Random Priority Research Articles

Strategic manipulation of preferences in the rank minimization mechanism

We consider one-sided matching problems, where agents are allocated items based on stated preferences. Posing this as an assignment problem, the average rank of obtained matchings can be minimized using the rank minimization (RM) mechanism. RM matchings can have significantly better rank distributions than matchings obtained by mechanisms with random priority, such as Random Serial Dictatorship. However, these matchings are sensitive to preference manipulation from strategic agents. In this work we consider a scenario where agents aim to be matched to their top-n preferred items using the RM mechanism, and strategically manipulate their preferences to achieve this. We derive a best response strategy for an agent to be assigned to their n most preferred items using the Hungarian algorithm, under a simplified cost function. This strategy is then extended to a first-order heuristic strategy for being matched to the top-n items in a setup that minimizes the average rank. Based on this finding, an empirical study is conducted examining the impact of the first-order heuristic strategy. The study utilizes data from both simulated markets and real-world matching markets in Amsterdam, taking into account variations in item popularity, fractions of strategic agents, and the preferences for the n most favored items. For most scenarios, RM yields more rank efficient matches than Random Serial Dictatorship, even when agents apply the first-order heuristic strategy. However, although highly market dependent, the matching performance can become worse when 50% of agents or more want to be matched to their top-1 or top-2 preferred items and apply the first-order heuristic strategy to achieve this.

Fair integer programming under dichotomous and cardinal preferences

One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables represent agents with dichotomous preferences, who only care about whether they are selected in the final solution. We develop several general-purpose algorithms to fairly select optimal solutions, for example, by maximizing the Nash product or the minimum selection probability, or by using a random ordering of the agents as a selection criterion (Random Serial Dictatorship). We also discuss in detail how to extend the proposed methods when agents have cardinal preferences. As such, we embed the “black-box” procedure of solving an integer linear program into a framework that is explainable from start to finish. Lastly, we evaluate the proposed methods on two specific applications, namely kidney exchange (dichotomous preferences), and the scheduling problem of minimizing total tardiness on a single machine (cardinal preferences). We find that while the methods maximizing the Nash product or the minimum selection probability outperform the other methods on the evaluated welfare criteria, methods such as Random Serial Dictatorship perform reasonably well in computation times that are similar to those of finding a single optimal solution.

Maximizing Net Present Value for Resource Constraint Project Scheduling Problems with Payments at Event Occurrences Using Approximate Dynamic Programming

Resource Constraint Project Scheduling Problems with Discounted Cash Flows (RCPSPDC) focuses on maximizing the net present value by summing the discounted cash flows of project activities. An extension of this problem is the Payment at Event Occurrences (PEO) scheme, where the client makes multiple payments to the contractor upon completion of predefined activities, with additional final settlement at project completion. Numerous approximation methods such as metaheuristics have been proposed to solve this NP-hard problem. However, these methods suffer from parameter control and/or the computational cost of correcting infeasible solutions. Alternatively, approximate dynamic programming (ADP) sequentially generates a schedule based on strategies computed via Monte Carlo (MC) simulations. This saves the computations required for solution corrections, but its performance is highly dependent on its strategy. In this study, we propose the hybridization of ADP with three different metaheuristics to take advantage of their combined strengths, resulting in six different models. The Estimation of Distribution Algorithm (EDA) and Ant Colony Optimization (ACO) were used to recommend policies for ADP. A Discrete cCuckoo Search (DCS) further improved the schedules generated by ADP. Our experimental analysis performed on the j30, j60, and j90 datasets of PSPLIB has shown that ADP–DCS is better than ADP alone. Implementing the EDA and ACO as prioritization strategies for Monte Carlo simulations greatly improved the solutions with high statistical significance. In addition, models with the EDA showed better performance than those with ACO and random priority, especially when the number of events increased.

An Axiomatization of the Random Priority Rule

An Axiomatization of the Random Priority Rule

Fairness and efficiency of the random serial dictatorship on preference domains with a tier structure

In this note, we study the envy-freeness and ordinal efficiency of the random serial dictatorship (RSD) rule on preference domains with a tier structure. Specifically, we obtain that the RSD rule is envy-free on restricted tier preference domains. For the ordinal efficiency axiom, we show that the almost-singleton condition is not sufficient for the RSD rule to be ordinally efficient. For assignment problems on the restricted tier preference domains, we characterize the condition under which the RSD rule is ordinally efficient.

Inefficiency of Random Serial Dictatorship under incomplete information

We study the problem of allocating n objects to n agents without monetary transfers in a setting where each agent's preference over objects is private. We assume that each agent's value vector (values for n objects) is independently drawn from an exchangeable distribution and show that the celebrated Random Serial Dictatorship mechanism is welfare inferior to another allocation method, the Random Boston mechanism, when the number of agents and objects is large. Specifically, every type of every agent has a strictly higher interim expected utility under the Random Boston mechanism than under the Random Serial Dictatorship mechanism. Moreover, this strict dominance holds even at the limit.

On slots’ scheduling

Server works in discrete time, and is equipped with a given sequence of per-date capacities. It has to accommodate a set of agents with unit jobs, arriving at different dates. It can process a job in several installments, however no monetary transfers are allowed. Server is given jobs’ birth dates and it only knows that agents want their jobs done as soon as possible, but not agents’ complete preferences over delays (thus, this is the model with ordinal input). We investigate how scheduling rules, coming from both assignment and queueing literature, fare in this setting. The tension between fairness and incentive compatibility, inherent to the assignment models, disappears on this domain, as both Serial and Random Priority assignment rules become strategy-proof and non-envious. This is also true for Uniform rule; but First Come First Serve or First Come Last Serve rules are not strategy-proof and generate envy.

A planner-optimal matching mechanism and its incentive compatibility in a restricted domain

In many random assignment problems, the central planner pursues their own policy objective, such as matching size and minimum quota fulfillment. Several practically important policy objectives do not align with agents' preferences and are known to be incompatible with strategy-proofness. This paper demonstrates that such policy objectives can be attained using mechanisms that satisfy Bayesian incentive compatibility within a restricted domain of von Neumann Morgenstern utilities. We establish that a mechanism satisfies Bayesian incentive compatibility in an inverse-bounded-indifference domain if and only if the mechanism satisfies the three axioms of swap monotonicity, lower invariance, and interior upper variance. We apply this axiomatic characterization to analyze the incentive property of the constrained random serial dictatorship mechanism (CRSD). CRSD is designed to generate an individually rational assignment that optimizes the central planner's policy objective function. Since CRSD satisfies these axioms, it is Bayesian incentive compatible within an IBI domain.

Axiomatic characterizations of the constrained probabilistic serial mechanism

Afacan (Games and Economic Behavior 110: 71-89, 2018) introduces an object allocation with random priorities problem. He proposes the constrained probabilistic serial (CPS) mechanism. This study, for the first time in the literature, provides axiomatic characterizations of CPS. The first result characterizes it via non-wastefulness, claimwise stability, constrained ordinal fairness, and surplus invariance to truncations. The other axiomatizes CPS via constrained stochastic efficiency, claimwise stability, and constrained ordinal fairness. The independence of the axioms is provided.

Optimal queue to minimize waste

We study an application of stochastic games in the dynamic allocation of two types of goods when agents have deferral rights. If all individuals strictly prefer one good to the other, the worse good can be wasted by successive rejections. We allow different goods to be allocated in different ways and study the combinations of three popular disciplines in an overloaded waiting list: FCFS (first-come-first-serve), LCFS(last-come-first-serve) and RP(random-priority). The first result is that the LCFS–FCFS queue (the better good allocated under LCFS and the worse good allocated under FCFS) does result in zero waste, but it is unfair. To restore fairness, the agent’s age matters and the older agent has a weakly higher probability of receiving goods. Our second result is that RP–FCFS is fair and induces less expected waste than FCFS when the waiting cost is uniformly distributed.

Overflow management with self-eliminations

We study admission control with packet redundancy, where large data items, called superpackets, exceed some Maximum Transmission Unit (MTU) and therefore are broken into several smaller packets. It is assumed that each superpacket is comprised of k packets, and that a superpacket is considered useful if at least (1−β)k of its packets arrive at the receiving end, for some redundancy parameter β∈[0,1). Our goal is to maximize the total profit of useful superpackets, under an overloaded network, where we are forced to drop packets.Our starting point is an algorithm, called priority, which is based on assigning a random priority to each superpacket. This algorithm was shown to perform well when β=0, with and without a buffer. However, the performance of priority deteriorates with the increase of β, since it delivers too many packets for high priority superpackets. To tackle this issue, we propose an online algorithm which introduces randomized self-elimination of packets, called pse. When there is no buffer, we show that the competitive ratio of pse is better than the competitive ratio of priority, for the case where (1−β)3⋅ρmax≤1, where ρmax is the maximal burst size-router capacity ratio. For real-world values (ρmax≤1.5), pse outperforms priority for β≥0.14. We also present simulation results, with a buffer, that demonstrate the behavior of pse in comparison with priority and tail-drop. It is shown that pse performs much better than priority when β is large. In fact, it is shown that pse behaves at least as good as both algorithms.

REORDER++: Enhanced Randomized Real-Time Scheduling Strategy Against Side-Channel Attacks

Embedded real-time systems are widely adopted in safety-critical domains such as aircrafts, automobiles and space vehicles. Unfortunately, with the sharp rise in the use of common-off-the-shelf components in systems and the drive towards remote communication through untrusted networks, such as WiFi, radio or cellular, the security is increasingly becoming the key consideration in real-time system design. In particular, the real-time system is vulnerable to side-channel attacks from the external networks, which attempt to infer the timing of task execution by exploiting the system deterministic execution patterns. In this paper, we present an enhanced online randomized scheduling strategy (named <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathsf {REORDER}$</tex-math></inline-formula> ++), which breaks the deterministic task execution pattern of systems by random priority inversions at run-time to counteract the timing side-channel attacks in dynamic-priority real-time systems. In order to realize the feasible priority inversions under real-time constraint, we propose an online priority inversion test to increase the opportunity of tasks' priority inversions by judging the feasibility of tasks' priority inversions at run-time. Owing to such online priority inversion test, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathsf {REORDER}$</tex-math></inline-formula> ++ can generate highly randomized schedule of real-time tasks to mitigate the side-channel attack vulnerability. Experiments with synthesized task sets show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathsf {REORDER}$</tex-math></inline-formula> ++ significantly outperforms the existing approaches in terms of schedule randomness.

Multi resource allocation with partial preferences

We provide efficient, fair, and non-manipulable mechanisms for the multi-type resource allocation problems (MTRAs) and multiple assignment problems where agents have partial preferences over bundles consisting of multiple divisible items. We uncover a natural reduction from multiple assignment problems to MTRAs, which preserves the properties of MTRA mechanisms. We extend the well-known random priority (RP) and probabilistic serial (PS) mechanisms to MTRAs with partial preferences as multi-type PS (MPS) and multi-type RP (MRP) and propose a new mechanism, multi-type general dictatorship (MGD), which combines the ideas of MPS and MRP. We show that for the unrestricted domain of partial order preferences, unfortunately, no mechanism satisfies both sd-efficiency and sd-envy-freeness, even as they each satisfy different weaker notions of the desirable properties of efficiency, fairness, and non-manipulability we consider. Notwithstanding this impossibility result, our main message is positive: When agents' preferences are represented by acyclic CP-nets, MRP satisfies ex-post-efficiency, sd-strategyproofness, and upper invariance, while MPS satisfies sd-efficiency, sd-envy-freeness, ordinal fairness, and upper invariance, recovering the properties of RP and PS; the MGD satisfies sd-efficiency, equal treatment of equals, and decomposability under the unrestricted domain of partial preferences. We introduce a natural domain of bundle net preferences, which generalizes previously studied domain restrictions of partial preferences for multiple assignment problems and is incomparable to the domain of acyclic CP-nets. We show that MRP and MPS satisfy all properties of the RP and PS under bundle net preferences as well.

An Aspects Framework for Component-Based Requirements Prediction and Regression Testing

Component-based software development has become more popular in recent decades. Currently, component delivery only includes interface specifications, which complicates the selection and integration of suitable components to build a new system. The majority of the components are reused, after appropriate modifications in accordance with the new system, or new version of the system. After components integration, errors may occur during the interaction of their features due to incomplete, ambiguous, or mismatched terms used in requirement analysis and specification, affecting component validation. Therefore, there is a need for a study that identifies challenges and covert concepts into practice by providing solutions to these challenges. The objective of this study is to identify some attributes and information sources that are essential during component-based development. The proposed framework is based on these attributes and information sources. In this study, we provide a taxonomy of attributes and information sources among different activities of component development, and propose a framework to improve the component development process. To investigate the proposed framework, we performed an experimental study to get real-world scenario results from industrial practitioners. The results showed that the proposed framework improves the process of component specification and validation without ambiguity and component failures. Additionally, compared with other methods (random priority, clustering-based and execution rate), the proposed framework successfully outperforms other methods. As a result, the proposed framework’s accuracy, F-measures, and fault identification rate were higher (i.e., greater than 80%) than those of other methods (i.e., less than 80%). The proposed framework will provide a significant guideline for practitioners and researchers.

Truthful facility assignment with resource augmentation: an exact analysis of serial dictatorship

We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space have to be assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their most-preferred points. We propose a resource augmentation framework, where a truthful mechanism is evaluated by its worst-case performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Among other results, we prove that Serial Dictatorship has approximation ratio g/(g-2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g/(g-2)$$\\end{document} when the capacities are multiplied by any integer g≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g \\ge 3$$\\end{document}. Our results suggest that with a limited augmentation of the resources we can achieve exponential improvements on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation.

Expectations-Based Loss Aversion May Help Explain Seemingly Dominated Choices in Strategy-Proof Mechanisms

Deferred acceptance (DA), a widely implemented algorithm, is meant to improve allocations: under classical preferences, it induces preference-concordant rankings. However, recent evidence shows that—in both real, large-stakes applications and experiments—participants frequently play seemingly dominated, significantly costly strategies that avoid small chances of good outcomes. We show theoretically why, with expectations-based loss aversion, this behavior may be partly intentional. Reanalyzing existing experimental data on random serial dictatorship (a restriction of DA), we show that such reference-dependent preferences, with a degree and distribution of loss aversion that explain common levels of risk aversion elsewhere, fit the data better than no-loss-aversion preferences. (JEL D11, D82, D91)

An improved procedure for colouring graphs of bounded local density

The chromatic number of graphs of maximum degree $\Delta$ has been studied extensively. A greedy coloring procedure shows that any graph has a proper coloring with $\Delta+1$ colors, and this is sharp, as shown by the complete graph of $\Delta+1$ vertices. However, this simple upper bound can often be improved significantly if one excludes some configurations locally or globally. For instance, it is known that triangle-free graphs have much smaller chromatic number, namely $O(\Delta/\log \Delta)$ (Johansson 1996). Consider a vertex $v$, and count the number of edges among its (at most $\Delta$) neighbors. This number is clearly at most ${\Delta \choose 2}$, and it is $0$ if the graph is triangle-free. We say that the graph is $\sigma$-sparse if for each vertex $v$, this number of edges is at most $(1-\sigma){\Delta \choose 2}$. Molloy and Reed proved that $\sigma$-sparse graphs, for $\sigma>0$, can be colored with $(1-\epsilon)\Delta$ colors, for some $\epsilon>0$ depending only on $\sigma$, by a simple randomized procedure: 1. color all the vertices with random colors, 2. uncolor vertices which have received the same color as some of their neighbors, and 3. color the uncolored vertices deterministically (since they have a specific structure, with high probability). This result is a crucial ingredient in a general approach consisting in dividing graphs into $\sigma$-sparse components on one side, and much denser components on the other side, that are colored using different techniques (dense components would typically be colored deterministically, or with random permutations of colors, rather than with random colors). This powerful approach, pioneered by Molloy and Reed, has been rediscovered recently in the field of distributed computing. Moreover, $\sigma$-sparse graphs appear the context of some longstanding open problems in graph coloring. One is a fascinating conjecture of Reed, which asserts that every graph with maximum degree $\Delta$ and clique number $\omega$ admits a proper coloring with at most $\lceil (\Delta+\omega+1)/2 \rceil$ colors. Another is a classic conjecture of Erdős and Nešetřil, which states that the edges of a graph of maximum degree $\Delta$ can be colored with $1.25\Delta^2$ colors in such a way that each color class forms a matching as an induced subgraph. This latter problem can be understood in terms of the chromatic number of squares of line graphs, and such graphs turn out to be $\sigma$-sparse, for a surprising large value of $\sigma$. The authors of the present paper obtain an improved bound on the chromatic number of $\sigma$-sparse graphs, which yields state-of-the-art progress on Reed's conjecture and the Erdős-Nešetřil conjecture. They achieve this through the implementation and analysis of a "random priority assignment" uncoloring procedure in Step 2 above, which allows for a more efficient iteration of Steps 1 and 2 in a semirandom coloring procedure. In this way, they not only improve on previous bounds, but also obtain a bound with a leading term that is asymptotically optimal as $\sigma \to 0$.

Sequential Blocked Matching

We consider a sequential blocked matching (SBM) model where strategic agents repeatedly report ordinal preferences over a set of services to a central planner. The planner's goal is to elicit agents' true preferences and design a policy that matches services to agents in order to maximize the expected social welfare with the added constraint that each matched service can be blocked or unavailable for a number of time periods. Naturally, SBM models the repeated allocation of reusable services to a set of agents where each allocated service becomes unavailable for a fixed duration. We first consider the offline SBM setting, where the strategic agents are aware of their true preferences. We measure the performance of any policy by distortion, the worst-case multiplicative approximation guaranteed by any policy. For the setting with s services, we establish lower bounds of Ω(s) and Ω(√s) on the distortions of any deterministic and randomised mechanisms, respectively. We complement these results by providing approximately truthful, measured by incentive ratio, deterministic and randomised policies based on random serial dictatorship which match our lower bounds. Our results show that there is a significant improvement if one considers the class of randomised policies. Finally, we consider the online SBM setting with bandit feedback where each agent is initially unaware of her true preferences, and the planner must facilitate each agent in the learning of their preferences through the matching of services over time. We design an approximately truthful mechanism based on the explore-then-commit paradigm, which achieves logarithmic dynamic approximate regret.

Beyond the worst-case analysis of random priority: Smoothed and average-case approximation ratios in mechanism design

A mechanism for the random assignment problem takes agents' private preferences over items as input and outputs an allocation. One of the mainstream mechanisms, Random Priority, is asymptotically the best mechanism for welfare maximization. However, its approximation ratio is Θ(n), which implies that there is a large discrepancy between its performance and the optimal social welfare. We evaluate the performance of Random Priority beyond the worst-case analysis in the hope of addressing the inconsistency between the widespread use of the mechanism in practice and the undesired theoretical performance guarantee. We show that with small random noise applied to the worst-case inputs, Random Priority has a constant smoothed approximation ratio. When agents' preference values are independent random variables, Random Priority is nearly optimal evaluated by the average-case approximation ratio. En route to these results, we develop analytics tools to show the insights that the efficiency loss is small on most instances. To our limited knowledge, this is the first work that introduces smoothed analysis to algorithmic mechanism design problems. These results may pave the way for further studies for approximate mechanism design problems beyond the worst-case analysis.

Random Serial Dictatorship for horizontal collaboration in logistics

In this paper, we propose the application of matching mechanisms to handle horizontal collaboration in logistics. Based on the requirements of a real-life setting, we introduce a new variation of matching under preferences. We provide a Random Serial Dictatorship (RSD) mechanism for finding a solution that incorporates Pareto optimality, incentive compatibility and fairness, which are desired properties for enabling collaboration between antagonistic participants. Further, we present an extensive experimental analysis that is twofold. We compare the proposed RSD mechanism to two well-known matching mechanisms, namely Maximising Cardinal Utilities (MAXCU) and Bundled Probabilistic Serial (BPS). We compare these mechanisms with respect to cardinal efficiency and envy, and highlight the complementarity between them for handling different settings. Most importantly, we show that RSD is the most appropriate choice for settings similar to the one motivating our study. Moreover, we examine the effect of randomisation of RSD to fairness. Finally, we discuss how our matching mechanism was applied in the real-life context of four 3rd Party Logistics providers. Results show that the proposed approach creates significant potential for synergies and may be used to support horizontal collaboration in logistics.