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We study the group-fair multi-period mobile facility location problems, where agents from different groups are located on a real line and arrive in different periods. Our goal is to locate k mobile facilities at each period to serve the arriving agents in order to minimize the maximum total group-fair cost and the maximum average group-fair cost objectives that measure the costs or distances of groups of agents to their corresponding facilities across all periods. We first consider the problems from the algorithmic perspective for both group-fair cost objectives. We then consider the problems from the mechanism design perspective, where the agents' locations and arrival periods are private. For both objectives, we design deterministic strategyproof mechanisms to elicit the agents' locations and arrival periods truthfully while optimizing the group-fair cost objectives and show that our mechanisms have almost tight bounds on the approximation ratios for certain periods and settings. Finally, we discuss the extensions of our results to the online setting where agent arrival information is only known at each period. 

A well-regarded fairness notion when dividing indivisible chores is envy-freeness up to one item (EF1), which requires that pairwise envy can be eliminated by the removal of a single item. While an EF1 and Pareto optimal (PO) allocation of goods can always be found via well-known algorithms, even the existence of such solutions for chores remains open, to date. We take an epistemic approach utilizing information asymmetry by introducing dubious chores–items that inflict no cost on receiving agents but are perceived costly by others. On a technical level, dubious chores provide a more fine-grained approximation of envy-freeness than EF1. We show that finding allocations with minimal number of dubious chores is computationally hard. Nonetheless, we prove the existence of envy-free and fractional PO allocations for n agents with only 2n−2 dubious chores and strengthen it to n−1 dubious chores in four special classes of valuations. Our experimental analysis demonstrates that often only a few dubious chores are needed to achieve envy-freeness. 

An important question in elections is determining whether a candidate can be a winner when some votes are absent. We study this determining winner with absent votes (WAV) problem with elections that take top-truncated ballots. We show that the WAV problem is NP-complete for single transferable vote, Maximin, and Copeland, and propose a special case of positional scoring rule such that the problem can be computed in polynomial time. Our results for top-truncated rankings differ from the results in full rankings as their hardness results still hold when the number of candidates or the number of missing votes are bounded, while we show that the problem can be solved in polynomial time in either case.