Editing Dempster–Shafer theory (section)

====Example producing counter-intuitive results in case of low conflict====
The following example shows where Dempster's rule produces a counter-intuitive result, even when there is low conflict.

:Suppose that one doctor believes a patient has either a brain tumor, with a probability of 0.99, or meningitis, with a probability of only 0.01. A second doctor also believes the patient has a brain tumor, with a probability of 0.99, and believes the patient suffers from concussion, with a probability of only 0.01. If we calculate m (brain tumor) with Dempster's rule, we obtain

::<math>m(\text{brain tumor}) = \operatorname{Bel}(\text{brain tumor}) = 1. \, </math>

This result implies ''complete support'' for the diagnosis of a brain tumor, which both doctors believed ''very likely''. The agreement arises from the low degree of conflict between the two sets of evidence comprised by the two doctors' opinions.

In either case, it would be reasonable to expect that:

:<math>m(\text{brain tumor}) < 1\text{ and } \operatorname{Bel}(\text{brain tumor}) < 1,\,</math>

since the existence of non-zero belief probabilities for other diagnoses implies ''less than complete support'' for the brain tumour diagnosis.