Equal precendence rule

Can someone help me how equal precedence works in this case?

I have a date attribute and equal precedence of both FIMMA and HR.

scenario 1:  dateAttribute : 6/6/2013; date from HR says: 12/31/2013. dateAttribute changes to 12/31/2013

scenario 2 : 1date Attribute: 12/31/2013; date from HR says: 6/7/2013. dateAttribute changes to 6/7/2013

Scenario 3:Admins change the date in FIM to 9/30/2013. date from HR stays the same(6/7/2013) . Would the date attribute be changed to 6/7/2013 in the next HR sync for equal precedence even if there is no change in HR?

Thanks!