Yes many, probably most marriages are based on an equal relationship. But many are not. And in the past most were not.

i would say most marriages (in western cultures at least) are based on the expectation of an equal relationship. however many still have not learned what actually is an equal relationship. (it's not splitting home chores 50/50).

for me an equal relation ship means that each of our wishes, goals and needs are of equal importance. it can mean that both partners work and split housework equally, but it also can mean something different.