# Mathematical way of identifying wrong suggestions or outliers

I have a hypothetical scenario where i have 100 classifiers to which if a person's name is given as input, it will return a class for the person.

Eg. Input1 -Donald Trump
30/100 classifiers returns politician as the class
20/100 classifiers returns business man as the class
10/100 classifiers returns leader as the class
10/100 classifiers returns american as the class
10/100 classifiers returns republican as the class
10/100 classifiers returns sportsman as the class
3/100 classifiers returns priest as the class
3/100 classifiers returns doctor as the class
2/100 classifiers returns engineer as the class
1/100 classifiers returns indian as the class
1/100 classifiers returns sportsman as the class

In the above case i take 10 votes as a threshold, i can somewhat correctly define Donald Trump, though a definition of sportsman might be wrong. However 10 seems to be a decent threshold

Input2 -Christiano Ronaldo
20/100 classifiers returns sportsman as the class
20/100 classifiers returns foot ball player as the class
13/100 classifiers returns real madrid as the class
13/100 classifiers returns manchesterunited as the class
12/100 classifiers returns juventus as the class
12/100 classifiers returns european as the class
2/100 classifiers returns portugese as the class
2/100 classifiers returns cricketer as the class
2/100 classifiers returns american as the class
2/100 classifiers returns chinese as the class
2/100 classifiers returns korean as the class

In the above example, if i take 12 votes as the threshold, it correctly defines Christiano Ronaldo, though we might be missing portugese tag since its vote is only 2. However we are doing a good job here i guess.

My problem is, if i have an api that returns the votes and class of famous persons this way, what is the best mathematical aproach to dynamically find the best possible threshold value above which i can say that the definition is correct and below which you need to have a look if the classes are correct

• In both your examples you could have taken the logarithm (base 10) of the number of classifiers out of 100, taken the floor of that value (or the ceiling), and neatly divided the two lists into two parts at the same places as your gut feeling led you to. I don't expect such a simple approach would work in more general cases, but it might get you started. – High Performance Mark Aug 7 '20 at 10:45
• what would be your expectation if classifiers distribution looks like [1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14] or [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]? – etiennedm Aug 7 '20 at 15:32