Sunday, May 05, 2013

A thought about estimating the probability of statements being true.

Is there objective truth? I suspect there is, but I am not sure we are ever really sure that we have identified it.

If you were to ask 1000 people what the probability of a specific statement being true would be, you would get an approximation to a distribution. I assume that you could fit a Beta Distribution to the results:

In fact, if you were to take a whole body of statements, say those made by Senators over the course of a year, and then ask a random group of people for each statement about the probability that the statement was true, you would get an approximation of a general distribution of the credence attributed to senatorial statements. This too could be represented by a Beta Distribution.

(The red curve might represent the difference in credibility between statements as judged by people from the senator's own political party and as judged by the members of the other party.)

It would be interesting to compare the distributions of credence probabilities

  • attributed to different statements by a single senator, and
  • attributed to different senator's corpuses of statements.

Now consider Bayes Law.

Using Bayes Law you could add information on the credibility of individual statements made by senators. For example, you could ask someone the probability that a specific statement was true, and adjust the Beta Distribution for all statements by all senators to reflect the specific view of that statement. You could ask others for the same judgement to add further information to the estimate of credibility.

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