Unsorted majorization of two lists
Jelly, 10 8 6 bytes

2 bytes thanks to @orlp.

2 bytes thanks to @Dennis.

_+\ṠQS


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1 for a&gt;b, -1 for a&lt;b, 0 for no majorization.

_+\ṠQS

_       Difference (vectorized)
 +\     Cumulative sum.
   Ṡ    Sign of every difference
    Q   Deduplicate
     S  Sum


If there were both 1 and -1 present (some cumulative sums are bigger, some smaller), then the last step would produce 0.