On each filter, check the "Only Relevant Values" and they should cascade for you how you are describing.
Mark Bradbourne is right on the money with his answer. They're called cascading quick filters and the only "gotcha" is that you can't control the direction they cascade. So if you've got 3-4 levels of filters setup to show "Only Relevant Values", selecting a value from level 4 will filter up to the other levels that are set to "Only Relevant Values".
A small bit of user training on how to use them will keep you from getting those questions about why they cascade up as well as down.