df <- data.frame("Earner_Number" = c(1,1,1,5), "Earner5" = c('Max', 'Alex','Ben','Mark'), "Earner1" = c("John","Dora","Ben",'Josh'))

>df
  Earner_Number Earner5 Earner1
1             1     Max    John
2             2    Alex    Dora
3             1     Ben Micelle
4             5    Mark    Josh

>df
Earner_Number Earner5 Earner1 Highest_Earner
1             1     Max    John           John
2             2    Alex    Dora        Neither
3             1     Ben Micelle       Michelle
4             5    Mark    Josh           Mark