Ensure Java synchronized locks are taken in order?

we have two threads accessing one list via a synchronized method. Can we

a) rely on the run time to make sure that each of them will receive access to the method based on the order they tried to or

b) does the VM follow any other rules

c) is there a better way to serialize the requests?

No, synchronized will give access in any order (Depends on the JVM implementation). This could even cause Threads to starve in some scenarios.

You can ensure the order by using ReentrantLock (since Java 5.0) with the fair=true option. (Lock lock = new ReentrantLock(true);)

No you cannot be sure that two calls to a synchronized method will occur in order. The order is unspecified and implementation dependent.

This is defined in the 17.1 Locks section of the JLS. Notice that is says nothing about the order in which threads waiting on a lock should gain access.

You can't rely on the order in which the particular method is called from each threads. If it is only two threads may be yes. But imagine if there are 3 threads and 1 thread already acquired access. The other 2 threads when they try to access will wait and any one of them can be awarded the access, and this does not depend on the order in which they called this method. So, it is not suggested to rely on the order.