The Mathematics of Digital Addiction

One of the early motives for the study of mathematics was to win at gambling. This led to the development of probability theory as a discipline within mathematics that is now a rich and varied field of study. Organizations like casinos apply probability theory to make sure that you will lose on average. If you hear stories about a big winner, that is consistent with losing on average. Keep firmly in mind that a big winner is more than paid for by the hundreds or thousands of losers that follow in their footsteps. Casinos like big winners, as long as they are not too common, a situation that a solid knowledge of probability helps ensure. Occupy Math has watched a huge line form after a dollar slot paid out $500 — the casino was not going to lose on average.

The only reason that casinos did not dislike Occupy Math’s father is that they did not notice him. Living in Kansas with relatives in California, it was not uncommon for Occupy Math’s family to drive to northern California. The trip was always planned to involve a stay at each end (east and west) of the state of Nevada so that Occupy Math’s father could use his system for beating the casinos. The system is this: walk past all the gambling to the restaurant. Enjoy an excellent and very reasonably priced meal, supported by gambling revenues. After dinner, leave, playing at most one nickel slot machine once. This system does not win big — with the casinos employing probability experts, no system can ever win big. This system wins small and it is pretty reliable.

The casinos don’t just use probability theory to ensure a profit.


There are many tragic stories about gambling addiction in history. Men who squandered the family fortune. Some people find gambling irresistible and manage to become addicted every bit as much as an alcoholic or a drug addict. Once you know that there is a substantial payout for figuring out how to make your gambling more addictive, you gain a stake in addictive games. Unlike alcohol, tobacco, or hard drugs, gambling does not require chemical intake. This means that the ability to become addicted to gambling is a fundamental feature of the human mind, at least in some people. Think about the lottery ads with pictures of deliriously happy people that have just done something really unlikely — won the lottery. This sort of advertisement exploits the fact that most people cannot do probability very well.

So far we have established that there are purely mental forms of addiction. In last week’s post on positive feedback loops, Occupy Math noted that social media are addictive. Here is a sharper question, are they addictive on purpose? It turns out the answer is a giant yes. Did you ever feel that not being invited to a party (or other event if you’re not a party person) was bad? This is fear of missing out, a documented feature of the human mind. Social networks exploit this to the hilt, by sending you messages when someone comments on or reacts to your post, for example.

Another addictive feature of social networks is that they are made of people.

Most human beings draw strength and validation (or weakness and despair) from the way their family and friends treat them. Social networks are a low-effort way to meet a lot of people. If you add in the important mathematical fact that if you sample a larger set you get more exceptional samples, then social networks let you find people you like just because there so many people out there. Social networks exploit this as well by reminding you of popular posts you made years ago, telling you about people’s birthdays, and advising you to celebrate an anniversary of becoming someone’s friend on a network. They also create community games that are social, not too difficult, and which offer lots of small rewards. Those intermittent rewards are tapping into the same mental space that gambling addiction lives in. Social media make their money by keeping you in their system so they have a strong motive to keep you in, making them a little bit like the mafia.

The Engine of Yes-mannery.

A yes-man is someone who agrees to curry favor. On a social network the combination of confirmation bias, choice of friends, and news filtering create a wonderful space where almost everyone agrees with you and, when an evil troll shows up, the local community unites to smite them. Social media are really good at creating a positive feedback loop that forges an unbreakable circle of yes-men. There is additional addictiveness in the implied social contract to agree with one another!

The first step in coping with an addiction is to realize you have it. People that try to go cold turkey from social media often fail. There is a belief, arising from one of the successful methods of dealing with alcoholism, that the only way to break an addiction is to go cold turkey. This is true for some people and some addictions — and not for others. Forcing yourself to interact with other people — or take walks — is a way of diluting your time on social media to levels that are more nearly harmless.

Never ascribe to malice…

Hanlon’s razor, in various forms, says that you should not ascribe to malice a behavior or result that may have other perfectly reasonable explanations. Suppose that a marketing firm is trying to find out what people like. If they simply test things and use a statistical analysis to figure out which products or sales techniques work the best or result in the most repeat business, it is possible they are detecting and exploiting addictiveness without knowing that’s what they are doing. An earlier Occupy Math post, With big data comes big responsibility discusses techniques that would let a system create a massively addictive product without the human managers noticing that was what was happening. Occupy Math thinks that’s even more scary than making something addictive on purpose.

Where is the math in this? Last week’s post on positive feedback loops contains some of it. A firm knowledge that a human familiar with probability is harder to cheat — and also harder to addict — is another good take-home message. Addictive systems are those that exploit a person’s pleasure centers, their sense of reward, to keep them engaged. They are unhealthy when the pleasure is no longer an accurate surrogate for a beneficial behavior. Occupy Math feels there is a need for a quantitative theory of addiction, only shadows of which currently exist. Clearly an addictive system is one that people have trouble giving up voluntarily — but that method of detection requires victims. If you work in social media, please examine your conscience. If you have thoughts on this topic, please comment or tweet!

I hope to see you here again
Daniel Ashlock
University of Guelph
Department of Mathematics and Statistics


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