The over-the-counter (OTC) government bond markets are characterised by their bilateral trading structures, which pose unique challenges to understanding and ensuring market stability and liquidity. In this paper, we develop a bespoke ABM that simulates market-maker interactions within a stylised government bond market. The model focuses on the dynamics of liquidity and stability in the secondary trading of government bonds, particularly in concentrated markets like those found in Australia and the UK. Through this simulation, we test key hypotheses around improving market stability, focusing on the effects of agent diversity, business costs, and client base size. We demonstrate that greater agent diversity enhances market liquidity and that reducing the costs of market-making can improve overall market stability. The model offers insights into computational finance by simulating trading without price transparency, highlighting how micro-structural elements can affect macro-level market outcomes. This research contributes to the evolving field of computational finance by employing computational intelligence techniques to better understand the fundamental mechanics of government bond markets, providing actionable insights for both academics and practitioners.

We present a novel solution for multimodal pathfinding in cities, which enables scenarios involving unlimited transfers at customized transfer speeds, requiring minimal preprocessing and storage efforts. We show that in this problem, classical variations of the TD-Dijkstra algorithm have better performance in terms of query runtime and memory usage than state-of-the-art algorithms, such as Connection Scan Algorithm [1] or Round-Based Public Transit Routing [2], since these do not require computing the transitive closure of the transfer graph. By incorporating techniques widely used in the field of computational geometry, we outperform the classical TD-Dijkstra approach, which saves all departure times for a node in a Balanced Search Tree (BST) structure [3]. We generalize the approach of storing departure times for each node and call it Timetable Nodes (TTN) [4], proposing two new versions of it: one using a Combined Search Tree (TTN-CST) and the other employing Fractional Cascading [5] (TTN-FC). Both modifications require minimal preprocessing efforts to store information about the public transport schedule, enabling them to function potentially on mobile devices and perform better than BST. We show theoretical and practical benefits of the TTN-FC over other approaches. TTN-FC accelerates pathfinding and reduces memory usage by a factor of$k$compared to TTN-CST and TTN-BST, where$k$is the number of outgoing edges from a node.

We introduce and analyze distance preservation games (DPGs). In DPGs, agents express ideal distances to other agents and need to choose locations in the unit interval while preserving their ideal distances as closely as possible. We analyze the existence and computation of location profiles that are jump stable (i.e., no agent can benefit by moving to another location) or welfare optimal for DPGs, respectively. Specifically, we prove that there are DPGs without jump stable location profiles and identify important cases where such outcomes always exist and can be computed efficiently. Similarly, we show that finding welfare optimal location profiles is NP-complete and present approximation algorithms for finding solutions with social welfare close to optimal. Finally, we prove that DPGs have a price of anarchy of at most 2.

We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both deterministic and randomized mechanisms approximate this. In addition, as Nash welfare is often put forwards as an equitable compromise between egalitarain and utilitarian outcomes, we consider how well mechanisms approximate the Nash welfare.

In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend---the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.

The fair allocation of resources to agents is a fundamental problem in society and has received significant attention and rapid developments from the game theory and artificial intelligence communities in recent years. The majority of the fair division literature can be divided along at least two orthogonal directions: goods versus chores, and divisible versus indivisible resources. In this survey, besides describing the state of the art, we outline a number of interesting open questions in three mixed fair division settings: (i) indivisible goods and chores, (ii) divisible and indivisible goods (i.e., mixed goods), and (iii) fair division of indivisible goods with subsidy.

Machine learning models have been instrumental in making decisions across domains, like mortgage lending and risk assessment in finance. However, these models have been found susceptible to biases, causing unfair decisions for a specific group of individuals. Such bias is generally based on some protected (or sensitive) attributes, such as age, sex, or race, and is still prevalent due to historical context or algorithmic bias. There have been several efforts to ensure equal opportunities for each individual/group, based on creditworthiness, rather than any social bias. Several pre-, in- and post-processing bias mitigation techniques have been proposed. However, these techniques perform data transformation or design new constraint/cost functions, which are task-specific, to achieve a fair prediction. Such techniques even require further access to the complete training/testing data. This paper proposes a novel post-processing bias mitigation technique that employs a model interpretation strategy to find the responsible model weights causing the bias. Pruning only a few model weights exhibits group fairness in model predictions while maintaining competitive accuracy levels, thus aligning with the goals of fairness and efficiency in decision-making. The proposed scheme requires access to only a few data samples representing the protected attributes, without exposing the complete training data. Through extensive experiments with multiple census datasets/methods, we demonstrate the efficacy of our approach, achieving up to a significant 50% reduction in bias while preserving the overall accuracy.

We identify strategy proof mechanisms for facility location that simultaneously approximate well both the maximum distance from the nearest facility and the minimum utility of any agent. Somewhat surprisingly, while the deterministic MEDIAN and the randomized ENDORAV mechanisms perform optimally with respect to approximating the maximum distance, neither perform optimally with respect to approximating the minimum utility. With deterministic mechanisms for locating a single facility, we prove that the MIDORNEAREST mechanism is optimal with respect to approximating both the maximum distance and the minimum utility. By comparison, the MEDIAN mechanism has an unbounded approximation ratio for approximating the minimum utility. With randomized mechanisms for locating a single facility, we construct the first mechanism that is optimal with respect to approximating the minimum utility. For deterministic and randomized mechanisms locating two or more facilities, we identify strategy proof mechanisms that are within a constant factor of optimal with respect to both objectives.

ChatGPT burst into people's lives at the end of 2022, heralding the arrival of large language models in particular, and generative AI in general. How best to see this moment in the development of AI. What is generative AI actually good for? And what are its limitations? And how might we tackle them? In this talk, I'll explore how to understand recent breakthroughs in AI, and discuss what might come next.

In peer mechanisms, the competitors for a prize also determine who wins. Each competitor may be asked to rank, grade, or nominate peers for the prize. Since the prize can be valuable, such as financial aid, course grades, or an award at a conference, competitors may be tempted to manipulate the mechanism. We survey approaches to prevent or discourage the manipulation of peer mechanisms. We conclude our survey by identifying several important research challenges.

Fair division considers the allocation of scarce resources among agents in such a way that every agent gets a fair share. It is a fundamental problem in society and has received significant attention and rapid developments from the game theory and artificial intelligence communities in recent years. The majority of the fair division literature can be divided along at least two orthogonal directions: goods versus chores, and divisible versus indivisible resources. In this survey, besides describing the state of the art, we outline a number of interesting open questions and future directions in three mixed fair division settings: (i) indivisible goods and chores, (ii) divisible and indivisible goods (mixed goods), and (iii) indivisible goods with subsidy which can be viewed like a divisible good.

We study a fair allocation problem of indivisible items under additive externalities in which each agent also receives utility from items that are assigned to other agents. This allows us to capture scenarios in which agents benefit from or compete against one another. We extend the well-studied properties of envy-freeness up to one item (EF1) and envy-freeness up to any item (EFX) to this setting, and we propose a new fairness concept called general fair share (GFS), which applies to a more general public decision making model. We undertake a detailed study and present algorithms for finding fair allocations.

An important feature of many real world facility location problems are capacity limits on the number of agents served by each facility. We provide a comprehensive picture of strategy proof mechanisms for facility location problems with capacity constraints that are anonymous and Pareto optimal. First, we prove a strong characterization theorem. For locating two identical facilities with capacity limits and no spare capacity, the INNERPOINT mechanism is the unique strategy proof mechanism that is both anonymous and Pareto optimal. Second, when there is spare capacity, we identify a more general class of strategy proof mechanisms that interpolates smoothly between INNERPOINT and ENDPOINT which are anonymous and Pareto optimal. Third, with two facilities of different capacities, we prove a strong impossibility theorem that no mechanism can be both anonymous and Pareto optimal except when the capacities differ by just a single agent. Fourth, with three or more facilities we prove a second impossibility theorem that no mechanism can be both anonymous and Pareto optimal even when facilities have equal capacity. Our characterization and impossibility results are all minimal as multiple mechanisms exist if we drop one property.

Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice. In our work, we propose a concept called Strong Proportionality, which ensures that when there are two groups of agents at different locations, both groups incur the same total cost. We show that although Strong Proportionality is a well-motivated and basic axiom, there is no deterministic strategyproof mechanism satisfying the property. We then identify a randomized mechanism called Random Rank (which uniformly selects a number $k$ between $1$ to $n$ and locates the facility at the $k$'th highest agent location) which satisfies Strong Proportionality in expectation. Our main theorem characterizes Random Rank as the unique mechanism that achieves universal truthfulness, universal anonymity, and Strong Proportionality in expectation among all randomized mechanisms. Finally, we show via the AverageOrRandomRank mechanism that even stronger ex-post fairness guarantees can be achieved by weakening universal truthfulness to strategyproofness in expectation.

We consider the problem of fairly dividing a set of indivisible items. Much of the fair division literature assumes that the items are “goods” that yield positive utility for the agents. There is also some work in which the items are “chores” that yield negative utility for the agents. In this paper, we consider a more general scenario in which an agent may have positive or negative utility for each item. This framework captures, e.g., fair task assignment, where agents can experience both positive and negative utility for each task. We demonstrate that whereas some of the positive axiomatic and computational results extend to this more general setting, others do not. We present several new and efficient algorithms for finding fair allocations in this general setting. We also point out several gaps in the literature regarding the existence of allocations that satisfy certain fairness and efficiency properties and examine the complexity of computing such allocations.

We study the pairwise organ exchange problem among groups motivated by real-world applications and consider two types of group formulations. Each group represents either a certain type of patient-donor pairs who are compatible with the same set of organs, or a set of patient-donor pairs who reside in the same region. We address a natural research question, which asks how to match a maximum number of pairwise compatible patient-donor pairs in a fair and individually rational way. We first propose a natural fairness concept that is applicable to both types of group formulations and design a polynomial-time algorithm that checks whether a matching exists that satisfies optimality, individual rationality, and fairness. We also present several running time upper bounds for computing such matchings for different graph structures.

We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the corresponding optimization problem, where the goal is to locate facilities to minimize either the total cost to all agents or the maximum cost of any agent is NP-hard. However, we show that the problem is fixed-parameter tractable, and the optimal solution can be computed in polynomial time whenever the number of facilities is bounded, or when all facilities have identical capacities. We then consider the problem from a mechanism design perspective where the agents are strategic and need not reveal their true locations. We show that several natural mechanisms studied in the uncapacitated setting either lose strategyproofness or a bound on the solution quality %on the returned solution for the total or maximum cost objective. We then propose new mechanisms that are strategyproof and achieve approximation guarantees that almost match the lower bounds.

We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems. We identify wide variety of such online fair division problems, as well as discuss new mechanisms and normative properties that apply to this online setting. The online nature of such fair division problems provides both opportunities and challenges such as the possibility to develop new online mechanisms as well as the difficulty of dealing with an uncertain future.

I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items. I discuss how a computational perspective has provided interesting insights into and understanding of how to divide items fairly and efficiently. This has involved bringing to bear tools such as those used in knowledge representation, computational complexity, approximation methods, game theory, online analysis and communication complexity.

We consider the problem of fairly dividing a set of items. Much of the fair division literature assumes that the items are ``goods'' i.e., they yield positive utility for the agents. There is also some work where the items are ``chores'' that yield negative utility for the agents. In this paper, we consider a more general scenario where an agent may have negative or positive utility for each item. This framework captures, e.g., fair task assignment, where agents can have both positive and negative utilities for each task. We show that whereas some of the positive axiomatic and computational results extend to this more general setting, others do not. We present several new and efficient algorithms for finding fair allocations in this general setting. We also point out several gaps in the literature regarding the existence of allocations satisfying certain fairness and efficiency properties and further study the complexity of computing such allocations.

We consider mechanisms for the online allocation of perishable resources such as energy or computational power. A main application is electric vehicle charging where agents arrive and leave over time. Unlike previous work, we consider mechanisms without money, and a range of objectives including fairness and efficiency. In doing so, we extend the concept of envy-freeness to online settings. Furthermore, we explore the trade-offs between different objectives and analyse their theoretical properties both in online and offline settings. We then introduce novel online scheduling algorithms and compare them in terms of both their theoretical properties and empirical performance.

We propose a novel mechanism for solving the assignment problem when we have a two sided matching problem with preferences from one side (the agents/reviewers) over the other side (the objects/papers) and both sides have capacity constraints. The assignment problem is a fundamental in both computer science and economics with application in many areas including task and resource allocation. Drawing inspiration from work in multi-criteria decision making and social choice theory we use order weighted averages (OWAs), a parameterized class of mean aggregators, to propose a novel and flexible class of algorithms for the assignment problem. We show an algorithm for finding an SUM-OWA assignment in polynomial time, in contrast to the NP-hardness of finding an egalitarian assignment. We demonstrate through empirical experiments that using SUM-OWA assignments can lead to high quality and more fair assignments.

Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks, Binarized Neural Networks, using the well-developed means of Boolean satisfiability. Our main contribution is a construction that creates a representation of a binarized neural network as a Boolean formula. Our encoding is the first exact Boolean representation of a deep neural network. Using this encoding, we leverage the power of modern SAT solvers along with a proposed counterexample-guided search procedure to verify various properties of these networks. A particular focus will be on the critical property of robustness to adversarial perturbations. For this property, our experimental results demonstrate that our approach scales to medium-size deep neural networks used in image classification tasks. To the best of our knowledge, this is the first work on verifying properties of deep neural networks using an exact Boolean encoding of the network.

As algorithms are given responsibility to make decisions that impact our lives, there is increasing awareness of the need to ensure the fairness of these decisions. One of the first challenges then is to decide what fairness means in a particular context. We consider here fairness in deciding how to match organs donated by deceased donors to patients. Due to the increasing age of patients on the waiting list, and of organs being donated, the current "first come, first served'' mechanism used in Australia is under review to take account of age of patients and of organs. We consider how to revise the mechanism to take account of age fairly. We identify a number of different types of fairness, such as to patients, to regions and to blood types and consider how they can be achieved.

We consider Max-min Share (MmS) fair allocations of indivisible chores (items with negative utilities). We show that allocation of chores and classical allocation of goods (items with positive utilities) have some fundamental connections but also differences which prevent a straightforward application of algorithms for goods in the chores setting and vice-versa. We prove that an MmS allocation does not need to exist for chores and computing an MmS allocation - if it exists - is strongly NP-hard. In view of these non-existence and complexity results, we present a polynomial-time 2-approximation algorithm for MmS fairness for chores. We then introduce a new fairness concept called optimal MmS that represents the best possible allocation in terms of MmS that is guaranteed to exist. We use connections to parallel machine scheduling to give (1) a polynomial-time approximation scheme for computing an optimal MmS allocation when the number of agents is fixed and (2) an effective and efficient heuristic with an ex-post worst-case analysis.

We consider a fair division setting in which items arrive one by one and are allocated to agents via two existing mechanisms: LIKE and BALANCED LIKE. The LIKE mechanism is strategy-proof whereas the BALANCED LIKE mechanism is not. Whilst LIKE is strategy-proof, we show that it is not group strategy-proof. Indeed, our first main result is that no online mechanism is group strategy-proof. We then focus on pure Nash equilibria of these two mechanisms. Our second main result is that computing a pure Nash equilibrium is tractable for LIKE and intractable for BALANCED LIKE. Our third main result is that there could be multiple such profiles and counting them is also intractable even when we restrict our attention to equilibria with a specific property (e.g. envy-freeness, Pareto efficiency).

Matching donations from deceased patients to patients on the waiting list account for over 85\% of all kidney transplants performed in Australia. We propose a simple mechanisms to perform this matching and compare this new mechanism with the more complex algorithm currently under consideration by the Organ and Tissue Authority in Australia. We perform a number of experiments using real world data provided by the Organ and Tissue Authority of Australia. We find that our simple mechanism is more efficient and fairer in practice compared to the other mechanism currently under consideration.

We study computational problems for two popular parliamentary voting procedures: the amendment procedure and the successive procedure. They work in multiple stages where the result of each stage may influence the result of the next stage. Both procedures proceed according to a given linear order of the alternatives, an agenda. We obtain the following results for both voting procedures: On the one hand, deciding whether one can make a specific alternative win by reporting insincere preferences by the fewest number of voters, the Manipulation problem, or whether there is a suitable ordering of the agenda, the Agenda Control problem, takes polynomial time. On the other hand, our experimental studies with real-world data indicate that most preference profiles cannot be manipulated by only few voters and a successful agenda control is typically impossible. If the voters' preferences are incomplete, then deciding whether an alternative can possibly win is NP-hard for both procedures. Whilst deciding whether an alternative necessarily wins is coNP-hard for the amendment procedure, it is polynomial-time solvable for the successive procedure.

We study an important crowdsourcing setting where agents evaluate one another and, based on these evaluations, a subset of agents are selected. This setting is ubiquitous when peer review is used for distributing awards in a team, allocating funding to scientists, and selecting publications for conferences. The fundamental challenge when applying crowdsourcing in these settings is that agents may misreport their reviews of others to increase their chances of being selected. We propose a new strategyproof (impartial) mechanism called Dollar Partition that satisfies desirable axiomatic properties. We then show, using a detailed experiment with parameter values derived from target real world domains, that our mechanism performs better on average, and in the worst case, than other strategyproof mechanisms in the literature.

We survey some recent research regarding strategic behaviour in resource allocation problems, focusing on the fair division of indivisible goods. We consider a number of computational questions like how a single strategic agent misreports their preferences to ensure a particular outcome, and how agents compute a Nash equilibrium when they all act strategically. We also identify a number of future directions like dealing with non-additive utilities, and partial or probabilistic information about the preferences of other agents.

Sequential allocation is a simple and attractive mechanism for the allocation of indivisible goods used in a number of real world settings. In sequential allocation, agents pick items according to a policy, the order in which agents take turns. Sequential allocation will return an allocation which is Pareto efficient – no agent can do better without others doing worse. However, sequential allocation may not return the outcome that optimizes the social welfare. We consider therefore the relationship between the welfare and the efficiency of the allocations returned by sequential allocation mechanisms. We then study some simple computational questions about what welfare is possible or necessary depending on the choice of policy. Over half the problems we study turn out to be tractable, and we give polynomial time algorithms to compute them. We also consider a novel control problem in which the Chair chooses a policy to improve social welfare. Again, many of the control problems we study turn out to be tractable, and our results give polynomial time algorithms. In this case, tractability is a good thing so that the Chair can improve the social welfare of the allocation.

The h-index is an important bibliographic measure used to assess the performance of researchers. Van Bevern et al. [Artif. Intel., to appear] showed that, despite computational worst-case hardness results, substantial manipulation of the h-index of Google Scholar author profiles is possible by merging articles. Complementing this work, we study the opposite operation, the splitting of articles, which is arguably the more natural operation for manipulation and which is also allowed within Google Scholar. We present numerous results on computational complexity (from linear-time algorithms to parameterized computational hardness results) and empirically indicate that at least small improvements of the h-index by splitting merged articles are easily achievable.

We survey existing rules of thumb, propose novel methods, and comprehensively evaluate a number of solutions to the problem of calculating the cost to serve each location in a single-vehicle transport setting. Cost to serve analysis has applications both strategically and operationally in transportation settings. The problem is formally modeled as the traveling salesperson game (TSG), a cooperative transferable utility game in which agents correspond to locations in a traveling salesperson problem (TSP). The total cost to serve all locations in the TSP is the length of an optimal tour. An allocation divides the total cost among individual locations, thus providing the cost to serve each of them. As one of the most important normative division schemes in cooperative games, the Shapley value gives a principled and fair allocation for a broad variety of games including the TSG. We consider a number of direct and sampling-based procedures for calculating the Shapley value, and prove that approximating the Shapley value of the TSG within a constant factor is NP-hard. Treating the Shapley value as an ideal baseline allocation, we survey six proxies for it that are each relatively easy to compute. Some of these proxies are rules of thumb and some are procedures international delivery companies use(d) as cost allocation methods. We perform an experimental evaluation using synthetic Euclidean games as well as games derived from real-world tours calculated for scenarios involving fast-moving goods; where deliveries are made on a road network every day. We explore several computationally tractable allocation techniques that are good proxies for the Shapley value in problem instances of a size and complexity that is commercially relevant.

We consider approval-based committee voting, i.e., the setting where each voter approves a subset of candidates, and these votes are then used to select a fixed-size set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (JR). This axiom requires that if a large enough group of voters exhibits agree- ment by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee. We show that for every list of ballots it is possible to select a committee that provides JR. We then check if this axiom is fulfilled by well-known approval-based voting rules. We show that the answer is negative for most of the rules we consider, with notable exceptions of PAV (Proportional Approval Voting), an extreme version of RAV (Reweighted Approval Voting), and, for a restricted preference domain, MAV (Minimax Approval Voting). We then introduce a stronger version of the JR axiom, which we call extended justified representation (EJR), and show that PAV satisfies EJR, while other rules do not. We also consider several other questions related to JR and EJR, including the relationship between JR/EJR and unanimity, and the complexity of the associated algorithmic problems.

Many models and mechanisms in resource and cost allocation have been developed that are simple and abstract. By means of two case studies, I argue that it is now timely to consider richer models for the fair division of resources and for the allocation of costs. Such models should have features like asynchronicity which reflect more of the true complexity of many fair division and cost allocation problems met in the real world. I suggest that computation can be used in such models to increase both efficiency and fairness of the allocations. As a result, we may be able to do more with fewer resources and greater fairness.

Balanced knockout tournaments are one of the most common formats for sports competitions, and are also used in elections and decision-making. We consider the computational problem of finding the optimal draw for a particular player in such a tournament. The problem has generated considerable research within AI in recent years. We prove that checking whether there exists a draw in which a player wins is NP-complete, thereby settling an outstanding open problem. Our main result has a number of interesting implications on related counting and approximation problems. We present a memoization-based algorithm for the problem that is faster than previous approaches. Moreover, we highlight two natural cases that can be solved in polynomial time. All of our results also hold for the more general problem of counting the number of draws in which a given player is the winner.

We study the computational complexity of controlling the result of an election by breaking ties strategically. This problem is equivalent to the problem of deciding the winner of an election under parallel universes tie-breaking. When the chair of the election is only asked to break ties to choose between one of the co-winners, the problem is trivially easy. However, in multi-round elections, we prove that it can be NP-hard for the chair to compute how to break ties to ensure a given result. Additionally, we show that the form of the tie-breaking function can increase the opportunities for control.

In many real world elections, agents are not required to rank all candidates. We study three of the most common methods used to modify voting rules to deal with such partial votes. These methods modify scoring rules (like the Borda count), elimination style rules (like single transferable vote) and rules based on the tournament graph (like Copeland) respectively. We argue that with an elimination style voting rule like single transferable vote, partial voting does not change the situations where strategic voting is possible. However, with scoring rules and rules based on the tournament graph, partial voting can increase the situations where strategic voting is possible. As a consequence, the computational complexity of computing a strategic vote can change. For example, with Borda count, the complexity of computing a strategic vote can decrease or stay the same depending on how we score partial votes.

We propose the PeerRank method for peer assessment. This constructs a grade for an agent based on the grades proposed by the agents evaluating the agent. Since the grade of an agent is a measure of their ability to grade correctly, the PeerRank method weights grades by the grades of the grading agent. The PeerRank method also provides an incentive for agents to grade correctly. As the grades of an agent depend on the grades of the grading agents, and as these grades themselves depend on the grades of other agents, we define the PeerRank method by a fixed point equation similar to the PageRank method for ranking web-pages. We identify some formal properties of the PeerRank method (for example, it satisfies axioms of unanimity, no dummy, no discrimination and symmetry), discuss some examples, compare with related work and evaluate the performance on some synthetic data. Our results show considerable promise, reducing the error in grade predictions by a factor of 2 or more in many cases over the natural baseline of averaging peer grades.

We study the impact on strategic voting of tie-breaking by means of considering the order of tied candidates within a random vote. We compare this to another non deterministic tie-breaking rule where we simply choose candidate uniformly at random. In general, we demonstrate that there is no connection between the computational complexity of computing a manipulating vote with the two different types of tie-breaking. However, we prove that for some scoring rules, the computational complexity of computing a manipulation can increase from polynomial to NP-hard. We also discuss the relationship with the computational complexity of computing a manipulating vote when we ask for a candidate to be the unique winner, or to be among the set of co-winners.

We study a simple sequential allocation mechanism for allocating indivisible goods between agents in which agents take turns to pick items.We focus on agents behaving strategically. We view the allocation procedure as a finite repeated game with perfect information. We show that with just two agents, we can compute the unique subgame perfect Nash equilibrium in linear time. With more agents, computing the subgame perfect Nash equilibria is more difficult. There can be an exponential number of equilibria and computing even one of them is PSPACE-hard. We identify a special case, when agents value many of the items identically, where we can efficiently compute the subgame perfect Nash equilibria. We also consider the effect of externalities and modifications to the mechanism that make it strategy proof.

Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting rules used in practice, the computational complexity increases. For example, it is already known that it is NP-hard to compute how a single voter can manipulate the result of single transferable voting (the elimination version of plurality voting). We show here that it is NP-hard to compute how a single voter can manipulate the result of the elimination version of veto voting, of the closely related Coombs’ rule, and of the elimination versions of a general class of scoring rules.

Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful cases: symmetry breaking constraints for row and column symmetry, and symmetry breaking constraints for eliminating value symmetry.

We study the computational complexity of finding the next most preferred solution in some common formalisms for representing constraints and preferences. The problem is computationally intractable for CSPs, but is polynomial for tree-shaped CSPs and tree-shaped fuzzy CSPs. On the other hand, it is intractable for weighted CSPs, even under restrictions on the constraint graph. For CP-nets, the problem is polynomial when the CP-net is acyclic. This remains so if we add (soft) constraints that are tree-shaped and topologically compatible with the CP-net.

We consider manipulation problems when the manipulator only has partial information about the votes of the non-manipulators. Such partial information is described by an {\em information set}, which is the set of profiles of the non-manipulators that are indistinguishable to the manipulator. Given such an information set, a {\em dominating manipulation} is a non-truthful vote that the manipulator can cast which makes the winner at least as preferable (and sometimes more preferable) as the winner when the manipulator votes truthfully. When the manipulator has full information, computing whether or not there exists a dominating manipulation is in P for many common voting rules (by known results). We show that when the manipulator has no information, there is no dominating manipulation for many common voting rules. When the manipulator's information is represented by partial orders and only a small portion of the preferences are unknown, computing a dominating manipulation is NP-hard for many common voting rules. Our results thus throw light on whether we can prevent strategic behavior by limiting information about the votes of other voters.

We prove that it is NP-hard for a coalition of two manipulators to compute how to manipulate the Borda voting rule. This resolves one of the last open problems in the computational complexity of manipulating common voting rules. Because of this NP-hardness, we treat computing a manipulation as an approximation problem where we try to minimize the number of manipulators. Based on ideas from bin packing and multiprocessor scheduling, we propose two new approximation methods to compute manipulations of the Borda rule. Experiments show that these methods significantly outperform the previous best known approximation method. We are able to find optimal manipulations in almost all the randomly generated elections tested. Our results suggest that, whilst computing a manipulation of the Borda rule by a coalition is NP-hard, computational complexity may provide only a weak barrier against manipulation in practice.

We present a new approach to enhancing answer set programming (ASP) with constraint programming (CP) techniques based on conflict-driven learning and lazy nogood generation.

Set and multiset variables in constraint programming have typically been represented using subset bounds. However, this is a weak representation that neglects potentially useful information about a set such as its cardinality. For set variables, the length-lex (LL) representation successfully provides information about the length (cardinality) and position in the lexicographic ordering. For multiset variables, where elements can be repeated, we consider richer representations that take into account additional information. We study eight different representations in which we maintain bounds according to one of the eight different orderings: length-(co)lex (LL/LC), variety-(co)lex (VL/VC), length-variety-(co)lex (LVL/LVC), and variety-length-(co)lex (VLL/VLC) orderings. These representations integrate together information about the cardinality, variety (number of distinct elements in the multiset), and position in some total ordering. Theoretical and empirical comparisons of expressiveness and compactness of the eight representations suggest that length-variety-(co)lex (LVL/LVC) and variety-length-(co)lex (VLL/VLC) usually give tighter bounds after constraint propagation. We implement the eight representations and evaluate them against the subset bounds representation with cardinality and variety reasoning. Results demonstrate that they offer significantly better pruning and runtime.

Nanson's and Baldwin's voting rules selecta winner by successively eliminatingcandidates with low Borda scores. We showthat these rules have a number of desirablecomputational properties. In particular,with unweighted votes, it isNP-hard to manipulate either rule with one manipulator, whilstwith weighted votes, it isNP-hard to manipulate either rule with a small number ofcandidates and a coalition of manipulators.As only a couple of other voting rulesare known to be NP-hard to manipulatewith a single manipulator, Nanson'sand Baldwin's rules appearto be particularly resistant to manipulation from a theoretical perspective.We also propose a number of approximation methodsfor manipulating these two rules.Experiments demonstrate that both rules areoften difficult to manipulate in practice.These results suggest that elimination stylevoting rules deserve further study.

We solve constraint satisfaction problems through translation to answer set programming (ASP). Our reformulations have the property that unitpropagation in the ASP solver achieves well defined local consistency properties like arc, bound and range consistency. Experiments demonstrate the computational value of this approach. 1

The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or more generally to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here we consider stable marriage problems with weighted preferences: each man (resp., woman) provides a score for each woman (resp., man). In this context, we consider the manipulability properties of the procedures that return stable marriages. While we know that all procedures are manipulable by modifying the preference lists or by truncating them, here we consider if manipulation can occur also by just modifying the weights while preserving the ordering and avoiding truncation. It turns out that, by adding weights, we indeed increase the possibility of manipulating and this cannot be avoided by any reasonable restriction on the weights.

Voting is a simple mechanism to combine together the preferences of multiple agents. Unfortunately, agents may try to manipulate the result by mis-reporting their preferences. One barrier that might exist to such manipulation is computational complexity. In particular, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NP-hardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. In this paper, we show that empirical studies are useful in improving our understanding of this issue. We consider two settings which represent the two types of complexity results that have been identified in this area: manipulation with unweighted votes by a single agent, and manipulation with weighted votes by a coalition of agents. In the first case, we consider Single Transferable Voting (STV), and in the second case, we consider veto voting. STV is one of the few voting rules used in practice where it is NP-hard to compute how a single agent can manipulate the result when votes are unweighted. It also appears one of the harder voting rules to manipulate since it involves multiple rounds. On the other hand, veto voting is one of the simplest representatives of voting rules where it is NP-hard to compute how a coalition of weighted agents can manipulate the result. In our experiments, we sample a number of distributions of votes including uniform, correlated and real world elections. In many of the elections in our experiments, it was easy to compute how to manipulate the result or to prove that manipulation was impossible. Even when we were able to identify a situation in which manipulation was hard to compute (e.g. when votes are highly correlated and the election is hung), we found that the computational difficulty of computing manipulations was somewhat precarious (e.g. with such hung elections, even a single uncorrelated voter was enough to make manipulation easy to compute).

We study propagation algorithms for the conjunction of two AllDifferent constraints. Solutions of an AllDifferent constraint can be seen as perfect matchings on the variable/value bipartite graph. Therefore, we investigate the problem of finding simultaneous bipartite matchings. We present an extension of the famous Hall theorem which characterizes when simultaneous bipartite matchings exists. Unfortunately, finding such matchings is NP-hard in general. However, we prove a surprising result that finding a simultaneous matching on a convex bipartite graph takes just polynomial time. Based on this theoretical result, we provide the first polynomial time bound consistency algorithm for the conjunction of two AllDifferent constraints. We identify a pathological problem on which this propagator is exponentially faster compared to existing propagators. Our experiments show that this new propagator can offer significant benefits over existing methods.

We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that we may be able to exploit both types of symmetry when finding solutions. We illustrate the potential of exploiting internal symmetries on two benchmark domains: Van der Waerden numbers and graceful graphs. By identifying internal symmetries we are able to extend the state of the art in both cases.

The stable marriage problem (SM) has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. In the classical formulation, n men and n women express their preferences over the members of the other sex. Solving an SM means finding a stable marriage: a matching of men to women with no blocking pair. A blocking pair consists of a man and a woman who are not married to each other but both prefer each other to their partners. It is possible to find a male-optimal (resp., female-optimal) stable marriage in polynomial time. However, it is sometimes desirable to find stable marriages without favoring a group at the expenses of the other one. In this paper we present a local search approach to find stable marriages. Our experiments show that the number of steps grows as little as O(nlog(n)). We also show empirically that the proposed algorithm samples very well the set of all stable marriages of a given SM, thus providing a fair and efficient approach to generate stable marriages.

Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry class. This simple but powerful idea can be used in a number of different ways. We describe one application within model restarts, a search technique designed to reduce the conflict between symmetry breaking and the branching heuristic. In model restarts, we restart search periodically with a random symmetry of the symmetry breaking constraints. Experimental results show that this symmetry breaking technique is effective in practice on some standard benchmark problems.

Abstract We present a new approach to enhancing Answer Set Programming (ASP) with Constraint Processing techniques which allows for solving interesting Constraint Satisfaction Problems in ASP. We show how constraints on finite domains can be decomposed into logic programs such that unit-propagation achieves arc, bound or range consistency. Experiments with our encodings demonstrate their computational impact.

Abstract. Preferences are not always expressible via complete linear orders: sometimes it is more natural to allow for the presence of incomparable outcomes. This may hold both in the agents ’ preference ordering and in the social order. In this paper we consider this scenario and we study what properties it may have. In particular, we show that, despite the added expressivity and ability to resolve conflicts provided by incomparability, classical impossibility results (such as Arrow’s theorem, Muller-Satterthwaite’s theorem, and Gibbard-Satterthwaite’s theorem) still hold. We also prove some possibility results, generalizing Sen’s theorem for majority voting. To prove these results, we define new notions of unanimity, monotonicity, dictator, triple-wise value-restriction, and strategy-proofness, which are suitable and natural generalizations of the classical ones for complete orders. 1

We study the CARDPATH constraint. This ensures a given constraint holds a number of times down a sequence of variables. We show that SLIDE, a special case of CARDPATH where the slid constraint must hold always, can be used to encode a wide range of sliding sequence constraints including CARDPATH itself. We consider how to propagate SLIDE and provide a complete propagator for CARDPATH. Since propagation is NP-hard in general, we identify special cases where propagation takes polynomial time. Our experiments demonstrate that using SLIDE to encode global constraints can be as efficient and effective as specialised propagators.

When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many values as variables, and each variable takes an unique value. In such problems, we can choose between a primal and a dual viewpoint. In the dual viewpoint, each dual variable represents one of the primal values, whilst each dual value represents one of the primal variables. Alternatively, by means of channelling constraints to link the primal and dual variables, we can have a combined model with both sets of variables. In this paper, we perform an extensive theoretical and empirical study of such primal, dual and combined models for two classes of problems: permutation problems and injection problems. Our results show that it often be advantageous to use multiple viewpoints, and to have constraints which channel between them to maintain consistency. They also illustrate a general methodology for comparing different constraint models.

We illustrate the use of phase transition behavior in the study of heuristics. Using an “annealed” theory, we define a parameter that measures the “constrainedness” of an ensemble of number partitioning problems. We identify a phase transition at a critical value of constrainedness. We then show that constrainedness can be used to analyze and compare algorithms and heuristics for number partitioning in a precise and quantitative manner. For example, we demonstrate that on uniform random problems both the Karmarkar–Karp and greedy heuristics minimize the constrainedness, but that the decisions made by the Karmarkar–Karp heuristic are superior at reducing constrainedness. This supports the better performance observed experimentally for the Karmarkar–Karp heuristic. Our results refute a conjecture of Fu that phase transition behavior does not occur in number partitioning. Additionally, they demonstrate that phase transition behavior is useful for more than just simple benchmarking. It can, for instance, be used to analyze heuristics, and to compare the quality of heuristic solutions.

Inductive theorem provers often diverge. This paper describes a simple critic, a computer program which monitors the construction of inductive proofs attempting to identify diverging proof attempts. Divergence is recognized by means of a ``difference matching'' procedure. The critic then proposes lemmas and generalizations which ``ripple'' these differences away so that the proof can go through without divergence. The critic enables the theorem prover Spike to prove many theorems completely automatically from the definitions alone.

We describe an extensive study of search in GSAT, an approximation procedure for propositional satisfiability. GSAT performs greedy hill-climbing on the number of satisfied clauses in a truth assignment. Our experiments provide a more complete picture of GSAT's search than previous accounts. We describe in detail the two phases of search: rapid hill-climbing followed by a long plateau search. We demonstrate that when applied to randomly generated 3SAT problems, there is a very simple scaling with problem size for both the mean number of satisfied clauses and the mean branching rate. Our results allow us to make detailed numerical conjectures about the length of the hill-climbing phase, the average gradient of this phase, and to conjecture that both the average score and average branching rate decay exponentially during plateau search. We end by showing how these results can be used to direct future theoretical analysis. This work provides a case study of how computer experiments can be used to improve understanding of the theoretical properties of algorithms.