Emotion in good luck and bad luck: predictions from simplicity theory

The feeling of good or bad luck occurs whenever there is an emotion contrast between an event and an easily accessible counterfactual alternative. This study suggests that cognitive simplicity plays a key role in the human ability to experience good and bad luck after the occurrence of an event.

💡 Research Summary

The paper proposes a novel account of why people experience feelings of good luck or bad luck, arguing that these emotions arise from a contrast between the actual event and an easily imagined counterfactual alternative. The authors critique existing models that rely primarily on objective probability (Rescher’s L = E·(1‑p)) or on a utility‑difference divided by a “distance” measure (Teigen’s L = Δu/D). They point out that such models cannot explain why a near‑miss that is physically close but cognitively complex (e.g., multiple winning sectors) feels less intense, nor can they capture pure surprise situations where utility is undefined.

To address these shortcomings, the authors introduce Simplicity Theory (ST), a framework derived from Kolmogorov complexity. In ST, each situation s has two complexity measures: the cognitive description length C(s) (the minimal description an observer can give) and the generation complexity C_w(s) (the minimal set of parameters the “world” must specify to produce s). The difference U(s) = C_w(s) − C(s) is called “unexpectedness”. A situation that is “too simple” (high U) is perceived as surprising and therefore emotionally salient. Emotional intensity is modeled as E(s) = E_h(s) + U(s), where E_h(s) is the baseline emotional value (often equated with utility V(s)).

The theory yields two key predictions. First, when a counterfactual s₂ is available, people will select the alternative that maximizes E(s₂) while minimizing the conditional generation complexity C_w_c(s₂|s₁), the extra information needed to imagine the world generating s₂ instead of the actual s₁. This leads to a formal expression for luck intensity: L₂ = E_h(s₂|s₁) + U(s₂) − C_w_c(s₂|s₁).
Second, the intensity of luck depends on three variables in a near‑miss scenario: the utility of the missed opportunity V(s⁺), the total number of possible outcomes l₀, and the distance δ between the actual outcome and the missed winning outcome. The derived formula (e.g., L₂ = V(s⁺) + log₂(l₀/δ) − 2) predicts that luck grows when the missed opportunity is valuable, the outcome space is large, and the miss is small. Conversely, if the counterfactual involves many winning regions (complexity factor k), the intensity is reduced by log₂(k), capturing the empirical observation that a “messier” near‑miss feels less striking.

To test these predictions, the authors conducted an online experiment with 61 highly educated participants (mostly engineering students). Nine short narratives were presented, each containing two or three decision points. Participants were instructed to choose the option that would maximize their emotional response. The stories covered a range of luck‑related situations (train collisions, missed subway doors, lottery wins, workplace injuries, lab accidents, medical diagnoses, etc.). Choices were designed to vary in counterfactual distance (seconds, minutes, or spatial gaps) and in the simplicity of the imagined alternative (single versus multiple winning sectors, simple versus complex causal chains).

Results showed a systematic preference for options that matched the ST predictions: participants tended to select the counterfactual that was closest in time or space to the actual event and that required the least additional descriptive complexity. For instance, in the train‑signal story (S1) participants overwhelmingly chose the option that minimized the time gap before the second train entered the single‑track, reflecting a small δ and low C_w_c. In the subway‑door story (S2) the preferred choice involved waiting the shortest possible extra minutes, again aligning with the model. Situations where the counterfactual was more elaborate (multiple possible causes or many winning regions) received fewer selections, confirming the predicted log₂(k) penalty.

The authors argue that their framework unifies several disparate findings: (1) it explains why low‑probability events can feel especially lucky when they are also cognitively simple; (2) it accounts for the strong emotional impact of near‑misses without invoking separate “distance” or “utility” terms; (3) it integrates counterfactual thinking into a quantitative model of emotion. They also acknowledge limitations: the sample is not representative of the general population, the measurement of cognitive complexity remains somewhat subjective, and the assumption that baseline emotion equals utility may not hold for pure surprise. Future work should test the model across cultures, develop objective algorithms for estimating C and C_w, and explore how negative emotions (fear, anger) fit into the same structure.

In conclusion, the paper offers a compelling alternative to probability‑based accounts of luck, positioning cognitive simplicity and unexpectedness as the core drivers of emotional reactions to fortunate or unfortunate events. By formalizing these ideas with Kolmogorov‑style complexity measures and validating them experimentally, the authors provide a robust theoretical tool that could inform research in cognitive psychology, behavioral economics, narrative theory, and human‑computer interaction.