After sorting the answer falls in a known place

If a value fills more than half of a list, then once the list is sorted the element exactly in the middle must be it: a block longer than half covers the middle wherever it sits. Some questions come down to looking at a single index after sorting.

1ordered = sorted(scores, reverse=True)
2rank = 0
3while rank < len(ordered) and ordered[rank] > rank:
4    rank += 1
5return rank

Sorting from large to small and comparing "which place am I in" with "what is my value": it counts the elements whose value is larger than their place. Definitions of the form "at least h of them are at least h", like the h-index, are read this way.

Sorting is not always the fastest way, and it is nearly always the easiest correct one. Solve by sorting first and see it pass; then ask "could I do it in one pass, without sorting?". For the majority element the answer is yes: a candidate and a counter are enough.

Tasks