A betting interpretation for probabilities and Dempster-Shafer degrees of belief

There are at least two ways to interpret numerical degrees of belief in terms of betting:

1.

You can offer to bet at the odds defined by the degrees of belief.

2.

You can make the judgement that a strategy for taking advantage of such betting offers will not multiply the capital it risks by a large factor.

Both interpretations can be applied to ordinary additive probabilities and used to justify updating by conditioning. Only the second can be applied to Dempster-Shafer degrees of belief and used to justify Dempster’s rule of combination.