Our initial attempt at a predictive and normative account of grounding
behavior is given in (1), where the left side represents the
probability that a particular action 
which communicates 
will be performed.
GC represents the Grounding criterion for , if this is low,
there is no need for the information to be grounded, and thus a low
probability that an agent will perform some action to ground it. The
importance for grounding a particular piece of information also
depends on the cost (with respect to the task) of non-grounding - how
will task performance degrade if the particular is not grounded. An
important factor in this is the persistence of the particular - it is
a waste of time to ground highly transient information that changes
before it's current value can be of use.
G represents the prior groundedness of . If it is already
well grounded, there is little need to perform further action, even if
it is crucial that the information be grounded. G will depend
in part on how much and what kind of information is provided
automatically by the environment (e.g., the shared visual situation
of the whiteboard). Another important factor is the perplexity of the
information - the probability that some information believed to be
grounded could be misunderstood or disagreed upon.
C represents the collaborative grounding cost of ,
including not only the effort required to perform the action, but also
the affiliated costs of understanding it as conveying , including
potential further actions (repairs) which may be required. If these
costs are high, there is not as much utility in performing the action,
while if they are low, the action may be performed, even when
grounding is not particularly crucial. C depends not only on the
features of the medium itself,
but also on the matching between the subject and the medium, e.g., how
familiar the subject is with the medium. For example sometimes
collaborators use an apparently more expensive medium simply because
they know how to use it and are reluctant to learn something new,
which requires an extra learning cost.
All of these aspects must, of course, be put relative to the beliefs
of a particular agent in order to be used predictively. Note, also,
that any of them can change throughout the course of a collaboration.
The importance that something be part of common ground is relative to
the local circumstances as well as the overall goals. Agents can also
change their minds as to whether something has been grounded or not.
Third or fourth turn repair of misunderstanding [McRoy and Hirst1995]
comes from precisely this case, where an agent previously believed
some 
had a relatively high degree of groundedness, but later
information reduced this level. Similarly, local context will play a
large role in determining whether a particular will be
effective at communicating some .
Further work is still needed to try to quantify the relative aspects
of this relation with respect to each other. In order to adapt (0)
from a proportionality to a true equality that could be used to
calculate the probability (or utility) of action, it is also necessary
to consider two other factors: what other actions 
might better convey , and what other actions (including both
communicating some 
, as well as other non-communicative
task-related acts) might also be useful to perform. For the former,
the grounding criterion and prior groundedness of will still be
useful, while for the latter some more global arbitration strategy
must be used to set priorities. In some domains, time, focus, and
local context are also important factors - sometimes one must perform
some acts before the balance of costs and benefits have been changed,
while other acts have more flexibility.