In the quest for a realistic implementation of mechanism design in demand response, a two-stage mechanism is proposed in this paper for sharing the cost of electricity among strategic, rational, and selfish household agents that have private information about their preferences. Whereas mechanisms in prior works charge the agents based on their day-ahead allocations, the proposed mechanism charges the agents based on their actual consumption and the degree of deviation from their day-ahead allocations. The mechanism's payment rule is a function of the inverse of the strictly proper spherical scoring rule multiplied by a quadratic term that is independent of the agent's reports. The mechanism is proven to be asymptotically incentive compatible and ex-ante weakly budget balanced under further conditions. The results of simulations also corroborate that, in the context of energy cost sharing, the mechanism is fair in allocating the payments from the agents as it assigns lower payments from agents that are more precise and more accurate in following the day-ahead appliance schedule allocated to them.