Excel- function to sum non-empty columns the find string if majority

I apologize for the confusing title, I was not sure how to phrase this question.

I have a (dynamic and constantly updating) database of stocks in column A. In columns B through J, there are names of people who have invested in the stock.

In each group of 4 stocks (so stock 1 through stock 4) each person can choose to invest in ONLY 2 stocks. However, each person does not always participate. For example, Person 10 below did not participate in picking stocks until the second round. And Person 9 only pariticpaed in picking stocks the first round (stocks 1-4).

I want to write a function that can tell me how often each person picked a stock that was in the majority

Stock 1 Person 1    Person 2                            
Stock 2 Person 3    Person 4    Person 5    Person 6    Person 7    Person 8    Person 9        
Stock 3 Person 2    Person 3    Person 4    Person 5    Person 6    Person 1    Person 7    Person 8    
Stock 4 Person 9                                
Stock 5 Person 6    Person 4    Person 3    Person 7    Person 1    Person 10           
Stock 6 Person 6    Person 8    Person 4    Person 3    Person 1    Person 10   Person 2        
Stock 7 Person 7                                
Stock 8 Person 2    Person 8

I want to find the percent of times each person was in the majority. For example, Person 10 was in the majority for both of the stocks that he/she picked. Therefore, Person 10 would be 100% (even though Person 10 did NOT vote in the first 4 stocks it should not be counted against his/her percentage).

Person 1, however, participated in picking stocks 1-8 and was in the majority 3/4 times. Her percentage would be 75%.

I honestly don't even know where to begin. The fact that I do not want the stocks a person did not pick between to count against them is making me confused. I hope my explanation makes sense, if anyone has suggestions about the first step to take, I would appreciate it!