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Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders
"... Usually a voting rule or correspondence requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a profile of part ..."
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Cited by 63 (13 self)
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Usually a voting rule or correspondence requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a profile of partial orders and a candidate c, two important questions arise: first, is c guaranteed to win, and second, is it still possible for c to win? These are the necessary winner and possible winner problems, respectively. We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We prove that for Copeland, maximin, Bucklin, and ranked pairs, the possible winner problem is NPcomplete; also, we give a sufficient condition on scoring rules for the possible winner problem to be NPcomplete (Borda satisfies this condition). We also prove that for Copeland and ranked pairs, the necessary winner problem is coNPcomplete. All the hardness results hold even when the number of undetermined pairs in each vote is no more than a constant. We also present polynomialtime algorithms for the necessary winner problem for scoring rules, maximin, and Bucklin.
Manipulating Tournaments in Cup and Round Robin Competitions
"... Abstract. In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial time. In addition, we show that finding the minimal ..."
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Abstract. In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial time. In addition, we show that finding the minimal number of games that need to be thrown to manipulate the result can also be determined in polynomial time. Finally, we show that there are several different variations of standard cup competitions where manipulation remains polynomial. 1
On the complexity of bribery and manipulation in tournaments with uncertain information
 in: Proceedings of the 25th International Florida Artificial Intelligence Research Society Conference, 2012
"... We study the computational complexity of optimal bribery and manipulation schemes for sports tournaments with uncertain information: cup; challenge or caterpillar; and round robin. Our results carry over to the equivalent voting rules: sequential pairwise elections, cup, and Copeland, when the set ..."
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We study the computational complexity of optimal bribery and manipulation schemes for sports tournaments with uncertain information: cup; challenge or caterpillar; and round robin. Our results carry over to the equivalent voting rules: sequential pairwise elections, cup, and Copeland, when the set of candidates is exactly the set of voters. This restriction creates new difficulties for most existing algorithms. The complexity of bribery and manipulation are well studied, almost always assuming deterministic information about votes and results. We assume that for candidates i and j the probability that i beats j and the costs of lowering each probability by fixed increments are known to the manipulators. We provide complexity analyses for cup, challenge, and round robin competitions ranging from polynomial time to NPPP. This shows that the introduction of uncertainty into the reasoning process drastically increases the complexity of bribery problems in some instances.
Clinching and elimination of playoff berth in the NHL
 International Journal of Operations Research
, 2008
"... AbstractThis paper considers the problem of determining as early as possible when teams in the NHL are mathematically qualified or eliminated from the playoffs. A mixed integer program formulation to determine mathematical qualification and elimination will be given via the rules outlined by the NHL ..."
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AbstractThis paper considers the problem of determining as early as possible when teams in the NHL are mathematically qualified or eliminated from the playoffs. A mixed integer program formulation to determine mathematical qualification and elimination will be given via the rules outlined by the NHL. We also give a slightly simplified version of the MIP that is more computationally tractable and computational results for the 2003–2004 NHL season in which our method is able to detect qualification and elimination earlier than the rules currently used by the sports media. KeywordsInteger program, Formulation, NHL, Applications 1.
Fixing a Balanced Knockout Tournament
"... Balanced knockout tournaments are one of the most common formats for sports competitions, and are also used in elections and decisionmaking. We consider the computational problem of finding the optimal draw for a particular player in such a tournament. The problem has generated considerable resea ..."
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Balanced knockout tournaments are one of the most common formats for sports competitions, and are also used in elections and decisionmaking. 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 NPcomplete, thereby settling an outstanding open problem. Our main result has a number of interesting implications on related counting and approximation problems. We present a memoizationbased 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.
Lessons Learned from Modelling the NHL Playoff Qualification Problem
"... Abstract. The modelling of complex problems tends to be most effective when modelling is calibrated using a concrete solver and modifications to the model are made as a result. In some cases, the final model is significantly different from the simple model that best fits the constraints of the probl ..."
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Abstract. The modelling of complex problems tends to be most effective when modelling is calibrated using a concrete solver and modifications to the model are made as a result. In some cases, the final model is significantly different from the simple model that best fits the constraints of the problem. While there are several projects that are attempting to create black box solvers with generic modelling languages, for the moment the modelling processes is intimately tied to the solving and search procedure. This paper looks at the changes to the simple model and the search procedures that were made to create an efficient solution to the NHL Playoff Qualification problem. The approaches for improving the model could be extended to other applications as the techniques are not specific to this problem. 1
Integer Programming and Sports Rankings
, 2013
"... Sports rankings are obtained by applying a system of rules to evaluate the performance of the participants in a competition. We consider rankings that result from assigning an ordinal rank to each competitor according to their performance. We develop an integer programming model for rankings that al ..."
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Sports rankings are obtained by applying a system of rules to evaluate the performance of the participants in a competition. We consider rankings that result from assigning an ordinal rank to each competitor according to their performance. We develop an integer programming model for rankings that allows us to calculate the number of points needed to guarantee a team the ith position, as well as the minimum number of points that could yield the ith place. The model is very general and can thus be applied to many types of sports. We discuss examples coming from football (soccer), ice hockey, and Formula 1. We answer various questions and debunk a few myths along the way. Are 40 points enough to avoid relegation in the Bundesliga? Do 95 points guarantee the participation of a team in the NHL playoffs? Moreover, in the season restructuration currently under consideration in the NHL, will it be easier or harder to access the playoffs? Is it possible to win the Formula 1 World Championship without winning at least one race or without even climbing once on the podium? Finally, we observe that the optimal solutions of the aforementioned model are associated to extreme situations which are unlikely to happen. Thus, to get closer to realistic scenarios, we enhance the model by adding some constraints inferred from the results of the previous years. 1
DECISION MAKING UNDER UNCERTAINTY: THEORETICAL AND EMPIRICAL
, 2012
"... This dissertation focuses on voting as a means of preference aggregation. Specifically, empirically testing various properties of voting rules and theoretically analyzing how much information it takes to make tampering with an election computationally hard. Groups of individuals have always struggle ..."
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This dissertation focuses on voting as a means of preference aggregation. Specifically, empirically testing various properties of voting rules and theoretically analyzing how much information it takes to make tampering with an election computationally hard. Groups of individuals have always struggled to come to consistent and fair group decisions and entire fields of study have emerged in economics, psychology, political science, and computer science to deal with the myriad problems that arise in these settings. In my research I have sought to gain a deeper understanding of the practical and theoretical issues that surround voting rules. This dissertation lies within the field of computational social choice, a subfield of artificial intelligence. This cross disciplinary area has broader impacts within the fields of economics, computer science, and political science. My theoretical work focuses on the computational complexity of the bribery and manipulation problems. The bribery problem asks if an outside agent can affect the results of a voting scenario given some budget constraints, while the manipulation problem asks if one or more voting agents can strategically misrepresent their votes to induce a more preferred outcome. These questions seem to hinge on the amount of information an agent has. In
A Hybrid Constraint Programming and Enumeration Approach for Solving NHL Playoff Qualification and Elimination Problems
"... Many sports fans invest a great deal of time into watching and analyzing the performance of their favorite team. However, the tools at their disposal are primarily heuristic or based on folk wisdom. We provide a concrete mechanism for calculating the minimum number of points needed to guarantee a pl ..."
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Many sports fans invest a great deal of time into watching and analyzing the performance of their favorite team. However, the tools at their disposal are primarily heuristic or based on folk wisdom. We provide a concrete mechanism for calculating the minimum number of points needed to guarantee a playoff spot and the minimum number of points needed to possibly qualify for a playoff spot in the National Hockey League (NHL). Our approach uses a combination of constraint programming, enumeration, network flows and decomposition to solve the problem efficiently. The technique can successfully be applied to any team at any point of the season to determine how well a team must do to make the playoffs.
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"... Int. J. Agent–Oriented Software Engineering, Vol. x, No. x, xxxx 1 A multiagent framework to retrieve and publish information on qualification and elimination data in sports tournaments ..."
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Int. J. Agent–Oriented Software Engineering, Vol. x, No. x, xxxx 1 A multiagent framework to retrieve and publish information on qualification and elimination data in sports tournaments