Aggregating the preferences of multiple agents into a collective decision is a common step in many important problems across areas of computer science including information retrieval, reinforcement learning, and recommender systems. As Social Choice Theory has shown, the problem of designing algorithms for aggregation rules with specific properties (axioms) can be difficult, or provably impossible in some cases. Instead of designing algorithms by hand, one can learn aggregation rules, particularly voting rules, from data. However, the prior work in this area has required extremely large models, or been limited by the choice of preference representation, i.e., embedding. We recast the problem of designing a good voting rule into one of learning probabilistic versions of voting rules that output distributions over a set of candidates. Specifically, we use neural networks to learn probabilistic social choice functions from the literature. We show that embeddings of preference profiles derived from the social choice literature allows us to learn existing voting rules more efficiently and scale to larger populations of voters more easily than other work if the embedding is tailored to the learning objective. Moreover, we show that rules learned using embeddings can be tweaked to create novel voting rules with improved axiomatic properties. Namely, we show that existing voting rules require only minor modification to combat a probabilistic version of the No Show Paradox.

Semidefinite programs (SDPs) are convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization and operational research. Noisy intermediate-scale quantum (NISQ) algorithms aim to make an efficient use of the current generation of quantum hardware. However, optimizing variational quantum algorithms is a challenge as it is an NP-hard problem that in general requires an exponential time to solve and can contain many far from optimal local minima. Here, we present a current term NISQ algorithm for solving SDPs. The classical optimization program of our NISQ solver is another SDP over a lower dimensional ansatz space. We harness the SDP based formulation of the Hamiltonian ground state problem to design a NISQ eigensolver. Unlike variational quantum eigensolvers, the classical optimization program of our eigensolver is convex, can be solved in polynomial time with the number of ansatz parameters and every local minimum is a global minimum. We find numeric evidence that NISQ SDP can improve the estimation of ground state energies in a scalable manner. Further, we efficiently solve constrained problems to calculate the excited states of Hamiltonians, find the lowest energy of symmetry constrained Hamiltonians and determine the optimal measurements for quantum state discrimination. We demonstrate the potential of our approach by finding the largest eigenvalue of up to $2^{1000}$ dimensional matrices and solving graph problems related to quantum contextuality. We also discuss NISQ algorithms for rank-constrained SDPs. Our work extends the application of NISQ computers onto one of the most successful algorithmic frameworks of the past few decades.

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Amazon picked a tough moment to come to New York. Progressive groups were in the ascendant and they turned their fire on an obvious target: a plan to lure a company run by the world's richest man with $3bn in subsidies and tax breaks. The abrupt collapse of Amazon's plan for a new headquarters, or HQ2, in Long Island City was a milestone victory for leftwing insurgents over establishment Democrats who backed the deal. "This is a new day in New York City politics," said Sasha Wijeyeratne, executive director of Caaav: Organizing Asian Communities. "They sauntered in here and said HQ2 was inevitable," she said.

Blue Cross/Blue Shield of Virginia AT&T's Merrimack Valley Works The US Army Laboratory Command's (Richmond, VA) has developed an (North Andover, MA) has developed Human Engineering Laboratory expert system to classify, evaluate the Expert Capacity and Material (Aberdeen Proving Ground, MD) has and process medical claims. The system, System (XCAM), an expert system awarded a $2.4 million contract to called MedScreen, reportedly which simplifies forecast evaluations Carnegie Group (Pittsburgh, PA) to can process up to 500 claims in 45 for a manufacturing operation The continue work on a knowledge-based minutes, an operation that used to system automates the analysis of logistics planning system. The system take several days to complete. The IBM (Armonk, NY) and Dragon Systems NRM has been successfully deployed ICL (Birmingham, England) has completed (Newton, MA) have jointly in a number of Australian banks, as a pilot test of an intelligent developed VoiceType, a speech recognition well as a food storage and distribution system for field service diagnosing system based on elements of center. ICL used a laptop-based allows hands-free typing.