L2 C4 S4

S4: Subjective Probability and Objective Probability

Both ideas are directly applicable to the MODEL, and can be translated in different ways into the complex reality. These can be understood with reference to the following diagram

Before the Random Draw is made, we have OBJECTIVE PROBABILITY. Suppose the population has N elements labeled 1,2,...,N and R is a random draw. Then we can say that P(R=>1)=1/N and the same is true for all integers I from 1 to N: P(R => I)= 1/N. This is a PRE-Experimental Statement, because probability ONLY EXISTS in the pre-experimental time.

After the experiment, the random draw R is a dead hand of history; the OUTCOME R which was not known and had the potential to be any number, now comes into existence. The probability that R produces R, symbolized by R=>R, is 1/N pre-experimentally, but this statement is NO LONGER TRUE post experimentally. After the experiment, there is no chance of the Random Draw producing something different from what was actually produced.

NOW suppose that we know that the Random Draw has been made, Probability has been extinguished, and there is no more OBJECTIVE UNCERTAINTY. HOWEVER suppose that we do not KNOW what happened. AN outcome was produced, but we have no knowledge of what the outcome was. Now we have a situation where SUBJECTIVE PROBABILITY rules can be used. From point of view of my personal knowledge about the world, the situation is the same as it was before the experiment. All the outcomes are equally likely for ME, since I dont know which one occurred. However, someone else who knows something about what happened may have different subjective probabilities. There are many SUBTLE differences between the situtation where there is objective uncertainty, and objective uncertainty. In objective uncertainty NO ONE knows what will happen, and the world itself will take different time paths depending on the outcome of random events. In SUBJECTIVE uncertainty, the path has already been taken, there are no options left anymore, the only uncertainty arises from my personal lack of knowledge of what has happened.