I'm new to http://stats.stackexchange, so please let me know if I'm doing something wrong.
I have the following problem:
Suppose that there is a car traveling along a flat surface. There are no roads on this surface, so the travel can be thought of as random.
There are five people in a helicopter flying above this surface, all of whom are observing this car from the helicopter, through the same window (in the helicopter).
After some time, each person is asked to predict where the car will be in one second. Each person gives a prediction, along with how confident they are of that prediction i.e. person
P says "I am
C% confident that in one second from now, the car will be at location
Given that there are five such people, how can I determine the most probable location of the car one second from now?
I don't think this really matters, but being a stats n00b, I'd rather provide this information than not: the number of people in the helicopter is variable. Five is just an example for this case. It's not fixed.
The observers in the helicopter have all been trained for such a prediction task. However, each observer specializes in predicting certain types of behavior. For example, one observer might be trained in predicting all types of left turns, etc.
Assume that human error does not exist and that all observers tell the truth. Also assume that they all have the same objective scale of measuring their own confidences.
A note on confidences: Confidence does not refer to a confidence interval, which talks about the range of possible/probable values for a variable. A bad example (but one that illustrates the underlying point): if observer A says "I will bet \$100 on my prediction being correct" and observer B says "I will bet \$150 on my prediction being correct", all other factors (such as how much each observer values their money) kept constant, observer B is more confident than observer A. Assume that all observers have been properly trained to correctly use a particular objective scale by which to measure their confidence levels.