The Computational Complexity of Random Serial Dictatorship

Computational social choice is a research area at the intersection of computer science, mathematics, and economics that is concerned with aggregation of preferences of multiple agents. Typical applications include voting, resource allocation, and fair division. This chapter highlights six representative research areas in contemporary computational social choice: restricted preference domains, voting equilibria and iterative voting, multiwinner voting, probabilistic social choice, random assignment, and computer-aided theorem proving.

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“…The computational properties of RSD mentioned in Sect. 5 also hold within the domain of assignment [7,10,118].…”

Section: Random Assignmentmentioning

confidence: 99%

“…6). While implementing RSD by uniformly selecting a sequence of agents and then running serial dictatorship is straightforward, it was shown that computing the resulting RSD probabilities is #P-complete [10], but fixed parameter tractable for parameters such as the number of voters or the number of alternatives [7].…”

Section: Probabilistic Social Choicementioning

confidence: 99%

Computational Social Choice: The First Ten Years and Beyond

Aziz

Brandt

Elkind

et al. 2019

Lecture Notes in Computer Science

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“…A single run is clearly not sufficient, as we need to compare probability distributions. Note that computing probabilities of alternatives in RSD explicitly is a computationally very challenging (#P-complete) problem (Aziz et al 2013). Therefore, we ran BRSD 1000 to 1,000,000 times with the same preferences but random permutations of the order of students and derived estimates for the different metrics.…”

Section: Field Experimentsmentioning

confidence: 99%

Randomized Scheduling Mechanisms: Assigning Course Seats in a Fair and Efficient Way

Bichler

Merting

2021

Production and Operations Management

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C ourse assignment is a very widespread problem in education and beyond. Typically, students have preferences for bundles of course seats or course schedules over the week, but courses have limited capacity. This is an interesting and frequent application of distributed scheduling, where payments cannot be used to implement the efficient allocation. First-Come First-Served (FCFS) is simple and the most widely used assignment rule in practice, but it leads to inefficient outcomes and envy in the allocation. It was recently shown that randomized economic mechanisms that do not require monetary transfers can have attractive economic and computational properties, which were considered incompatible for deterministic alternatives. We use a mixed-methods design including field and laboratory experiments, a survey, and simulations to analyze such randomized mechanisms empirically. Implementing randomized scheduling in the field also required us to develop a solution to a new preference elicitation problem that is central to these mechanisms. The results of our empirical work shed light on the advantages that randomized scheduling mechanisms have over FCFS in the field, but also on the challenges. The resulting course assignment system was adopted permanently and is now used to solve course assignment problems with more than 1700 students every year.

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“…The one-sided matching problem was introduced in [25] and has been studied extensively ever since. Over the years, several different mechanisms have been proposed with various desirable properties related to truthfulness, fairness and economic efficiency with Probabilistic Serial [2, 10,11,26] and Random Priority [3,8,15,37] being the two prominent examples. In the indivisible goods setting, the Top Trading Cycles (TTC) method is well-studied and generalized to investigate various problems.…”

Section: Related Workmentioning

confidence: 99%

Average-case Analysis of the Assignment Problem with Independent Preferences

Gao

Zhang

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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The fundamental assignment problem is in search of welfare maximization mechanisms to allocate items to agents when the private preferences over indivisible items are provided by self-interested agents. The mainstream mechanism Random Priority is asymptotically the best mechanism for this purpose, when comparing its welfare to the optimal social welfare using the canonical worst-case approximation ratio. Despite its popularity, the efficiency loss indicated by the worst-case ratio does not have a constant bound [20]. Recently, [16] show that when the agents' preferences are drawn from a uniform distribution, its average-case approximation ratio is upper bounded by 3.718. They left it as an open question of whether a constant ratio holds for general scenarios. In this paper, we offer an affirmative answer to this question by showing that the ratio is bounded by 1/µ when the preference values are independent and identically distributed random variables, where µ is the expectation of the value distribution. This upper bound also improves the upper bound of 3.718 in [16] for the Uniform distribution. Moreover, under mild conditions, the ratio has a constant bound for any independent random values. En route to these results, we develop powerful tools to show the insights that in most instances the efficiency loss is small. * jie.zhang@soton.ac.uk

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The Computational Complexity of Random Serial Dictatorship

Cited by 28 publications

References 8 publications

Computational Social Choice: The First Ten Years and Beyond

Computational Social Choice: The First Ten Years and Beyond

Randomized Scheduling Mechanisms: Assigning Course Seats in a Fair and Efficient Way

Average-case Analysis of the Assignment Problem with Independent Preferences

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