We consider a multi-agent resource allocation setting in which an agent's utility may decrease or increase when an item is allocated. We take the group envy-freeness concept that is well-established in the literature and present stronger and relaxed versions that are especially suitable for the allocation of indivisible items. Of particular interest is a concept called group envy-freeness up to one item (GEF1). We then present a clear taxonomy of the fairness concepts. We study which fairness concepts guarantee the existence of a fair allocation under which preference domain. For two natural classes of additive utilities, we design polynomial-time algorithms to compute a GEF1 allocation. We also prove that checking whether a given allocation satisfies GEF1 is coNP-complete when there are either only goods, only chores or both.

Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to jump to single transferable vote (STV) as the solution for achieving PR. Some of the most prominent electoral reform movements around the globe are pushing for the adoption of STV. It has been termed a major open problem to design a voting rule that satisfies the same PR properties as STV and better monotonicity properties. In this paper, we first present a taxonomy of proportional representation axioms for general weak order preferences, some of which generalise and strengthen previously introduced concepts. We then present a rule called Expanding Approvals Rule (EAR) that satisfies properties stronger than the central PR axiom satisfied by STV, can handle indifferences in a convenient and computationally efficient manner, and also satisfies better candidate monotonicity properties. In view of this, our proposed rule seems to be a compelling solution for achieving proportional representation in voting settings.

Earlier this year, the Institute of Electrical and Electronics Engineering's (IEEE) published "AI's 10 to Watch" – a list of 10 people who are doing phenomenal work in the field of artificial intelligence. A Pakistani researcher Haris Aziz, who had graduated from LUMS, had his name published in this prestigious list for his work in the field related to computational social choice, an intersection between artificial intelligence and economics. Its seems that was just the beginning of the road for Haris Aziz, who is now back in the news for solving an'unsolvable' mathematical situation. Who will get the larger share of the profit from a business? Shall it be equally allocated or otherwise? Perhaps its your child's birthday and its time to cut and divide the cake in a way that none of the children gets sad by his/her share?