  We consider a new setting of facility location games with ordinal
preferences. In such a setting, we have a set of agents and a set of
facilities. Each agent is located on a line and has an ordinal preference over
the facilities. Our goal is to design strategyproof mechanisms that elicit
truthful information (preferences and/or locations) from the agents and locate
the facilities to minimize both maximum and total cost objectives as well as to
maximize both minimum and total utility objectives. For the four possible
objectives, we consider the 2-facility settings in which only preferences are
private, or locations are private. For each possible combination of the
objectives and settings, we provide lower and upper bounds on the approximation
ratios of strategyproof mechanisms, which are asymptotically tight up to a
constant. Finally, we discuss the generalization of our results beyond two
facilities and when the agents can misreport both locations and preferences.
