Fuzzy-trace theory assumes that decision-makers process qualitative “gist” representations and quantitative “verbatim” representations in parallel. We develop a lattice model of fuzzy-trace theory that explains both processes. Specifically, the model provides a novel formalization of how (a) decision-makers encode multiple representations of options in parallel, (b) representations compete or combine so that choices often turn on the simplest representation of encoded gists, and © choices between representations are made based on positive versus negative valences associated with social and moral principles stored in long-term memory (e.g., saving lives is good). The model integrates effects of individual differences in numeracy, metacognitive monitoring and editing, and sensation seeking. We conducted a systematic review of variations on framing effects and the Allais Paradox, both core phenomena of risky decision-making, and tested whether our model could predict observed choices: The model successfully predicted 82 of 88 (93%) pairs of studies (comparing gain to loss conditions) demonstrating 16 variations on effects, theoretically critical manipulations that eliminate or exaggerate framing effects. When examining these conditions individually, the model successfully predicted 153 (90%) of 170 eligible studies. Parameters of the model varied in theoretically meaningful ways with differences in numeracy, metacognitive monitoring, and sensation seeking, accounting for risk preferences at the group level. New experiments show similar results at the individual level. The model is also shown to be scientifically parsimonious using standard measures. Relations to current theories, such as Cumulative Prospect Theory, and potential extensions are discussed.