# The qualitative paradox of non-conglomerability

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## Abstract

A probability function is non-conglomerable just in case there is some proposition *E* and partition \(\pi \) of the space of possible outcomes such that the probability of *E* conditional on any member of \(\pi \) is bounded by two values yet the unconditional probability of *E* is not bounded by those values. The paradox of non-conglomerability is the counterintuitive—and controversial—claim that a rational agent’s subjective probability function can be non-conglomerable. In this paper, I present a qualitative analogue of the paradox. I show that, under antecedently plausible assumptions, an analogue of the paradox arises for rational comparative confidence. As I show, the qualitative paradox raises its own distinctive set of philosophical issues.

## Keywords

Probability Paradoxes Non-conglomerability Comparative confidence Qualitative probability Fair infinite lotteries Monotone continuity## Notes

### Acknowledgments

Thanks to Francesca Zaffora Blando, J. T. Chipman, Alan Hájek, Thomas Icard, Hanti Lin, audiences at the 2016 ANU Probability Workshop and the 2016 University of Western Ontario LMP Graduate Student Conference, anonymous referees, and especially Rachael Briggs and Kenny Easwaran for valuable discussions and comments.

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