How to Predict Popularity

If the many functions of digital social media networks could be summed up in one word, it would likely be “sharing”. Through a myriad of apps and platforms, we share our thoughts, feelings, opinions, ideas, and more – with our friends and family, with our online social circles, with strangers, and even with companies.

Lionel Zhepeng Li

14 Jul 2023

This ever-growing, non-stop festival of sharing is, in the words of Zhepeng (Lionel) Li from the University of Hong Kong and two co-authors from the University of Arizona and Temple University, creating bridges between “online interactions and offline behaviours”. Their study, What Will Be Popular Next?, focuses on how these bridges affect the popularity of various places and things.

A study of patterns

The research team conducted their work through the lens of social focus theory, essentially looking at patterns in the things that connect people and groups. This study of social networks goes back to the 1980s, long before the advent of digital social media. Social focus theory was designed to examine “a set of connected entities … adopted by a network of social individuals.” These entities are shared affiliations – clubs, parties, films, books; all manner of shared interests – around which people organise their social lives. The entities are called “social foci”, while the people are known as “social actors”.

In basic social networks, the social actors connect with the various social foci and tell other social actors about these foci. This leads to more social actors adopting the foci, making them increasingly popular in a process called “contagious adoption”. Simply put, the more people talk about something, the more popular it becomes – something that has been common in human societies since the dawn of societies themselves.

So it was in the early days of social focus theory. Today, its researchers are obliged to consider the effects of the (relatively) recent phenomenon of digital social networks. Platforms such as Twitter, Facebook, Weibo, and a plethora of others promote “the wide spread of online content among people. Once published, online content [like tweets, posts or videos] spreads [often very quickly] among users through the platforms’ reposting, citing or commenting mechanisms”. Digitisation has turbocharged social networks, leading to a far more broad and rapid spread of social foci than at any point in history. Hence the concept of “going viral” – the almost-overnight spike in the popularity of all kinds of content – clever and funny advertisements, horrific videos of human savagery, memes, political causes, and so on.

Narrowing down the foci

Social focus theory is vast and the options for research topics are many. In this case, the researchers chose to zero in on a single question: “How can information about social networking be leveraged to predict which social foci will be popular in the future?” Put another way, they ask, “How can the popularity of entities be predicted?”

To answer the question, the authors took a fresh look at the concept of social diffusion – the way in which “new ideas and practices spread within and between communities.” In their literature review, they discovered that most research to date has focused on “single-item diffusion, or the adoption of a single independent social focus” – basically looking at how one thing becomes popular. But in the digital world of the 2020s, “multiple social foci can attract the same user base” – i.e. we can be interested in “Everything, Everywhere, All at Once” (you should see that film, if you haven’t). So, the team developed a complex interactive model to predict the popularity ranking of social hotspots – both online and offline.

The potential real-world benefits of these predictions are immense. Take marketing: if marketers and advertisers could have a list of the most popular businesses, it would be both useful and profitable – they could prioritise the right ads for the right audiences, personalise ads better and increase the all-important click-through rate (the percentage of people who click through to a website from an online ad). There are security and retail-related benefits as well, which we will get to later.

A challenging model

So that’s the background. The researchers’ task was then simple and straightforward – just create a mathematical model to measure and predict the popularity of social foci and then sit back and enjoy success, right? No. Not really. Creating such a model involved overcoming a number of major challenges, most of which stem from the fact that people are immensely complicated creatures. For example, people don’t just influence their friends and families towards one social focus, they influence them to “adopt multiple social foci that coexist and compete”. Modelling these behaviours is absolutely not straightforward.

The authors’ model was based on a two-mode social network, pictured above. Such networks show “how individuals, by their agency, create social structures while, at the same time, social structures … constrain and shape the behaviour of the individuals embedded in them.” They theorised that the various interactions and interplays between the social actors and foci actually mean that “peer influences among social actors for adopting social foci and the attractiveness of social foci for engaging social actors are contingent upon each other” – a type of mutual dependency that had not been addressed in earlier studies. Their description of these interactions gives a glimpse into the complexity of their task:

“For example, when social actor ?₁ decides whether to adopt social focus ?₁, actor ?₁ is under the social influence of direct friend ?₂ who has visited ?₁ . At the same time, ?₁ is also influenced by ?₂ and ?₃ who have both visited ?₂, and is also influenced by ?₄ and ?₅ who have both visited ?₃.”

They then used a “bilateral recursive process” (AKA complicated math) to encode the mutual dependencies and produce measurable data, and then devised a machine-learning technique that would produce predictions about ranking popularity.

To test their model, they used three different data sets – two from social network platforms and one from a Canadian bookstore’s mobile platform that lets readers share opinions about the books they read with other users. The digital social networks, one in China and one in the US, had a check-in function enabling users to share their locations with their friends. The social actors were the users and the social foci were the places at which they checked in – restaurants, hotels, stores, and so on. For the bookstore’s platform, the actors were the readers and the books the social foci.

Then began the testing and re-testing phase of their study. Each data set was evaluated by comparing two types of social foci ranking lists – the predicted rank and the true rank. These lists were evaluated using four mathematical metrics which examined different dimensions of performance to provide robust data. These were then evaluated to ensure accuracy and comparison with other methods of benchmarking data.

Skipping ahead to a solid conclusion

This process involved hard work, more complicated math and undoubtedly a number of challenges and changes of approach – par for the course in research studies of this magnitude. With apologies to the researchers, we will skip over this part entirely and instead join them at the happy end of their research journey. They were able to prove that their model not only worked, but that it consistently outperformed other methods. This meant that both their approach and their findings will have useful applications in academia and to different businesses and industries.

In terms of academia, the team proved that previous difficulties in measuring mutual dependency could be overcome by using machine learning in combination with a learning algorithm, something that will prove useful in future studies; as will their finding that just a few key social network characteristics, rather than a large set, are enough to make robust predictions about popularity.

But the real strengths of this study are the practical implications of their findings. Businesses that are associated with a particular social focus “can benefit from knowing their future popularity ranking in advance” – a predicted rise in rankings will give them time to coordinate staff, stock and inventory, while a predicted drop will give them time to plan an advertising campaign or cut costs. Similarly, digital platforms that use location-based services stand to benefit from accurate popularity rankings, helping improve advertising revenue and allowing companies to improve their click-through rate through better targeted ads.

There are also public security benefits. “Identifying hotspot areas where crimes may occur in the future is an effective strategy for allocating police resources”, the authors say. Identifying potential future crime hotspots will allow for “predictive police patrolling”, whereby police resources can be put in place in a particular area ahead of time to ward off any trouble or improve response times.

In a wider sense, knowing what will be popular with various groups of people in different places will be immensely helpful with all manner of jobs, from retail store placement decisions, to point-of-interest recommendations for tourism authorities and businesses, to mobility and access decisions for local governments, and much more.

As human beings, we have a natural tendency to share things with our friends, families and communities. This sharing is often portrayed in a negative light, given its potential for hacking and loss of data privacy, but for studies like Li et al’s, the data we provide is helping to make society safer and more successful – showing that sometimes, sharing can actually be caring.

About this Research

Zhepeng (Lionel) Li, Yong Ge, and Xue Bai (2021). What Will Be Popular Next? Predicting Hotspots in Two-Mode Social Networks. MIS Quarterly 45(2) :925-966

Read the original article

Reference

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Translation

Long held assumptions about the mutually incremental relationship between quantities and discounts have been upended by new research. The rule of thumb that the bigger the purchase quantity, the higher the discount is shown not to hold true for medium-sized customers buying products such as semiconductors, with implications for other products and industries.

Pile them high and sell them cheap. Buy more, save more. These slogans, and the thinking that lies behind them, have been accepted principles of product sales and marketing for generation.

The logic seems indisputable from the points of view of both the seller and manufacturer and that of the buyers. If a seller or manufacturer makes a large number of identical items and a single customer wants to buy a large part of this total production, then that buyer will receive the goods at a cheaper price than a buyer who wishes to buy a much smaller amount of the same product. The accepted theory has been that the seller is eager to dispose of his stock as quickly and as easily as possible, and so a big customer will get a better deal. By the same logic, it follows that customers who buy progressively smaller amounts of the same product will receive progressively smaller discounts.

However, the underlying premise behind these assumptions – that the bigger the purchase, the bigger the discount – has now been shown to be valid for only part of the story. In a new study by Wei ZHANG, Sriram DASU and Reza AHMADI entitled “Higher Prices for Larger Quantities? Nonmonotonic Price-Quantity Relations in B2B Markets,” published in 2017 by the Institute for Operational Research and the Management Sciences in Maryland, USA, the first part of the established belief holds true: the biggest customers do receive the biggest discounts. These customers remain the most valuable to a seller or manufacturer as they account for the bulk of sales. They are therefore typically able to use their size and bandwidth to exert pressure successfully on the seller to get a large discount.

The research focused on investigating the impact of a buyer’s purchase quantity on the discount offered. In this case, the seller was a microprocessor company selling semi-conductors, which are a short-life cycle product. The company negotiates with each of its buyers to set a price for the product. The buyers are mainly large electronic consumer goods manufacturers. In line with established beliefs, the research showed that the discounts received by smaller customers increased in line with the quantities they purchased, and the smaller the quantity they purchased, the smaller the discount they received.

What is unexpected is the experience of medium sized buyers. According to established logic, these customers would be expected to receive bigger discounts on their purchase price than smaller buyers. But this is not the case. In fact, the researchers found that as the quantities bought increase, the discount decreases, and then increases again for the biggest quantities.

“Contrary to our intuition, larger quantities can actually lead to higher prices,” say ZHANG, DASU and AHMADI.Thus, while previous beliefs of a bigger purchase quantity meaning a bigger discount would have resulted in a curve heading steadily north-eastwards, the results of ZHANG, DASU and AHMADI’s studies is an N-shaped curve. This unexpected result is rooted in the importance of capacity to the seller and its impact on the price negotiation process, explain ZHANG, DASU and AHMADI.

To understand the importance of capacity in price setting requires a switch in focus from the buyer’s mind-set to that of the seller. The seller or manufacturer is not concerned solely with getting the best possible price for the product, they also place a value on capacity.

‘’Large buyers accelerate the selling process and small buyers are helpful in consuming the residual capacity,” write ZHANG and his team. “However, satisfying midsized buyers may be costly because supplying these buyers can make it difficult to utilise the remaining capacity, which may be too much for small buyers but not enough for large buyers. Therefore, midsized buyers are charged a “premium.”

To get the best price for all his products, the seller needs to avoid transactions of a medium size and instead plan his sales based on a rationing decision. The rationing decision depends on the remaining capacity level, purchase quantity, demand distribution and the buyer’s profit margin before subtracting the cost of this product. The calculation can be done by following a dynamic capacity rationing formula devised by the researchers. The formula is based on the need for the seller to find a balance between controlling the capacity allocated to each buyer while still offering a capacity range that is acceptable to the buyer.

Ultimately, ZHANG & Co, say, “The seller should reserve capacity for buyers who are willing to pay more.”

The pertinence of the research is clearly of most use to firms manufacturing or selling semi-conductors. This is a highly competitive industry with several unique features and is characterised in particular by fast changing technological developments. In the semi-conductor industry, manufacturing costs are high and lead times are long and these factors lead to inflexible capacities. It is common practice in the industry for sellers to allocate capacity to different product lines based on demand forecasts and to start work on the related production several months ahead of the planned delivery date. Customers arrive sequentially and differ mainly in the quantities of product they order. Although products have a set price, the actual price paid is typically agreed after a process of negotiation, with big buyers usually driving a hard bargain. Because of the nature of the business, negotiation on prices is inevitable, explain the researchers.

“Buyers know that the marginal production cost of microprocessors is low and that sellers are eager to discount prices to fully utilise their capacities. Moreover, buyers can allocate their business among competing sellers.”

But while buyers may have an advantage when it comes to price, sellers often have an advantage when it comes to selling and controlling capacity. Buyers are free to meet their needs by buying from different semiconductor suppliers, but they tend to decide on suppliers early on in the purchasing process. This is because the technical features offered by different suppliers vary, and once selected, these features will impact the design of the buyers’ products and will be difficult and costly to change. That means that buyers tend to keep to their chosen supplier.

The lessons that can be drawn from the study may also be useful to some degree to other businesses and products. Inflexible capacities are also a feature of many businesses in the tourism industry, for example, although the researchers note there are different characteristics and constraints involved – for example, hotel rooms do not go out of date in the same way that semiconductor products become obsolete. Hotel rooms, airline and coach seats are all fixed number items that the seller or owner needs to sell in quantities to his best advantage. The main customers in these industries include bulk buyers such as travel agencies and resellers who want to buy in large quantities but who also want to negotiate the best prices. As in the semi conductor business, the individually agreed deals are closely interconnected, with the price and quantity agreed for one buyer impacting the price and quantity to be agreed for the remaining buyers. The researchers recommend that sellers develop a price-quantity analysis model that can help them optimise their prices. As with semi-conductors, the key point for the seller is the need to control the quantity being sold to each buyer before negotiating the price.

“Basically, given that each transaction has an impact on subsequent transaction, a good model of the price-quantity relation is necessary for the optimisation of the trade-off between the profit from the current buyers and that of future buyers,” they explain.

Contributing Reporter: Liana Cafolla

Source: Wei Zhang, Sriram Dasu, Reza Ahmadi (2017). Higher Prices for Larger Quantities? Nonmonotonic Price–Quantity Relations in B2B Markets. Management Science 63(7): 2108-2126.

https://pubsonline.informs.org/doi/10.1287/mnsc.2016.2454

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