offer valuable insight into one of the most dangerous underground operations in the world. The model considered four forces that shape cartel size: recruitment, arrests (or incapacitation), conflict with rival cartels, and internal breakdown (saturation).”

Stats on Mexican drug cartels. Source: Science magazine

The numbers are stark. By 2022, cartels had between 160,000 and 185,000 active members. This means cartels rival some of Mexico’s largest employers, like the retail giant Walmart. In 2012, the researchers estimated there were 115,000 cartel members.

“In order to sustain these numbers, the cartels have to recruit at least 370 people per week, otherwise they would collapse. Week after week, they manage to hit this quota and perhaps even more.”

“The study took into account a total of 150 active cartels in Mexico as of 2020. These cartels were identified through open-source data, including reports from national and local newspapers, and narco (narcotics) blogs.”

“ ‘We take one equation for each cartel, so we got a system of 150 equations. Each equation tells you the size of that cartel and why it changes according to the different structure conflicts and so on. We take this equation and then when we solve it,’ said Prieto-Curiel.”

The article reports the current breakdown of cartels in Mexico: “At the top of the food chain looms Cártel Jalisco Nueva Generación (CJNG). Its reach extends across 77 state-level conflicts, like tentacles spreading out to strangle territories in its grip. With an estimated 28,764 members, CJNG has built a fortress of alliances in 55 different regions.”

“Then there is the Sinaloa Cartel, an empire whose name has echoed through decades of narco history. It commands an army of 17,825 members, locked in rivalries that span 19 states, but also bolstered by alliances in 34 regions. Once the undisputed giant, it now shares the battlefield with other rising forces.”

“Other major cartels include La Nueva Familia Michoacana with 10,736 estimated members and the Cártel del Noreste with 8,992 members. La Unión Tepito, an urban cartel entrenched in the heart of Mexico City, counts 7,561 members.”

“Lower down the food chain are countless smaller organizations, often no more than 200 members strong. But each group, no matter its size, feeds the same cycle of violence. The clashes between the ten largest cartels generate only 15% of fatalities. The rest — the bulk of the bloodshed — comes from a relentless war waged by and against smaller, fragmented cartels, who are often targeted for elimination or used as pawns in bigger gang rivalries by the major cartels.”

Notice what it says in that last paragraph: “The clashes between the ten largest cartels generate only 15% of fatalities.”

The researchers’ prediction? “The researchers estimate that if current trends continue, the violence in Mexico will worsen significantly over the next five years. By 2027, they predict:
A 26% increase in cartel membership, further solidifying the cartels’ hold on the country.
40% more cartel-related casualties compared to 2022 levels.”

Four Projections. Source: Science magazine

Why arrests aren’t solving the problem: “The traditional strategy of incapacitation — arresting cartel members and putting them behind bars — seems logical. After all, fewer criminals should mean less crime. But the study shows this approach is flawed. For every cartel member arrested, new recruits step in, often drawn from communities where opportunities are scarce and violence is a constant presence.”

“Roughly 37% of cartel members over the past decade were either killed or jailed, yet there are more cartel criminals than ever.”

“The authors found that even if arrests doubled, this approach would lead to an 8% increase in weekly casualties and a 6% growth in cartel membership. Arresting more cartel members destabilizes the power balance between cartels, triggering more violent conflicts as groups scramble to fill the void left by imprisoned leaders.”

U.S. President-elect Donald Trump thinks he has a solution: “President-elect Donald Trump promises to escalate the battle against Mexican drug gangs. Trump said that ‘we need a military operation’ against the traffickers, although he’s provided few details. His Vice-president, JD Vance, said that hundreds of thousands of American soldiers ‘are pretty pissed off’. He added, ‘I think we’ll send them in to do battle with the Mexican drug cartels.’ If that were indeed the case, this could end in disaster, ironically making cartels stronger than ever in the long run.”

So what is the solution of the researchers? “If arrests don’t work, what does? The answer lies in prevention. The study shows that cutting recruitment in half would reduce cartel-related homicides by 25% and shrink cartel membership by 11%. This strategy, the researchers argue, is more effective and sustainable.”

“ ‘The only thing that would decrease violence… was lowering the number of people who joined the organizations in the first place,’ Prieto-Curiel said.”

That makes sense but is easier said than done.

“The study calls for structural investments in a proactive strategy that targets individuals at risk rather than a traditional reactive approach.”

“Yet this would be no small feat. Reducing recruitment means addressing the social and economic conditions that push people toward cartels in the first place. Young men, who make up the bulk of cartel recruits, often face bleak futures. Cartels offer not just money, but a sense of purpose and belonging. Breaking this cycle requires massive investment in education, job creation, and community support.”

“The researchers emphasize that even if recruitment were to drop to zero overnight, it would still take years to return to the levels of violence seen a decade ago. The cartel population is simply too large, and their networks too entrenched.”

“Mexico’s fight against cartel violence is at a crossroads. The data makes it clear: the current strategy of arrests and crackdowns is a losing battle. The cartels are too resilient, their recruitment pipelines too robust. To truly reduce violence, Mexico must pivot toward a proactive approach.”

“This means providing alternatives to the cartel life. It means investing in youth, creating opportunities where there are none, and breaking the cycle of poverty and violence that feeds the cartels.”

On the other hand, says the article, “…Prieto-Curiel pointed out that recruitment isn’t driven solely by poverty, challenging a common misconception: ‘Those regions in which you have more cartel presence are not the poor ones, those cities with a higher cartel presence are not the poor ones’…”

According to the study, “Tackling recruitment has a triple effect: first, it lowers the number of cartel members, reducing the violence they can create by having fewer killers. Second, it lowers the number of targets, so fewer people are vulnerable to suffering more violence. And third, it reduces the cartel’s capacity for future recruitment…”

Prieto-Curiel had some criticism for the showbiz industry:

“Prieto-Curiel criticized how media, particularly shows like Narcos, glamorize cartel leaders and distort reality for vulnerable youth: ‘In the past 10 years… in Netflix, they are showing these cartel capos as the hero, as the person that is successful, that has all the houses, that travels with the cars. But that is not true.’ “

“He argued that such portrayals create dangerous misconceptions, making cartel life seem attractive. The reality, he stressed, is that most cartel members face grim outcomes: ‘When you see that member of the cartel being successful, what you’re not seeing is that there are the other 174,999 members of a cartel… They are the ones that get arrested, murdered, killed.’

“ ‘It’s a harsh reality,’ Prieto-Curiel said. ‘When a young person joins a cartel, the chances they will be dead or in prison within 10 years are extremely high.’

“He estimated that 50% to 60% of new recruits end up dead or incarcerated within a decade.”

“ ‘The chances that they will finish dead in the next 10 years is 100 times higher than a person in the street.’ ”

“He also pointed to the way cartels use social networks to recruit. When one person joins, it often pulls in their family, friends, and neighbors. ‘The chances are that not only you, but your whole network, will end up dead or in prison,’ he warned.”

Here’s how the article sums up the situation: “Without a change in strategy, the violence will continue, claiming more lives and destabilizing more communities. The path forward seems more clear now – but it requires courage, vision, and a willingness to invest in Mexico’s most vulnerable citizens. If Mexico hopes to break free from the cycle of cartel violence, the solution lies not in more arrests, but in fewer recruits. The country’s future depends on it.”

It seems obvious that reducing the amount of recruits to the cartels would improve the situation.

But how do you do it? How do you dissuade these young men from accepting easy money with the drug cartels ? How do you get them to look at the big picture and their likely future?

That’s the challenge.

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One Response to A Mathematical Study of the Mexican Drug Cartels

  1. william kaliher says:

    this is sobering in many ways.

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