Lets suppose we grouped people into 8 different types (for example, INTx, ESFx, etc.), and had three dichotomies used for typing people (for example, I/E, T/F, N/S). If we could guess which side of each dichotomy a person was on with 90% accuracy, we could guess his type with 72.9% accuracy. That is, we might be 90% sure a person is a feeler, 90% sure that he's an extrovert, and 90% sure that he's a sensor, so we'd be 0.9^3 = 72.9% sure that all three of our guesses are correct and that he's an ESFx.
Based on these 3 basic dichotomies can add 4 more control (extra) in a similar way as they are introduced Reynin.
So, here is a combination of dichotomies types:
Where 1,2,3 - basic dichotomy
4,5,6,7 - control, where:
4 = 1 * 2
5 = 1 * 3
6 = 2 * 3
7 = 1 * 2 * 3
Horizontal lines: number of dichotomy
Vertical lines: number type.
Assume that the probability of a precise definition of control is also dichotomies 0.9.
Suppose that the true type - a type of number 1.
But we can also add more dichotomies to increase our chances of a correct typing; say we add four more dichotomies. These are superfluous in a sense, since they don't give us any extra information (for example, one dichotomy may have IxTxs and ExFxs on one side and ExTxs and IxFxs on the other, but we can figure out on which side of this dichotomy an individual belongs solely based on the earlier I/E and T/F dichotomies). Suppose that we can guess on which side of these new dichotomies a person lies with 90% accuracy. Now we will guess all 7 dichotomies correctly 0.9^7 = 47.8% of the time.
But even if we only guess 6 dichotomies correctly, we'll still get the type right, because of the 8 types, only one type will agree with 6 of our dichotomies, while the others will agree with 4. This depends on how the dichotomies are chosen; basically, they must be chosen so that every two types agree on exactly 3 dichotomies (see the chart with pluses and minuses for how this is possible). That way, if we get 6 out of 7 dichotomies right for a person of type X, only 3 of those dichotomies will be in common with a person of type Y; then even if we mistype on the 7th dichotomy, the person will have at most 4 dichotomies in common with type Y. So how often will this occur? For example, what are the odds of guessing the first dichotomy wrong and the rest right? That's simply 0.1 * (0.9)^6 = 5.3%. But you can also guess the second dichotomy wrong and the rest right with a probability of 5.3%; in total, then, there is a 7 * 0.053 = 37.1% of guessing exactly one dichotomy wrong, but getting the type right. So there is approximately a 37.1% + 47.8% = 85% chance of getting at most one dichotomy wrong, and therefore getting the type right.
For convenience of comparison of the results counted, just as it makes the algorithm Calc2008.txt
With this method of formation of any type of dichotomies is different from any other 4 dichotomies ie: the minimum distance = 4, which can be seen from the example of a type.
If all of the dichotomy identified correctly, then the code will be received by type 1 and type will be determined with certainty.
If a single mistake is made then get the following picture: the difference between the code of the first type will be equal to 1, between any other difference would be 3 and a type that will eventually set to as the most likely - the first, so that the bug will be fixed too.
In all such combinations = 7
Probability of occurrence of combinations of dichotomies without error = 0.478
Probability of occurrence of combinations of dichotomies with a single error = 0.053
Total probability of correct typing = 0.478 + 7 * 0.053 = 0.85
What is already more than the first: 0.729
Next: When receiving a combination of dichotomies with a double error type is classified as a "type not defined" because there are always two types, the minimum distance to which is the same.
The number of such combinations 7C2 = 21
The probability of this outcome = 7C2 * 0.9 * 0.1 ^ 5 ^ 2 = 0.124
The very same probability of error in this case is = 0.026
It turned out that the probability of correct identification of TIM is 97% and 3% error.
Progress is very significant.