Editing Dempster–Shafer theory (section)

====Example producing correct results in case of high conflict====
The following example shows how Dempster's rule produces intuitive results when applied in a preference fusion situation, even when there is high conflict.

:Suppose that two friends, Alice and Bob, want to see a film at the cinema one evening, and that there are only three films showing: X, Y and Z. Alice expresses her preference for film X with probability 0.99, and her preference for film Y with a probability of only 0.01. Bob expresses his preference for film Z with probability 0.99, and his preference for film Y with a probability of only 0.01. When combining the preferences with Dempster's rule of combination it turns out that their combined preference results in probability 1.0 for film Y, because it is the only film that they both agree to see.

:Dempster's rule of combination produces intuitive results even in case of totally conflicting beliefs when interpreted in this way. Assume that Alice prefers film X with probability 1.0, and that Bob prefers film Z with probability 1.0. When trying to combine their preferences with Dempster's rule it turns out that it is undefined in this case, which means that there is no solution. This would mean that they can not agree on seeing any film together, so they do not go to the cinema together that evening. However, the semantics of interpreting preference as a probability is vague: if it is referring to the probability of seeing film X tonight, then we face the [[False dilemma|fallacy of the excluded middle]]: the event that actually occurs, seeing none of the films tonight, has a probability mass of 0.