Strategy-Proof Interval Selection

We investigate interval selection problems in which a society chooses an interval from a discrete ordered set. We consider a domain of interval-monotonic preferences, where each voter has an interval of acceptable integers, benefits from enlarging the selected interval by including acceptable integers, and is worse off when unacceptable integers are included. We study how different institutional frameworks affect the design of strategy-proof interval choice functions. In particular, we distinguish between unrestricted interval selection and the expansion of a commonly accepted status quo interval. We show that the latter transforms interval selection into a separable multidimensional choice problem, whereas unrestricted interval selection remains intrinsically multidimensional. This institutional distinction leads to fundamentally different characterizations of strategy-proof interval choice functions.