The Mathematics of Persuasion

The same processes that power artificial intelligence also exploit human psychology - here's the hidden truth about social media algorithms.

The fundamental human desire to seek enjoyment often conflicts with our daily exposure to feelings of boredom and a lack of motivation. This dilemma has greatly contributed towards the growth of social media platforms such as TikTok, Instagram and Facebook, resulting in surges in their number of users; creating a global market expected to reach $466.56 billion by 2029, according to market analysis by The Business Research Company. Social media is often a supposed cure to these feelings, having a major influence on the lives of young people across the globe.

These highly emotion-driven platforms highlight the immense power of algorithms at a large scale. However, the true mathematical reasoning behind your social media feeds is hidden and vastly unheard of.  

What Are Social Media Algorithms?

In computer science, algorithms are defined as a precise set of mathematical rules or instructions that solve a problem or perform a task. Now, algorithms are often designed to optimise systems, increase speed and maximise efficiency. But, what happens when they are used to optimise human metrics? 

Well, put simply, social media platforms such as TikTok, Instagram and Youtube often tailor their user's feeds using advanced algorithms designed to do just that: optimise human metrics including time and attention.

These platforms use machine learning algorithms, a form of artificial intelligence, that learns patterns from user's behavioural data to predict what each user is most likely to engage with. 

How Do Social Media Algorithms Work?

According to a TIME article, the Facebook algorithm has a point value assigned to variables representing each type of engagement users can perform on a post. For each potential post that could be shown to you, these variables are multiplied by the probability the algorithm has determined that you will perform that form of engagement on the post if it is shown to you. This probability is calculated based on various metrics such as your past engagement activity on similar content and any personal information the platform has about you (age, gender, location, etc.). Simply, the total of this calculation is stored in a separate variable, representing the post's personalised score for you - this is why everyone's social media feed is different. Then, your feed is ordered by posts according to these post's scores in descending order.

Other social media companies such as TikTok and Instagram have also implemented similar sophisticated algorithms with recommender systems, which gives scores to all the videos and returns the highest rated ones to the user, maximising the amount of time the user spends on these platforms. 

The mechanism behind these platforms is a mathematical process known as optimisation, the same principle that powers much of artificial intelligence. It involves adjusting parameters to maximise (or minimise) a numerical goal (in this case, user engagement) according to a particular objective function - a formula designed to maximise or minimise certain variables. As Narayanan (2023) describes, social media algorithms are engagement-maximising systems rather than information-curating ones; these mathematical programs have no regard for the type of content it provides the user. Similarly, researchers Chen et al. (2021) created a computer model that depicts how algorithms can optimise influence on social media platforms by dynamically adjusting to user's behaviour over time, through a process called reinforcement learning - the same method used to train many AI systems. These studies reveal that the mathematics behind social platforms is not static computation but a continuous search for the most effective way to hold human attention.

How Can Video Scores Be Calculated?

A general point score formula derived from an internal TikTok document, named "TikTok Algo 101", obtained by The New York Times states:

Score = Plike × Vlike + Pcomment × Vcomment + Eplaytime × Vplaytime + Pplay × Vplay

This formula is a simplified model representation of the variables algorithms use to determine the content and order of user feeds. Whilst these symbols are not clearly defined in the document, its similarity to other algorithms such as Facebook's allow us to identify their individual meanings. For instance, the variables starting with a 'P' most likely represent the algorithm's determined probability of you performing that particular type of engagement. Similarly, the variables beginning with a 'V' are surely the point value assigned to this type of engagement. On the other hand, the variable 'Eplaytime' would intuitively be the user's estimated duration that they would watch the video; thus 'Vplaytime' would hold the value held by each second of a video the user, as a result, watches.

Therefore, we can deduce that social media algorithms are designed to keep you on their platform for longer - by displaying content you are most likely to engage with. But surely, a repost holds more significance than a simple like, right? 

Here's where the 'V' variables come into play: since each form of engagement holds a different value, each 'V' variable differs depending on the engineer's decisions to attribute certain weightings to each type. As a result, the algorithm accounts for the strength of a person's probabilistic engagement on a video based on the value of its corresponding 'V' variable.

Why Do These Algorithms Matter?

These symbols may appear harmlessly mathematical, but their real-world consequences are deeply psychological. Each variable in this formula is effectively a lever that measures how much of your attention the algorithm can capture.   In optimisation terms, the goal is not truth or usefulness - it's engagement and engagement means keeping you on the platform for as long as possible. This means the algorithm will inevitably learn to prioritise whatever content triggers the strongest emotional reaction. Whether this strong emotion is joy or outrage, humour or fear, admiration or anxiety, the algorithm does not care - because why would it when its sole purpose is to capture a limited human resource. Not food, water or even money. It's attention - the factor that determines whether we pour all of our focus on scrolling endlessly through mini vlogs, dance trends or memes, or building the life we truly want.

The psychology behind this is both simple and alarming. Every time you like, repost or even scroll, your brain releases dopamine - a neurotransmitter responsible for motivation and pleasure. Social media exploits this system by giving you small, rapid bursts of reward with minimal effort. Psychologists refer to this as cheap dopamine, as it tricks your brain into feeling fulfilled without real achievement. Over time, these spikes and crashes desensitise dopamine receptors, making it harder to find motivation in everyday life. Research collated by the United States National Library of Medicine has suggested that excessive social media use is associated with reduced activity in the prefrontal cortex, the part of your brain responsible for focus, willpower and impulse control - the very qualities required to prevent addiction.

It's not surprising, then, that in a survey of 135,000 young people, 70% feel unable to stop scrolling even when they want to. The more time spent in algorithmic loops, the more the brain learns to crave stimulation instead of meaning. Considering this, social media doesn't just consume attention - it rewires the mind to seek distractions.

Do Your Thoughts Create Your Feed or Vice Versa?

The Wall Street Journal's investigation into TikTok's algorithm revealed that even a few minutes of watch time could send users into deep "rabbit holes" of emotionally charged content. The reason is simple - emotional intensity equals higher engagement, which the system is built to maximise. Through this, algorithms transform emotions into data points, feeding users a stream of viral videos designed to provoke instant reactions. Over time, this constant switching between emotions leads to shortened attention spans, addictive behaviour, and in some cases anxiety and depression.

In other words, the mathematics of optimisation doesn't just guide what we see online, but it guides how we feel and think. Scrolling through social media becomes the digital equivalent of scrolling through emotions, one post at a time.

Conclusion: We Are Not Systems

I began this article with the idea that algorithms are designed to optimise systems - and that they always will.

Except, there is one problem: we are not systems. We have emotion, conscience and free will. We are human. And yet, we have allowed algorithms built to increase profits, shorten attention spans and keep millions addicted, to control our thoughts and rewire our neural pathways - stimulating us with a false reality instead of letting us live our own.

The question is simple: how do you think the real world will ever compete with the dopamine rush engineered by these platforms - the same chemical reward we evolved to feel when we achieve, connect or create? It won’t. And until we recognise that, we risk losing the very sense of fulfilment that makes us human.

Bibliography

The Business Research Company (2025). Social Media Market Size, Share, And Trends Analysis | 2025 Global Market Report. [online] Thebusinessresearchcompany.com. Available at: https://www.thebusinessresearchcompany.com/market-insights/social-media-market-insights-2025.

Giansiracusa, N. (2025). How the Secret Algorithms Behind Social Media Actually Work. [online] TIME. Available at: https://time.com/7308120/secret-algorithms-behind-social-media/.

Narayanan, A. (2023). Understanding Social Media Recommendation Algorithms. [online] Knight First Amendment Institute at Columbia University. Available at: https://knightcolumbia.org/content/understanding-social-media-recommendation-algorithms.

Chen, M., Zheng, Q.P., Boginski, V. and Pasiliao, E.L. (2021). Influence maximization in social media networks concerning dynamic user behaviors via reinforcement learning. Computational Social Networks, [online] 8(1). doi:https://doi.org/10.1186/s40649-021-00090-3.

Smith, B. (2021). How TikTok Reads Your Mind. The New York Times. [online] 5 Dec. Available at: https://www.nytimes.com/2021/12/05/business/media/tiktok-algorithm.html.

Wadsley, M. and Ihssen, N. (2023). A Systematic Review of Structural and Functional MRI Studies Investigating Social Networking Site Use. Brain Sciences, [online] 13(5), pp.787–787. doi:https://doi.org/10.3390/brainsci13050787.

NL Times (2025). 70 percent of young Dutch people struggle to stop scrolling on social media. [online] NL Times. Available at: https://nltimes.nl/2025/01/31/70-percent-young-dutch-people-struggle-stop-scrolling-social-media.

Wall Street Journal (2021). Investigation: How TikTok’s Algorithm Figures Out Your Deepest Desires. [online] WSJ. Available at: https://www.wsj.com/video/series/inside-tiktoks-highly-secretive-algorithm/investigation-how-tiktok-algorithm-figures-out-your-deepest-desires/6C0C2040-FF25-4827-8528-2BD6612E3796.