Resistance to bribery when aggregating soft constraints

We consider a multi-agent scenario, where the preferences of several agents are modelled via soft constraint problems and need to be aggregated to compute a single ”socially optimal” solution. We study the resistance of various ways to compute such a solution to influence the result, such as those based on the notion of bribery. In doing this, we link the cost of bribing an agent to the effort needed by the agent to make a certain solution optimal, by only changing preferences associated to parts of the solution. This leads to the definition of four notions of distance from optimality of a solution in a soft constraint problem. The notions differ on the amount of information considered when evaluating the effort.