This paper recommends using mosaics, rather than (σ-)algebras, as collections of events in decision under uncertainty. We show how mosaics solve the main problem of Savage's (1954) uncertainty model, a problem pointed out by Duncan Luce.
Using mosaics, we can connect Luce's modeling of uncertainty with Savage's. Thus, the results and techniques developed by Luce and his co-authors become available to currently popular theories of decision making under uncertainty and ambiguity.

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Chai, J., Li, C., Wakker, P., Wang, T., & Yang, J. (2016). Reconciling Savage's and Luce's modeling of uncertainty: The best of both worlds. Journal of Mathematical Psychology, 75, 10–18. doi:10.1016/