On 2012-07-22 7:27 AM, James A. Donald wrote:
Of course as the chain gets
longer, one's confidence in the chain exponentially approaches zero, but
as the chain has more links in parallel, one's confidence in the chain
exponentially approaches unity.
You have reason to trust Bob and Carol because they both gave you your
due, and reason to trust Dave because both Bob and Carol say Dave gave
them their due. This is almost the same as the "determine truth by
consensus" rule, but unlike the consensus rule, free from positive
feedback loops, provided one uses Bayesian probability throughout.
This difference between the quite disastrous consensus rule, and this
rule, is the correct use of Bayesian probability.
Suppose you trust Bob, and Bob gives you reason to trust Carol, and
Carol introduces you to twenty entities all of which allegedly trust
Carol and each other and allegedly have reason to do so.
Then your confidence in each of those entities should be very nearly
equal to your trust in Carol, but the existence of these entities should
not in themselves raise your trust of Carol. If it does you are
vulnerable to the fake or erroneous consensus effect.
Suppose, however, you have reason to trust Dave, and Dave trusts one of
these entities. Then your reason to trust all of these entities,
including Carol, just went up.
In a highly connected group, Bayesian probability will rapidly approach
certainty, which looks like the consensus rule, but with guard against
positive feedback locking one into a fake or erroneous consensus.
What you are looking for is truth about each entities propensity to pay
its bandwidth and storage debts.
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