There are lots of properties in SSAS that have no useful purpose, or whose purpose is somewhat obscure, and one property I’ve always wondered about is the DependsOnDimension property of a dimension. You can find it in the Dimension Editor in BIDS but there’s no indication in the description as to what it does, so in a moment of idle curiosity I Googled Binged it; the best information I found was this forums answer from 2007 from Matt Carroll:

DependsOnDimension is really just a hint for use when designing aggregations using the Aggregation Design Wizard or the Usage Based Optimization Wizard.  Normally the aggregation design algorithm estimates the size of aggregations assuming dimesions are independent, but this property lets it know that one dimension is strongly determined by another dimension.  This should not affect your browsing experience in any way.

In Analysis Services 2000, DependsOnDimension was also used as part of the definition of virtual dimensions as a way of specifying the source for virtual dimension’s levels.

I did some quick experiments in BIDS and couldn’t see any evidence that setting this property affected what aggregations were designed by the Aggregation Design Wizard, but they weren’t exhaustive tests by any means. If you’re taking the trouble to enter row counts and set the AggregationUsage property you should probably try setting it if you have any dimensions that are very closely linked, just in case it does have an impact.