The Anna Karenina Principle in Everyday Data

Happy families may resemble one another, while unhappy families differ in their own ways. Variations of this pattern appear in optimism, emotional language, student answers, and other multidimensional data.

A familiar principle

“All happy families are alike; each unhappy family is unhappy in its own way.” This famous opening line from Tolstoy’s Anna Karenina expresses what is often called the Anna Karenina principle.

All necessary conditions must be present for a system to be successful or “happy.” If even one element is missing, it can fail. Since different elements can be missing in different cases, failure takes many forms.

Optimistic people may be more alike when imagining the future

A recent fMRI study asked participants to imagine various future situations and examined their brain activity. The paper reports that optimistic individuals showed shared neural representations during episodic future thinking: when imagining the future, their brains were more similar to one another.

I came across this newly published paper while browsing and it brought the Anna Karenina principle to mind.

  • K. Yanagisawa, R. Nakai, K. Asano, E.S. Kashima, H. Sugiura & N. Abe, “Optimistic people are all alike: Shared neural representations supporting episodic future thinking among optimistic individuals,” Proceedings of the National Academy of Sciences of the United States of America, 122(30), e2511101122.
  • https://doi.org/10.1073/pnas.2511101122

Positive emotions and words may be more similar

Positive emotion words appear to have more similar properties than negative emotion words. Negative words may also carry more information than positive words, because each one can identify a different deficiency or source of dissatisfaction.

Product reviews are a simple example. Positive reviews often resemble one another, whereas negative reviews vary widely because each reviewer may be angry about something different.

  • Plisiecki H, Sobieszek A. “Emotion topology: extracting fundamental components of emotions from text using word embeddings.” Frontiers in Psychology. 2024;15:1401084.
  • https://doi.org/10.3389/fpsyg.2024.1401084
  • Toivonen R, Kivelä M, Saramäki J, Viinikainen M, Vanhatalo M, Sams M. “Networks of emotion concepts.” PLoS One. 2012;7(1):e28883.
  • https://doi.org/10.1371/journal.pone.0028883
  • Wu Z, Jiang Y. “Disentangling latent emotions of word embeddings on complex emotional narratives.” CCF International Conference on Natural Language Processing and Chinese Computing, 2019, pp. 587–595.
  • https://link.springer.com/chapter/10.1007/978-3-030-32236-6_53

Correct short answers cluster; wrong answers spread out

Before ChatGPT appeared, I briefly worked on attempts to apply NLP techniques to short-form responses in computer-based school tests for grading. As expected, correct answers tended to resemble one another, while incorrect answers were wrong in many different ways.

With today’s LLMs, this would probably be possible at a level of accuracy that was difficult to imagine at the time. It is striking how much things have changed.

  • Brooks M, Basu S, Jacobs C, Vanderwende L. “Divide and correct: using clusters to grade short answers at scale.” Proceedings of the First ACM Conference on Learning at Scale, 2014, pp. 89–98.
  • https://doi.org/10.1145/2556325.2566243
  • Schleifer AG, Klebanov BB, Ariely M, Alexandron G. “Anna Karenina strikes again: Pre-trained LLM embeddings may favor high-performing learners.” arXiv:2406.06599, 2024.
  • https://arxiv.org/abs/2406.06599
  • Gurin Schleifer A, Beigman Klebanov B, Alexandron G. “Uncovering Measurement Biases in LLM Embedding Spaces: The Anna Karenina Principle and Its Implications for Automated Feedback.” International Journal of Artificial Intelligence in Education, 2025.
  • https://doi.org/10.1007/s40593-025-00485-7

A possible way to examine the pattern

When comparing two groups of multidimensional data, one possible expectation is that one group will lie closer to its centroid while the other will not. This can be tested, with PCA or UMAP/t-SNE visualizations as an additional illustration.

If a difference between positive and negative groups fits this pattern, calling it the Anna Karenina principle makes it sound suitably impressive.