In my opinion, the concept of first person and third person perspective is really a special case of a continuum.
A first person observation of an event occurs when the event is 100%
coupled with the continued existence of the observer.
A third person observation of an event occurs when the coupling between the event and the observer's existence is 0%.
A continuum of possibilities exists between the two. In Tegmark suicide experiment for example, the observation of the very preliminary phase of the experiment is third person. The observation of the non-explosion of the pack of dynamite is first person.
Modifying that experiment slightly, let's say that the detonation of
the deadly explosive is intended if a quantum coin lands tail. Let's say
the the mechanism operates in two steps in rapid non-observable succession
with the following probabilities:.
1) A 50% chance p1 that the electrical circuit fires, which is a function of the outcome states of the coin. If or when the circuit fires it generates a visible spark intended to trigger the explosive.
2) A 50% chance p2 that the chemical responds to the spark and detonates. (because it is (quantum?) wet for example)
Here is the Third Person Perspective:
Coin Head - Probability = (1-p1) = 0.50
Coin Tail => Spark => Non Detonation; Probability = (1-p1)(1-p2) = 0.25
Coin Tail => Spark => Detonation; Probability = (1-p1)p2 = 0.25
The third person probability of live outcome is (1-p1)
+ (1-p1)(1-p2) = 0.75
The First Person Perspective is obtained by normalizing the third person probabilities such that the sum of the live outcomes equals 1.
Coin Head => Probability = (1-p1)/((1-p1) + (1-p1)(1-p2)) = 0.50/0.75 = 0.67
Coin Tail => Spark => Non Detonation; Probability = (1-p1)(1-p2)/((1-p1) + (1-p1)(1-p2)) = 0.33
Coin Tail => Spark => Detonation; Probability = 0.0
This illustrates the difference in the observations. Observing a spark
with no detonation has a probability of 0.25 for a third person observer
but 0.33 for a first person observer. The spark itself is neither a first
nor third person event. It is in-between.