arXiv subjects

Rakshitha

Publications and source records attributed to Rakshitha.

2 recordsLinked to original sources

arXiv2025

Best of Both Worlds Guarantees for Equitable Allocations

Equitability is a well-studied fairness notion in fair division, where an allocation is equitable if all agents receive equal utility from their allocation. For indivisible items, an exactly equitable allocation may not exist, and a natural relaxation is EQ1, which stipulates that any inequitability should be resolved by the removal of a single item. In this paper, we study equitability in the context of randomized allocations. Specifically, we aim to achieve equitability in expectation (ex ante EQ) and require that each deterministic outcome in the support satisfies ex post EQ1. Such an allocation is commonly known as a `Best of Both Worlds' allocation, and has been studied, e.g., for envy-freeness and MMS. We characterize the existence of such allocations using a geometric condition on linear combinations of EQ1 allocations, and use this to give comprehensive results on both existence and computation. For two agents, we show that ex ante EQ and ex post EQ1 allocations always exist and can be computed in polynomial time. For three or more agents, however, such allocations may not exist. We prove that deciding existence of such allocations is strongly NP-complete in general, and weakly NP-complete even for three agents. We also present a pseudo-polynomial time algorithm for a constant number of agents. We show that when agents have binary valuations, best of both worlds allocations that additionally satisfy welfare guarantees exist and are efficiently computable.

cs.GT↗

arXiv2024

EF1 Allocations for Identical Trilean and Separable Single-Peaked Valuations

In the fair division of items among interested agents, envy-freeness is possibly the most favoured and widely studied formalisation of fairness. For indivisible items, envy-free allocations may not exist in trivial cases, and hence research and practice focus on relaxations, particularly envy-freeness up to one item (EF1). A significant reason for the popularity of EF1 allocations is its simple fact of existence. It is known that EF1 allocations exist for two agents with arbitrary valuations; agents with doubly-monotone valuations; agents with Boolean valuations; and identical agents with negative Boolean valuations. We consider two new but natural classes of valuations, and partly extend results on the existence of EF1 allocations to these valuations. Firstly, we consider trilean valuations - an extension of Boolean valuations - when the value of any subset is 0, $a$, or $b$ for any integers $a$ and $b$. Secondly, we define separable single-peaked valuations, when the set of items is partitioned into types. For each type, an agent's value is a single-peaked function of the number of items of the type. The value for a set of items is the sum of values for the different types. We prove EF1 existence for identical trilean valuations for any number of agents, and for separable single-peaked valuations for three agents. For both classes of valuations, we also show that EFX allocations do not exist.

cs.GT↗