You're right, the same example dawned on me last night after I used up all of
my computer time.
But the Hasse diagram of the partial order does yield a weighted DAG (directed
acyclic graph) where the
weight of each coalition is the sum of the weights of the factions that are
included in it. If we agree that
edges are directed from coalition to subcoalition, then the only source is the
set of all factions. [A
source is a node that has at least one edge leaving it, but no edge entering
it; i.e. indegree=0,
outdegree>0.]
Here's how to order the factions:
While there remains at least one edge in the graph ..
remove the heaviest edge leaving the most recently exposed source.
EndWhile
The factions play in the order that they are exposed.
[The weight of an edge is the weight of the node that it enters. A node is
exposed at the stage its
indegree reaches zero. In the original DAG the only source is considered to be
the "most recently
exposed source."]
This generalizes the order that I gave for trees, i.e.if the DAG is a tree,
this order agrees with the order
that I gave for that case.
It is clear that this algorithm takes O(n) steps where n is the number of edges
in the DAG.
----- Original Message -----
From: Jameson Quinn
> > The Hasse diagram for a partially ordered set is a tree.
> >
>
> No, it's not. Or at least, not if I understand your terms
> correctly. If
> there are three candidates [ABC], and all vote types exist, then
> is [A] a
> leaf on the [AB] branch or on the [AC] branch?
>
> JQ
>
----
Election-Methods mailing list - see http://electorama.com/em for list info
