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The Almost Crash-Elaborated

We elaborate the almost-crash example slightly to say ``might have been a head-on collision'' instead of ``would have been a head-on collision''. In this uncertain world, it is more realistic.

Suppose the driver estimates (triggered by the passenger's statement) that it will take seconds to complete the pass and get back in the right lane. He also estimates that it will take seconds to drop back and get in line and that if he stays in the left lane and a car comes over the hill at that instant, he collision will occur in seconds. He concludes that if a car comes over the hill at that embarrassing moment the probability of a collision is 0.2. He estimates the probability of a car coming over the hill at that instant is between 0.001 and 0.0001. He concludes that the odds, while small, are unacceptable.

We have expressed this example numerically, as might be appropriate for a robot. Formalizing this aspect of human behavior might not be so numerical.

We can suppose that his estimate of the required passing time is not an a priori estimate based on a theory of driving but is based on how rapidly he was overtaking the other car, i.e. is based on this experience. Thus he learns to change his driving rules from an experience of collision that he didn't quite have. Much case-based reasoning in real life is based on counterfactuals, although the theories described in [Lenz et al., 1998, Leake and Plaza, 1997] do not include counterfactual cases.

John McCarthy
Wed Jul 12 14:10:43 PDT 2000