A distance-based theory of lottery complexity
Abstract
We propose a measure of lottery complexity that combines probabilistic dispersion with dissimilarity between outcomes. Taking degenerate lotteries, which yield a single outcome with certainty, as the simplest alternatives, we measure complexity by proximity to this class. Specifically, for each degenerate lottery, we compute the expected distance between its certain outcome and the lottery's outcomes, and take the minimum across all degenerate lotteries. We provide an axiomatic characterization establishing uniqueness up to positive rescaling, study how complexity changes under outcome compression, and characterize maximally complex lotteries. Finally, we introduce Complexity-Adjusted Expected Utility preferences and characterize adherence to stochastic dominance and strong risk aversion.
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BibTeX
@misc{principi2026distancebased,
title = {{A distance-based theory of lottery complexity}},
author = {Giulio Principi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.14464},
eprint = {2608.14464},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.14464},
}
RIS
TY - UNPB
TI - A distance-based theory of lottery complexity
AU - Giulio Principi
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2608.14464
UR - https://arxiv.org/abs/2608.14464
AB - We propose a measure of lottery complexity that combines probabilistic dispersion with dissimilarity between outcomes. Taking degenerate lotteries, which yield a single outcome with certainty, as the simplest alternatives, we measure complexity by proximity to this class. Specifically, for each degenerate lottery, we compute the expected distance between its certain outcome and the lottery's outcomes, and take the minimum across all degenerate lotteries. We provide an axiomatic characterization establishing uniqueness up to positive rescaling, study how complexity changes under outcome compression, and characterize maximally complex lotteries. Finally, we introduce Complexity-Adjusted Expected Utility preferences and characterize adherence to stochastic dominance and strong risk aversion.
ER -