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Fair infinite lotteries


This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.


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Thanks to Hannes Leitgeb, Vieri Benci, Richard Pettigrew, and Lieven Decock for valuable discussions and comments. The contribution of SW was supported by the Odysseus Grant Formal Epistemology: Foundations and Applications funded by the Research Foundation Flanders (FWO-Vlaanderen). The contribution of LH was in part supported by the AHRC project Foundations of Structuralism (AH/H001670/1).

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Correspondence to Sylvia Wenmackers.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Wenmackers, S., Horsten, L. Fair infinite lotteries. Synthese 190, 37–61 (2013).

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  • Foundations of probability
  • Non-standard analysis
  • Countable additivity
  • Infinity