Compound Beliefs by Counting

Compound beliefs are computed by running the counting method through a chance tree of imagined worlds.

You believe 0.3 in rain tomorrow, and believe the farmers' market runs at 0.9 on dry days but only 0.5 in rain. In how many of your 1,000 tomorrows do you shop at the market? Split the panel: 300 rainy worlds, 700 dry. Of the 300 rainy ones, half have a market — 150. Of the 700 dry ones, nine-tenths do — 630. Market worlds in total: 780 of 1,000, so your belief in shopping tomorrow is 0.78. Every step was multiply-along or add-across from this unit's opening — the only new ingredient was that the counts came from beliefs instead of records.