The Friendship and Enmity Paradoxes

The friendship paradox is a phenomenon in social network analysis that states that, on average, individuals tend to have fewer friends than their friends have. This paradox arises from the inherent structure of social networks, where popular individuals with a large number of friends are more likely to be included in the friend lists of others. As a result, when considering a random sample of individuals and comparing their friend counts to the average friend count of their friends, the majority of individuals will have fewer friends on average. This paradox highlights the interesting and counterintuitive nature of social network dynamics.

Reference [1] extended this concept further and introduced the so-called enmity paradox. It showed that a person’s enemies have more enemies, on average than a person does. Specifically, the authors pointed out,

… in a mixed world of positive and negative ties, we study the conditions for the existence of the paradox, both theoretically and empirically, finding that, for instance, a person’s friends typically have more enemies than a person does. We also confirm the “generalized” enmity paradox for non- topological attributes in real data, analogous to the generalized friendship paradox (e.g., the claim that a person’s enemies are richer, on average, than a person is). As a consequence, the naturally occurring variance in the degree distribution of both friendship and antagonism in social networks can skew people’s perceptions of the social world.

They also discussed the implications of these paradoxes,

These paradoxes have further implications. Our understanding of social norms and of our social standing is influenced by our perceptions regarding those around us. For instance, the friendship paradox can help explain systematic biases in social perceptions such as regarding the prevalence of binge drinking and risky behaviors [16, 26]. Furthermore, the friendship paradoxes can explain why a given behavior in a society can be amplified. This can occur in two interwoven phases, where popular individuals act more intensely for activities associated with strategic complementarities, and those who are prone to certain behaviors interact more with other people who are also involved in that behavior, amplifying the effects of this behavior [16]. As a result, perceptions of behavior increase and this could contribute to an increase in the behavior along the lines of the perception. Misperceptions about the habits of one’s enemies could act similarly.

An example of the friendship paradox in the trading world can be observed in the popularity of options income strategies. Promoters of these strategies claim that individuals can earn regular income by selling options, emphasizing that many options expire worthless. However, it is important to recognize that these strategies are often riskier than they may initially appear. The allure of easy income from options selling can mask the underlying risks involved. In the financial world, gains typically come with risks, and it is crucial to exercise caution and thoroughly understand the potential risks before engaging in such strategies.

Can you think of an example of the enmity paradox in the financial market? Let us know in the comments below.

References

[1] Amir Ghasemian, Nicholas A. Christakis, The Enmity Paradox, 2023, https://arxiv.org/abs/2304.10076