Random Priority Research Articles

Probabilistyczne metody podziału zbioru dóbr niepodzielnych

In fair distribution of a set of indivisible goods it is problematic to provide basic equality if the goods differ in value. One of the most popular solutions to the problems are lotteries. The paper presents seven selected probabilistic procedures: random distribution, lexicographic procedure of equal chances of satisfaction, random serial dictatorship, core from random endowments, probabilistic serial, top trading cycles from equal division and random priority with infi nite k factor. Some of these procedures always lead to the same result as some other procedure, therefore these procedures are equivalent. The formal features of the procedures are also analysed in the paper: ordinal efficiency, ex post effi ciency, and both strong and week version of: envy-freeness, proportionality, equitability, and individual strategy-proofness.

Integrating estimation of distribution algorithms versus Q-learning into Meta-RaPS for solving the 0-1 multidimensional knapsack problem

Finding near-optimal solutions in an acceptable amount of time is a challenge when developing sophisticated approximate approaches. A powerful answer to this challenge might be reached by incorporating intelligence into metaheuristics. We propose integrating two methods into Meta-RaPS (Metaheuristic for Randomized Priority Search), which is currently classified as a memoryless metaheuristic. The first method is the Estimation of Distribution Algorithms (EDA), and the second is utilizing a machine learning algorithm known as Q-Learning. To evaluate their performance, the proposed algorithms are tested on the 0-1 Multidimensional Knapsack Problem (MKP). Meta-RaPS EDA appears to perform better than Meta-RaPS Q-Learning. However, both showed promising results compared to other approaches presented in the literature for the 0-1 MKP.

Obvious Dominance and Random Priority

We introduce a general class of simplicity standards that vary the foresight abilities required of agents in extensive-form games. Rather than planning for the entire future of a game, agents are presumed to be able to plan only for those histories they view as simple from their current perspective. Agents may update their so-called strategic plan as the game progresses, and, at any point, for the called-for action to be simply dominant, it must lead to unambiguously better outcomes, no matter what occurs at non-simple histories. We use our gradated approach to simplicity to provide characterizations of simple mechanisms. While more demanding simplicity standards may reduce the flexibility of the designer in some cases, this is not always true, and many well-known mechanisms are simple, including ascending auctions, posted prices, and serial dictatorship-style mechanisms. In particular, we explain the widespread popularity of the well-known Random Priority mechanism by characterizing it as the unique mechanism that is efficient, fair, and simple to play.

The performance of a single-server queue with preemptive random priorities

Queues in which customers who belong to different classes have different priority levels is an old subject. Usually one looks for the performance of each class given its priority level. We suggest here a new model. Specifically, we consider the M/G/1 queue model in which all customers are identical ex-ante, but prior to joining the queue they draw a random (preemptive) priority level. We derive the Laplace–Stieltjes transform (LST) of a customer given his drawn priority parameter. From that the LST of an arbitrary customer can be integrated out. We present a number of proofs that provide some insight into the model. Special attention is given to the case of exponential service (the M/M/1 queue) and to finding the first moment of waiting. In particular, we show that the model is ä middle of the road” one in the sense that the mean sojourn time lies between the corresponding means under the First-Come First-Served FCFS and the Last-Come First-Served with Preemption Resume (LCFS-PR) (or equivalently, Egalitarian Processor Sharing (EPS)) schemes. Finally, we show how the new scheme may lead to an improvement in the utilization of the server when customer decides whether or not to join. We conclude with a few words on the corresponding model but without preemption.

On the consistency of random serial dictatorship

The random serial dictatorship (RSD) can be generalized to indivisible object allocation problems allowing fractional endowments such that symmetry, ex-post efficiency and strategy-proofness are preserved. However, there exists a consistent extension of RSD if and only if the population is less than four. The inconsistency of the generalized RSD is a common feature of strategy-proof rules that satisfy minimal fairness and efficiency properties: symmetry, ex-post efficiency, consistency and strategy-proofness are not compatible.

Efficient lottery design

There has been a surge of interest in stochastic assignment mechanisms that have proven to be theoretically compelling thanks to their prominent welfare properties. Contrary to stochastic mechanisms, however, lottery mechanisms are commonly used in real life for indivisible goods allocation. To help facilitate the design of practical lottery mechanisms, we provide new tools for obtaining stochastic improvements in lotteries. As applications, we propose lottery mechanisms that improve upon the widely used random serial dictatorship mechanism and a lottery representation of its competitor, the probabilistic serial mechanism. The tools we provide here can be useful in developing welfare-enhanced new lottery mechanisms for practical applications such as school choice.

Fairness and group-strategyproofness clash in assignment problems

No group-strategyproof and ex-post Pareto optimal random matching mechanism treats equals equally. Every mechanism that arises out of the randomization over a set of non-bossy and strategyproof mechanisms is non-bossy. Random serial dictatorship, which arises out of a randomization over all deterministic serial dictatorships is non-bossy but not group-strategyproof.

Strategy-Proof Probabilistic Mechanisms for Public Decision with Money

We study strategy-proof probabilistic mechanisms in a binary public decision model when monetary transfers are allowed. We consider not only the pivotal mechanism, the majority voting mechanism, the random serial dictatorship mechanism, and the unanimity mechanism, but also the random chair pivotal mechanism (Faltings 2005), which is a probabilistic variant of the pivotal mechanism.We first show that the random chair pivotal mechanism, the majority voting mechanism, the random serial dictatorship mechanism, and the unanimity mechanism are second-best efficient.Next, we calculate the expected welfare of the mechanisms by the Monte Carlo method, where each agent's valuation is independently, identically, and uniformly (or normally) distributed. These calculations exhibit that the random chair pivotal mechanism is more efficient than the other mechanisms. We also show that in large economies, the random chair pivotal mechanism is efficient, while the other mechanisms might be highly inefficient.Finally, we characterize the random chair pivotal mechanism with strategy-proofness, budget-balance, equal treatment of equals, and decision-robustness.

Tiered Housing Allocation with Preannounced Rankings: An Experimental Analysis

We study in the laboratory a variant of the house allocation with existing tenants problem where subjects are partitioned into tiers with hierarchical privileges, and they know their position in the priority queue before making their decision. We evaluate the performance of the modified versions of three well-known mechanisms: Top Trading Cycle (TTC), Gale-Shapley, and Random Serial Dictatorship (RSD) with Squatting Rights. For all three mechanisms, we find low rates of participation (around 40%), high rates of truth-telling conditional on participation (around 90%), high proportions of fair allocations (above 90%), and significant efficiency losses. We also observe differences across mechanisms: RSD is ranked highest in efficiency and TTC is ranked lowest in fairness. We then show that position in the queue has a positive and significant impact on participation whereas tier has little effect on behavior. Finally, the individual analysis reveals that the majority of subjects who do not play according to the theory still follow discernible patterns of participation and preference revelation.

Convex strategyproofness with an application to the probabilistic serial mechanism

We consider two natural notions of strategyproofness in random object-assignment mechanisms based on ordinal preferences. The two notions are stronger than weak strategyproofness but weaker than strategyproofness. We demonstrate that the two notions are equivalent, provide a geometric characterization of the new intermediate property which we call convex strategyproofness, and then show that the (generalized) probabilistic serial mechanism is, in fact, convexly strategyproof. We finish by showing that the property of weak envy-freeness of the random serial dictatorship can be strengthened in an analogous manner.

The Complexity of Computing the Random Priority Allocation Matrix

The random priority (RP) mechanism is a popular way to allocate n objects to n agents with strict ordinal preferences over the objects. In the RP mechanism, an ordering over the agents is selected uniformly at random; the first agent is then allocated his most-preferred object, the second agent is allocated his most-preferred object among the remaining ones, and so on. The outcome of the mechanism is a bi-stochastic matrix in which entry (i, a) represents the probability that agent i is given object a. It is shown that the problem of computing the RP allocation matrix is #P-complete. Furthermore, it is NP-complete to decide if a given agent i receives a given object a with positive probability under the RP mechanism, whereas it is possible to decide in polynomial time whether or not agent i receives object a with probability 1. The implications of these results for approximating the RP allocation matrix as well as on finding constrained Pareto optimal matchings are discussed.

A New Under-Frequency Load Shedding Technique Based on Combination of Fixed and Random Priority of Loads for Smart Grid Applications

This paper presents a new under-frequency load shedding technique based on the combination of random and fixed priority of loads. It has been observed that placing all of the loads in the distribution system with fixed priority results in un-optimum load shedding. On the other hand, designing the load priority with a combination of random and fixed priority provides the technique with some sort of flexibility in achieving the optimal load shedding. The validation of the proposed scheme on different scenarios proves that the proposed technique is capable of achieving the optimal load shedding and recovering frequency to nominal value without any overshoot.

An equilibrium analysis of the probabilistic serial mechanism

Two prominent mechanisms in the random assignment problem are the random priority (RP) and the probabilistic serial (PS). When agents are truthful, the outcomes obtained under PS have superior efficiency and fairness properties, but unlike RP, PS is vulnerable to strategizing. We study incentives of agents under PS. We find that when agents strategize, in equilibrium an outcome may be obtained under PS which is not efficient or fair and which is worse in some respects than the RP outcome. The results of our equilibrium analysis of PS call for caution when implementing it in “small” assignment problems.

On Manipulablity of Random Serial Dictatorship in Sequential Matching with Dynamic Preferences

We consider the problem of repeatedly matching a set of alternatives to a set of agents in the absence of monetary transfer. We propose a generic framework for evaluating sequential matching mechanisms with dynamic preferences, and show that unlike single-shot settings, the random serial dictatorship mechanism is manipulable.

Winner Determination Algorithms for Combinatorial Auctions with Sub-cardinality Constraints

We examine the winner determination problem for combinatorial auctions with sub-cardinality constraints (WDP-SC). In this type of auction, bidders submit bids for packages of items of interest together with a specific number of items they want. All items in a package are equally acceptable, but each bidder wants only the specified number of items in their package and not necessarily all. This type of auction is particularly relevant in cases where bidders are interested in items in close proximity to one another and view items as largely substitutable. We show that WDP-SC is NP-hard. We then develop an integer programming (IP) formulation and two approximation algorithms for solving WDP-SC: one based on simulated annealing (SA) and one based on the Metaheuristic for Randomized Priority Search (Meta-RaPS). We assess the performance of these three methods through computational tests performed on sets of large benchmark problems (ranging from 1000 to 10,000 bids) generated from four different distributions: two developed specifically to simulate proximity concerns, and two others previously used in the literature. IP produced the best solutions for 1000-bid problems, but in many cases SA and Meta-RaPS produced better solutions than IP on larger problems. Both IP and Meta-RaPS appear to be robust solution methods for this problem and consistently produced high-quality solutions across all problem sizes and distributions.

Matching with Dynamic Ordinal Preferences

We consider the problem of repeatedly matching a set of alternatives to a set of agents with dynamic ordinal preferences. Despite a recent focus on designing one-shot matching mechanisms in the absence of monetary transfers, little study has been done on strategic behavior of agents in sequential assignment problems. We formulate a generic dynamic matching problem via a sequential stochastic matching process. We design a mechanism based on random serial dictatorship (RSD) that, given any history of preferences and matching decisions, guarantees global stochastic strategyproofness while satisfying desirable local properties. We further investigate the notion of envyfreeness in such sequential settings.

Computational aspects of random serial dictatorship

Two fundamental problems in economics are voting and assignment. In both settings, random serial dictatorship is a well-established mechanism that satisfies anonymity, ex post efficiency, and strategyproofness. We present an overview of recent results on the computational complexity of problems related to random serial dictatorship.

The M/G/1 queueing model with preemptive random priorities

For the M/G/1 model, we look into a preemptive priority scheme in which the priority level is decided by a lottery. Such a scheme has no effect on the mean waiting time in the non-preemptive case (in comparison with the First Come First Served (FCFS) regime, for example). This is not the case when priority comes with preemption. We derived the resulting mean waiting time (which is invariant with respect to the lottery performed) and show that it lies between the corresponding means under the FCFS and the Last Come First Served with Preemption Resume (LCFS-PR) (or equivalently, the Egalitarian Processor Sharing (EPS)) schemes. We also derive an expression for the Laplace-Stieltjes transform for the time in the system in this model. Finally, we show how this priority scheme may lead to an improvement in the utilization of the server when customer decide whether or not to join.

A metaheuristic algorithm for project selection and scheduling with due windows and limited inventory capacity

Purpose – The purpose of this paper is to provide an effective solution for a complex planning problem encountered in heavy industry. The problem entails selecting a set of projects to produce from a larger set of solicited projects and simultaneously scheduling their production to maximize profit. Each project has a due window inside of which, if accepted, it must be shipped. Additionally, there is a limited inventory buffer where lots produced early are stored. Because scheduling affects which projects may be selected and vice-versa, this is a particularly difficult combinatorial optimization problem. Design/methodology/approach – The authors develop an algorithm based on the Metaheuristic for Randomized Priority Search (Meta-RaPS) as well as a greedy heuristic and an integer programming (IP) model. The authors then perform computational experiments on a large set of benchmark problems over a wide range of characteristics to compare the performance of each method in terms of solution quality and time required. Findings – The paper shows that this problem is very difficult to solve using IP, with even small instances unable to be solved optimally. The paper then shows that both proposed algorithms will in seconds often outperform IP by a large margin. Meta-RaPS is particularly robust, consistently producing the best or very near-best solutions. Practical implications – The Meta-RaPS algorithm developed enables companies facing this problem to achieve higher profits through improved decision making. Moreover, this algorithm is relatively easy to implement. Originality/value – This research provides an effective solution for a difficult combinatorial optimization problem encountered in heavy industry which has not been previously addressed in the literature.

Parametrized algorithms for random serial dictatorship

Voting and assignment are two of the most fundamental settings in social choice theory. For both settings, random serial dictatorship (RSD) is a well-known rule that satisfies anonymity, ex post efficiency, and strategyproofness. Recently, it was shown that computing the resulting probabilities is #P-complete both in the voting and assignment setting. In this paper, we present efficient parametrized algorithms to compute the RSD probabilities for parameters such as the number of agent types, alternatives, or objects. When the parameters are small, then the respective algorithms are considerably more efficient than the naive approach of going through all permutations of agents.