  Items shared through Social Media may affect more than one user's privacy ---
e.g., photos that depict multiple users, comments that mention multiple users,
events in which multiple users are invited, etc. The lack of multi-party
privacy management support in current mainstream Social Media infrastructures
makes users unable to appropriately control to whom these items are actually
shared or not. Computational mechanisms that are able to merge the privacy
preferences of multiple users into a single policy for an item can help solve
this problem. However, merging multiple users' privacy preferences is not an
easy task, because privacy preferences may conflict, so methods to resolve
conflicts are needed. Moreover, these methods need to consider how users' would
actually reach an agreement about a solution to the conflict in order to
propose solutions that can be acceptable by all of the users affected by the
item to be shared. Current approaches are either too demanding or only consider
fixed ways of aggregating privacy preferences. In this paper, we propose the
first computational mechanism to resolve conflicts for multi-party privacy
management in Social Media that is able to adapt to different situations by
modelling the concessions that users make to reach a solution to the conflicts.
We also present results of a user study in which our proposed mechanism
outperformed other existing approaches in terms of how many times each approach
matched users' behaviour.
