Subjective (Bayesian) Probability and wagering

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TonyChanYT

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Step 1:

When there is no clear binary (yes or no) answer to an issue, I automatically resort to probabilistic reasoning by weighing the evidence. This process is dynamic. As I learn more evidence, my opinion may change dynamically. I seldom refute anything 100%; I weigh every piece of evidence. E.g., What is the probability that the Shroud of Turin shows the image of Jesus?.

Let proposition P1 = The Shroud of Turin shows the image of Jesus.
P2 = The Shroud of Turin does not show the image of Jesus.

Between 0 and 10, how much weight do I put on each of the above propositions?

For P1, I assign 7; P2, 3.

Once I have assigned weights to these propositions, how can anyone tell I didn't do it arbitrarily or whimsically?

Luckily, there is a mathematically sound answer to this question. That's

Step 2:

After a probability (or weight) is assigned, there is a scientific way to assess one's weighting scheme.

The strength of my subjective beliefs can be measured objectively as the process of wagering based on probabilities/weights. My personal belief system should be coherent even if it is subjective. You want to train yourself to be a reasonable coherent wagerer in life. In general, you can use the Bayes rule to make any life decision optimally. In practice, the better you estimate the three input probabilities of the Bayes Formula, the better your decision. This is the stuff of actuarial science.

See also

 
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Wrangler

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Welcome to CyB Tony!

I appreciate your approach.

Let proposition P1 = The Shroud of Turin shows the image of Jesus.P2 = The Shroud of Turin does not show the image of Jesus.

Between 0 and 10, how much weight do I put on each of the above propositions?

For P1, I assign 7; P2, 3.

Once I have assigned a weight to a proposition, how can anyone tell that I didn't just do it arbitrarily or whimsically?

Luckily, there is a mathematically sound answer to this question.
Three basic problems.

1st, you are presenting conclusions as premises.

2nd, the question is binary; it is true or false. There is not probability of it being true. The premises supporting the binary conclusion may have probability but not the conclusion.

3rd, from your link 'In the Bayesian view, a probability is assigned to a hypothesis,' means no one would take the bet IF they accepted the probability you assign to it.