Soft, capacitive tactile (pressure) sensors are important for applications including human-machine interfaces, soft robots, and electronic skins. Such capacitors consist of two electrodes separated by a soft dielectric. Pressing the capacitor brings the electrodes closer together and thereby increases capacitance. Thus, sensitivity to a given force is maximized by using dielectric materials that are soft and have a high dielectric constant, yet such properties are often in conflict with each other. Here, a liquid metal elastomer foam (LMEF) is introduced that is extremely soft (elastic modulus 7.8 kPa), highly compressible (70% strain), and has a high permittivity. Compressing the LMEF displaces the air in the foam structure, increasing the permittivity over a large range (5.6-11.7). This is called "positive piezopermittivity." Interestingly, it is discovered that the permittivity of such materials decreases ("negative piezopermittivity") when compressed to large strain due to the geometric deformation of the liquid metal droplets. This mechanism is theoretically confirmed via electromagnetic theory, and finite element simulation. Using these materials, a soft tactile sensor with high sensitivity, high initial capacitance, and large capacitance change is demonstrated. In addition, a tactile sensor powered wirelessly (from 3 m away) with high power conversion efficiency (84%) is demonstrated.