Balenciaga Crocs: How Fashion Trends Emerge Through a Learning Model

This is an academic paper for Computational Economics Course at Davidson College with Dr. Shyam Gouri Suresh. Written December 10th 2021. This paper was a group project with Clay Tribus ’22 and Sam Cascio ’22.

“In order to be irreplaceable one must always be different.” 

— Coco Chanel

  1. Introduction

In general, fashion trends originate with high-status individuals or brands and eventually become commercially popular. However, the opposite sometimes occurs when high-status celebrities and luxury brands copy symbols or trends associated with the low or working-class. Jeans with holes or rips were worn by people who presumably could not afford new pairs. Yet, when Gucci intentionally tore a pair of jeans, they sold for $3,000 and distressed jeans were the next fashion craze. Similarly, crocs are typically associated with functionality and comfort and are typically worn by young children. Nevertheless, this year Balenciaga put out a line of “Women’s Balenciaga Crocs Madame 80mm”– a high-heeled Croc (Figure 1). The opposite of functionality and comfort of the croc as well as the style and prestige of the luxury brand, Balenciaga Crocs sell for $625. How can this be?

Figure 1: Women’s Balenciaga Crocs Madame 80mm

In this paper, we focus on how social status and signaling among consumers lead to emerging fashion trends. Empirical evidence on signalings indicates that high-status individuals will use fashion styles associated with low-status groups to distinguish themselves from the middle-class, often by mixing low-status icons with high-status styles — hence heeled crocs. Bellezza and Bergetrickle call this process trickle-round signaling. We aim to test how preferences for functionality and conformity influence fashion trends.  

People’s decision of when to buy clothes, what to buy, and how long to keep their products ultimately is dependent on consumer discretion. Consumers’ fashion decisions are functional and emotional, based on social influences, monetary limitations, preferences, and the functionality of the products they purchase. We intend to reproduce these complex interactions in a simplified model in order to demonstrate how fashion trends arise. In our model, we aim to see how high-status influence creates fashion trends. 

  1. Description

Applying the “Opinion Follower” model introduced by Apriasz et. al, we use an agent-based learning model of an artificial society that contains three interacting groups: “snobs”followers”  and “commons”. Followers conform to all other individuals, whereas snobs conform only to their own group and actively distinguish themselves from the other (Apriasz, Krueger, Marcjasz, Sznajd-Weron 2016). Commons are the last group who also conform to all other individuals, but unlike followers, they will prioritize practicality over style due to financial constraints. These three groups represent a high, middle, and low class in society. 

Agents in a network make decisions on when to buy clothes, and what styles to wear based on random variables and based on their personal preferences and limitations associated with their identity as a snob, follower or common. In the next stage of interactions of the simulation, agents will optimize based on a learning model that works as follows: snobs will repeat an action if it conforms to other snobs and is less likely to repeat a style if many followers or commons also have that style, followers are more likely to repeat a style if many snobs have that style, and commons  are also more likely to repeat a style if followers or snobs are using that style, but have fewer opportunities to change styles and prioritize practicality above style. Lastly, when a follower or common is evaluating the performance of a garment, they weigh the value of a snob wearing that outfit by a specified consideration value.  

Each iteration some agents choose from a discrete set of fashion choices. In our simple model, each agent chooses a top and a bottom. Unlike in Bellezza and Berger’s experimental design which pre-assigns class associations to styles, we allow agents to choose randomly, and thus, any trends that arise are an emergent property. There are 10 styles for each top and bottom. Each style is given two scores on a scale of 0 to 1 — one for practicality and one for aesthetic beauty. Snobs consider only the style of a garment when evaluating the performance of an outfit whereas followers consider both the practicality and the style. Commons also consider the practicality and the style but weigh the practicality three times more than other groups, and if the practicality is below 0.2 they will penalize the outfit when evaluating its performance. 

In our model, snobs represent the elites of society and are able to change their style every round. Followers have slightly less means than the elites change their style every other round. Lastly, commons are most limited, and can only change style every fourth round. The rounds are staggered, so that not every common or follower chooses in the same round. 

  1. Results

Figure 1: Average Ending Weight vs. The Style and Practicality Quality of the Garment

Figure 1 demonstrates three main insights. First, snobs learn to pick better styles while commons don’t. This could be explained by the snobs’ only considering the style of the garment and the popularity amongst other snobs. Second, commons learn to pick practical clothing while snobs do not. Similarly, this is due to the consideration for practicality over style and the conforming and nonconforming aspects of each group. Third, followers tend to pick better styles and better practicality. Since followers just follow the snobs’ leaders, it makes sense they will end up with higher scores in both style and practicality. Moreover, the graphs make it clear that snobs have the most stylish fashion sense, but wear the least practical clothes. In contrast, commons wear the most practical clothes but are the least stylish.  Followers wear clothes that are both fashionable and practical, but their clothes are not as stylish as those of the snobs nor as practical as the commons

In 18.4% out of 1000 trials, snobs display trickle round signaling to mean that the snobs chose one garment that is popular amongst the commons and one that is not while both styles are not copied by the followers. Only 7.9% did the agents end style coverage into one most popular outfit. The majority of the time, the agents converged into two popular styles though there is no discernable pattern to which two groups coverage indicating that this pattern is due to randomness. In addition, it is not clear that if the simulation was to continue that the number of ending styles would change because there is no way to tell if the system is fully stabilized. 

Figure 2: Variations in the Outcomes of Most Popular Styles

Figure 2 shows some of the variations of outcomes that resulted from our analysis, with the number of rounds on the x-axis and the styles (from 1-10) on the y-axis. Each line represents the popular garment amongst the snobs (red), followers (blue), and commons (green). The top two graphs show instances where convergence occurs early in the simulation, showing that agents have the ability to learn fashion trends quickly. The middle two show instances of slower convergence, and even varying “trending styles.” In one example, the snobs and followers conform, while the other shows no mixing of group styles. The bottom two graphs show much slower learning and even fewer instances of convergence, and in some cases, it is clear to see the snobs going in opposite styles from the commons. Throughout all of these graphs, we can conclude that fashion is unpredictable and the learning methods can vary from quickly conforming or evidence of no conforming at all.

Table 2: Comparing Gini Coefficient and Style Creation to Follower Snob-consideration
Common Snob-ConsiderationAverage of Gini CoefficientAverage of Number of Ending Styles
10.863 (0.073)2.33 (0.601)
20.851 (0.071)2.29 (0.588)
30.855 (0.088)2.37 (0.611)
40.837 (0.091)2.26 (0.627)
50.849 (0.081)2.31 (0.595)
60.853 (0.076)2.34 (0.587)
70.853 (0.08)2.24 (0.585)
80.853 (0.07)2.3 (0.686)
90.854 (0.08)2.33 (0.634)
100.861 (0.08)2.3 (0.557)
Notes: Standard Deviations Across Trials in Parenthesis

Table 1 shows the commons’ snob-consideration level’s effect on the variation in the Gini coefficient measuring the inequality in style preferences and an average number of ending styles. The number of ending styles counts the styles that are most popular amongst the three groups, so there can be at most three and as little as one. Table 2 shows the followers’ snob-consideration effect on the variation in the Gini coefficient and an average number of ending styles. Both tables reveal very little change across the Gini coefficients and number of ending styles. The average Gini coefficients of approximately 0.85 show high levels of inequality indicating that the agents develop their own unique sense of style with very little conformity on average. This can be explained by the predominant nature of the model, where snobs are heavily nonconforming and commons have high practicality constraints relative to the other groups. The average number of ending styles around 2.3 shows the innovative nature of the snobs and commons that are always ending in different styles. Overall, the overlapping standard deviations for both commons and followers indicate that snob-consideration had no influence over the conformity of the system. This is due to the non-conformity of the snobs which pushes them to abandon styles quickly and keep the system in a constant state of innovation.

Table 2: Comparing Gini Coefficient and Style Creation to Follower Snob-consideration
Follower Snob-considerationAverage of Gini CoefficientAverage of Number of Ending Styles
10.84 (0.097)2.26 (0.627)
20.849 (0.085)2.31 (0.659)
30.849 (0.075)2.27 (0.598)
40.855 (0.079)2.38 (0.613)
50.85 (0.085)2.28 (0.65)
60.86 (0.064)2.31 (0.524)
70.864 (0.068)2.25 (0.573)
80.847 (0.082)2.41 (0.585)
90.858 (0.078)2.19 (0.628)
100.857 (0.073)2.41 (0.585)
Notes: Standard Deviations Across Trials in Parenthesis
  1. Conclusion

The interconnections between snobs, followers, and commons within this lab help us discover many interesting insights into the fashion world. The non-conforming nature of the snobs and the conforming nature of the followers and commons shows that the social cycles within fashion are constantly evolving, and there are always going to be innovations in the fashion industry. These innovations occur on both the popularity to conform to certain styles, and the importance of functionality/practicality of certain styles. These recurring cycles show that changes in fashion are extremely irregular, making them hard to predict. No one could’ve predicted crocs with high heels to blow up in the fashion industry as they did, and it can only lead us to wonder what to expect next.

An extension of this fashion trends model would be to investigate the financial aspect of these different types of social members. For instance, is it more or less expensive to follow these fashion trends? How do financial restrictions limit individuals to become either followers, snobs, or commons? An investigation into these financial trends of fashion could provide more insight into what actually influences the unpredictability of fashion and if social status and conforming nature is not the only factor.

  1. References

Apriasz, R., Krueger, T., Marcjasz, G., & Sznajd-Weron, K. (2016). The Hunt Opinion Model—An Agent-Based Approach To Recurring Fashion Cycles. PloS one, 11(11), e0166323.

Bellezza, S., & Berger, J. (2020). Trickle-Round Signals: When Low Status Is Mixed With High. Journal of Consumer Research, 47(1), 100-127.

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