Add quick and dirty doc about state resolution

docs/state_resolution.rst

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+State Resolution
+================
+This section describes why we need state resolution and how it works.
+
+
+Motivation
+-----------
+We want to be able to associate some shared state with rooms, e.g. a room name
+or members list. This is done by having a current state dictionary that maps
+from the pair event type and state key to an event.
+
+However, since the servers involved in the room are distributed we need to be
+able to handle the case when two (or more) servers try and update the state at
+the same time. This is done via the state resolution algorithm.
+
+
+State Tree
+------------
+State events contain a reference to the state it is trying to replace. These
+relations form a tree where the current state is one of the leaf nodes.
+
+Note that state events are events, and so are part of the PDU graph. Thus we
+can be sure that (modulo the internet being particularly broken) we will see
+all state events eventually.
+
+
+Algorithm requirements
+----------------------
+We want the algorithm to have the following properties:
+- Since we aren't guaranteed what order we receive state events in, except that
+  we see parents before children, the state resolution algorithm must not depend
+  on the order and must always come to the same result. 
+- If we receive a state event whose parent is the current state, then the
+  algorithm will select it.
+- The algorithm does not depend on internal state, ensuring all servers should
+  come to the same decision.
+
+These three properties mean it is enough to keep track of the current state and
+compare it with any new proposed state, rather than having to keep track of all
+the leafs of the tree and recomputing across the entire state tree.
+
+
+Current Implementation
+----------------------
+The current implementation works as follows: Upon receipt of a newly proposed
+state change we first find the common ancestor. Then we take the maximum
+across each branch of the users' power levels, if one is higher then it is
+selected as the current state. Otherwise, we check if one chain is longer than
+the other, if so we choose that one. If that also fails, then we concatenate
+all the pdu ids and take a SHA1 hash and compare them to select a common
+ancestor.