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. A well-known algorithm to solve this problem is the Gale-Shapley algorithm, which runs in polynomial time. It has been proven that stable marriage procedures can always be manipulated. Whilst the Gale-Shapley algorithm is computationally easy to manipulate, we prove that there exist stable marriage procedures which are NP-hard to manipulate. We also consider the relationship between voting theory and stable marriage procedures, showing that voting rules which are NP-hard to manipulate can be used to define stable marriage procedures which are themselves NP-hard to manipulate. Finally, we consider the issue that stable marriage procedures like Gale-Shapley favour one gender over the other, and we show how to use voting rules to make any stable marriage procedure gender neutral.
@cite_0 suggested lying strategies for an individual woman, and proposed an algorithm to find the best partner with the male optimal procedure. We instead focus on the complexity of determining if the procedure can be manipulated to obtain a better result. Moreover, we also provide a universal manipulation scheme that, under certain conditions on the profile, assures that the female optimal partner is returned.
@cite_0
1557896792
Given a set of n men represented by n points lying on a line, and n women represented by n points lying on another parallel line, with each person having a list that ranks some people of opposite gender as his her acceptable partners in strict order of preference. In this problem, we want to match people of opposite genders to satisfy people’s preferences as well as making the edges not crossing one another geometrically. A noncrossing blocking pair w.r.t. a matching M is a pair (m, w) of a man and a woman such that they are not matched with each other but prefer each other to their own partners in M, and the segment (m, w) does not cross any edge in M. A weakly stable noncrossing matching (WSNM) is a noncrossing matching that does not admit any noncrossing blocking pair. In this paper, we prove the existence of a WSNM in any instance by developing an (O(n^2) ) algorithm to find one in a given instance. The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position. 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. A well-known algorithm to solve this problem is the Gale-Shapley algorithm, which runs in polynomial time. It has been proven that stable marriage procedures can always be manipulated. Whilst the Gale-Shapley algorithm is computationally easy to manipulate, we prove that there exist stable marriage procedures which are NP-hard to manipulate. We also consider the relationship between voting theory and stable marriage procedures, showing that voting rules which are NP-hard to manipulate can be used to define stable marriage procedures which are themselves NP-hard to manipulate. Finally, we consider the issue that stable marriage procedures like Gale-Shapley favour one gender over the other, and we show how to use voting rules to make any stable marriage procedure gender neutral. Abstract This article reports an experimental study that aimed to quantitatively analyze motion coordination patterns across digits 2–5 (index to little finger), and examine the kinematic synergies during manipulative and gestic acts. Twenty-eight subjects (14 males and 14 females) performed two types of tasks, both right-handed: (1) cylinder-grasping that involved concurrent voluntary flexion of digits 2–5, and (2) voluntary flexion of individual fingers from digit 2 to 5 (i.e., one at a time). A five-camera opto-electronic motion capture system measured trajectories of 21 miniature reflective markers strategically placed on the dorsal surface landmarks of the hand. Joint angular profiles for 12 involved flexion–extension degrees of freedom (DOF's) were derived from the measured coordinates of surface markers. Principal components analysis (PCA) was used to examine the temporal covariation between joint angles. A mathematical modeling procedure, based on hyperbolic tangent functions, characterized the sigmoidal shaped angular profiles with four kinematically meaningful parameters. The PCA results showed that for all the movement trials ( n =280), two principal components accounted for at least 98 of the variance. The angular profiles ( n =2464) were accurately characterized, with the mean (±SD) coefficient of determination ( R 2 ) and root-mean-square-error (RMSE) being 0.95 (±0.12) and 1.03° (±0.82°), respectively. The resulting parameters which quantified both the spatial and temporal aspects of angular profiles revealed stereotypical patterns including a predominant (87 of all trials) proximal-to-distal flexion sequence and characteristic interdependence – involuntary joint flexion induced by the voluntarily flexed joint. The principal components' weights and the kinematic parameters also exhibited qualitatively similar variation patterns. Motor control interpretations and new insights regarding the underlying synergistic mechanisms, particularly in relation to previous findings on force synergies, are discussed. Lying in order to manipulate the Gale-Shapley matching algorithm has been studied by Dubins and Freedman (1981) and by Gale and Sotomayor (1985), and was shown to be generally more appealing to the proposed-to side (denoted as the women in Gale and Shapley's seminal paper (1962)) than to the proposing side (denoted as men there). It can also be shown that in the case of lying women, for every woman who is better off due to lying, there exists a man who is worse off. In this paper, we show that an even stronger dichotomy between the goals of the sexes holds, namely, if no woman is worse off then no man is better off, while a form of sisterhood between the lying and the "innocent" women also holds, namely, if none of the former is worse off, then neither is any of the latter. These results are robust: they generalize to the one-to-many variants of the algorithm and do not require the resulting matching to be stable (i.e. they hold even in out-of-equilibria situations). The machinery we develop in our proofs sheds new light on the structure of lying by women in the Gale-Shapley matching algorithm. This paper is based upon an undergraduate thesis (2007) by the first author. This paper addresses strategies for the stable marriage problem. For the Gale-Shapley algorithm with men proposing, a classical theorem states that it is impossible for every cheating man to get a better partner than the one he gets if everyone is truthful. We study how to circumvent this theorem and incite men to cheat. First we devise coalitions in which a nonempty subset of the liars get better partners and no man is worse off than before. This strategy is limited in that not everyone in the coalition has the incentive to falsify his list. In an attempt to rectify this situation we introduce the element of randomness, but the theorem shows surprising robustness: it is impossible that every liar has a chance to improve the rank of his partner while no one gets hurt. To overcome the problem that some men lack the motivation to lie, we exhibit another randomized lying strategy in which every liar can expect to get a better partner on average, though with a chance of getting a worse one. Finally, we consider a variant scenario: instead of using the Gale-Shapley algorithm, suppose the stable matching is chosen at random. We present a modified form of the coalition strategy ensuring that every man in the coalition has a new probability distribution over partners which majorizes the original one. Conversational participants tend to immediately and unconsciously adapt to each other's language styles: a speaker will even adjust the number of articles and other function words in their next utterance in response to the number in their partner's immediately preceding utterance. This striking level of coordination is thought to have arisen as a way to achieve social goals, such as gaining approval or emphasizing difference in status. But has the adaptation mechanism become so deeply embedded in the language-generation process as to become a reflex? We argue that fictional dialogs offer a way to study this question, since authors create the conversations but don't receive the social benefits (rather, the imagined characters do). Indeed, we find significant coordination across many families of function words in our large movie-script corpus. We also report suggestive preliminary findings on the effects of gender and other features; e.g., surprisingly, for articles, on average, characters adapt more to females than to males. The purpose of this investigation was to identify the factors associated with the distress experienced after the breakup of a romantic relationship, both at the time of the breakup (assessed retrospectively) and at the time the questionnaire was completed. Four categories of variables were examined as possible correlates of post-breakup distress: variables associated with the initiation of the relationship, characteristics of the relationship while it was intact, conditions at the time of the breakup and individual difference variables. The sample consisted of 257 young adults (primarily college students; 83 male and 174 female) who had experienced a recent breakup (M = 21 weeks since breakup). The variables most highly associated with distress at the time of the breakup were non-mutuality in alternatives (i.e. partner having more inter-est in alternatives), commitment, satisfaction, greater effort in relationship initiation, being left' by the other and fearful attachment style. The variables most highl... This paper provides the first comprehensive analysis of Uber's driver-partners, based on both survey data and anonymized, aggregated administrative data. Uber has grown at an exponential rate over the last few years, and drivers who partner with Uber appear to be attracted to the platform in large part because of the flexibility it offers, the level of compensation, and the fact that earnings per hour do not vary much with hours worked, which facilitates part-time and variable hours. Uber's driver-partners are more similar in terms of their age and education to the general workforce than to taxi drivers and chauffeurs. Uber may serve as a bridge for many seeking other employment opportunities, and it may attract well-qualified individuals because, with Uber's star rating system, driver-partners' reputations are explicitly shared with potential customers. Most of Uber's driver-partners had full- or part-time employment prior to joining Uber, and many continued in those positions after starting to drive with the Uber platform, which makes the flexibility to set their own hours all the more valuable. Uber's driver-partners also often cited the desire to smooth fluctuations in their income as a reason for partnering with Uber. We study strategic issues in the Gale-Shapley stable marriage model. In the first part of the paper, we derive the optimal cheating strategy and show that it is not always possible for a woman to recover her women-optimal stable partner from the men-optimal stable matching mechanism when she can only cheat by permuting her preferences. In fact, we show, using simulation, that the chances that a woman can benefit from cheating are slim. In the second part of the paper, we consider a two-sided matching market found in Singapore. We study the matching mechanism used by the Ministry of Education (MOE) in the placement of primary six students in secondary schools, and discuss why the current method has limited success in accommodating the preferences of the students, and the specific needs of the schools (in terms of the “mix” of admitted students). Using insights from the first part of the paper, we show that stable matching mechanisms are more appropriate in this matching market and explain why the strategic behavior of the students need not be a major concern. (Stable Marriage; Strategic Issues; Gale-Shapley Algorithm; Student Posting Exercise) We present a novel peer-to-peer backup technique that allows computers connected to the Internet to back up their data cooperatively: Each computer has a set of partner computers, which collectively hold its backup data. In return, it holds a part of each partner's backup data. By adding redundancy and distributing the backup data across many partners, a highly-reliable backup can be obtained in spite of the low reliability of the average Internet machine. Because our scheme requires cooperation, it is potentially vulnerable to several novel attacks involving free riding (e.g., holding a partner's data is costly, which tempts cheating) or disruption. We defend against these attacks using a number of new methods, including the use of periodic random challenges to ensure partners continue to hold data and the use of disk-space wasting to make cheating unprofitable. Results from an initial prototype show that our technique is feasible and very inexpensive: it appears to be one to two orders of magnitude cheaper than existing Internet backup services. Multi-winner elections model scenarios where voters must select a fixed-size group of candidates based on their individual preferences. In such scenarios, it is often the case that voters are incentivized to manipulate, i.e. misreport their preferences in order to obtain a better outcome. In this paper, we study the complexity of manipulating multi-winner elections under scoring rules, with a particular focus on the role of tie-breaking rules. We consider both lexicographic tie-breaking rules, which break ties according to a fixed ordering of the candidates, and a natural randomized tie-breaking rule. We describe polynomial-time manipulation algorithms for several special cases of our problem. Specifically, we show that finding a successful manipulation is easy if the underlying voting rule is k-Approval or the number of candidates to be elected is bounded by a constant (for both types of tie-breaking rules), as well as if the manipulator's utility function only takes values in 0, 1 and the ties are broken in the manipulator's favor. This paper describes the use of ordered probit models to examine the risk of different injury levels sustained under all crash types, two-vehicle crashes, and single-vehicle crashes. The results suggest that pickups and sport utility vehicles are less safe than passenger cars under single-vehicle crash conditions. In two-vehicle crashes, however, these vehicle types are associated with less severe injuries for their drivers and more severe injuries for occupants of their collision partners. Other conclusions also are presented; for example, the results indicate that males and younger drivers in newer vehicles at lower speeds sustain less severe injuries. In human-computer collaboration involving haptics, a key issue that remains to be solved is to establish an intuitive communication between the partners. Even though computers are widely used to aid human operators in teleoperation, guidance, and training, because they lack the adaptability, versatility, and awareness of a human, their ability to improve efficiency and effectiveness in dynamic tasks is limited. We suggest that the communication between a human and a computer can be improved if it involves a decision-making process in which the computer is programmed to infer the intentions of the human operator and dynamically adjust the control levels of the interacting parties to facilitate a more intuitive interaction setup. In this paper, we investigate the utility of such a dynamic role exchange mechanism, where partners negotiate through the haptic channel to trade their control levels on a collaborative task. We examine the energy consumption, the work done on the manipulated object, and the joint efficiency in addition to the task performance. We show that when compared to an equal control condition, a role exchange mechanism improves task performance and the joint efficiency of the partners. We also show that augmenting the system with additional informative visual and vibrotactile cues, which are used to display the state of interaction, allows the users to become aware of the underlying role exchange mechanism and utilize it in favor of the task. These cues also improve the user's sense of interaction and reinforce his her belief that the computer aids with the execution of the task. This paper concerns the problem of dynamic parameter identification of robot manipulators and proposes a closed-loop identification procedure using modified Fourier series (MFS) as exciting trajectories. First, a static continuous friction model is involved to model joint friction for realizable friction compensation in controller design. Second, MFS satisfying the boundary conditions are firstly designed as periodic exciting trajectories. To minimize the sensitivity to measurement noise, the coefficients of MFS are optimized according to the condition number criterion. Moreover, to obtain accurate parameter estimates, the maximum likelihood estimation (MLE) method considering the influence of measurement noise is adopted. The proposed identification procedure has been implemented on the first three axes of the QIANJIANG-I 6-DOF robot manipulator. Experiment results verify the effectiveness of the proposed approach, and comparison between identification using MFS and that using finite Fourier series (FFS)... Online dating sites have become popular platforms for people to look for potential romantic partners. Different from traditional user-item recommendations where the goal is to match items (e.g., books, videos, etc) with a user's interests, a recommendation system for online dating aims to match people who are mutually interested in and likely to communicate with each other. We introduce similarity measures that capture the unique features and characteristics of the online dating network, for example, the interest similarity between two users if they send messages to same users, and attractiveness similarity if they receive messages from same users. A reciprocal score that measures the compatibility between a user and each potential dating candidate is computed and the recommendation list is generated to include users with top scores. The performance of our proposed recommendation system is evaluated on a real-world dataset from a major online dating site in China. The results show that our recommendation algorithms significantly outperform previously proposed approaches, and the collaborative filtering-based algorithms achieve much better performance than content-based algorithms in both precision and recall. Our results also reveal interesting behavioral difference between male and female users when it comes to looking for potential dates. In particular, males tend to be focused on their own interest and oblivious towards their attractiveness to potential dates, while females are more conscientious to their own attractiveness to the other side of the line. Voting is a general method for preference aggregation in multiagent settings, but seminal results have shown that all (nondictatorial) voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationally. A number of recent papers study the complexity of manipulating existing protocols. This paper is the first work to take the next step of designing new protocols that are especially hard to manipulate. Rather than designing these new protocols from scratch, we instead show how to tweak existing protocols to make manipulation hard, while leaving much of the original nature of the protocol intact. The tweak studied consists of adding one elimination preround to the election. Surprisingly, this extremely simple and universal tweak makes typical protocols hard to manipulate! The protocols become NP-hard, #P-hard, or PSPACE-hard to manipulate, depending on whether the schedule of the preround is determined before the votes are collected, after the votes are collected, or the scheduling and the vote collecting are interleaved, respectively. We prove general sufficient conditions on the protocols for this tweak to introduce the hardness, and show that the most common voting protocols satisfy those conditions. These are the first results in voting settings where manipulation is in a higher complexity class than NP (presuming PSPACE @math NP). In this paper, we studied the strategies to enhance synchronization on directed networks by manipulating a fixed number of links. We proposed a centrality-based manipulating (CBM) method, where the node centrality is measured by the well-known PageRank algorithm. Extensive numerical simulation on many modeled networks demonstrated that the CBM method is more effective in facilitating synchronization than the degree-based manipulating method and the random manipulating method for adding or removing links. The reason is that the CBM method can effectively narrow the incoming degree distribution and reinforce the hierarchical structure of the network. Furthermore, we apply the CBM method to the links rewiring procedure where at each step one link is removed and one new link is added. The CBM method helps to decide which links should be removed or added. After several steps, the resulting networks are very close to the optimal structure from the theoretical analysis and the evolutionary optimization algorithm. The numerical simulations on the Kuramoto model further demonstrate that our method has an advantage in shortening the convergence time to synchronization on directed networks. We describe a new method to automatically discriminate between patients with Alzheimer's disease (AD) or mild cognitive impairment (MCI) and elderly controls, based on multidimensional classification of hippocampal shape features. This approach uses spherical harmonics (SPHARM) coefficients to model the shape of the hippocampi, which are segmented from magnetic resonance images (MRI) using a fully automatic method that we previously developed. SPHARM coefficients are used as features in a classification procedure based on support vector machines (SVM). The most relevant features for classification are selected using a bagging strategy. We evaluate the accuracy of our method in a group of 23 patients with AD (10 males, 13 females, age+ -standard-deviation (SD)=73+ -6 years, mini-mental score (MMS)=24.4+ -2.8), 23 patients with amnestic MCI (10 males, 13 females, age+ -SD=74+ -8 years, MMS=27.3+ -1.4) and 25 elderly healthy controls (13 males, 12 females, age+ -SD=64+ -8 years), using leave-one-out cross-validation. For AD vs controls, we obtain a correct classification rate of 94 , a sensitivity of 96 , and a specificity of 92 . For MCI vs controls, we obtain a classification rate of 83 , a sensitivity of 83 , and a specificity of 84 . This accuracy is superior to that of hippocampal volumetry and is comparable to recently published SVM-based whole-brain classification methods, which relied on a different strategy. This new method may become a useful tool to assist in the diagnosis of Alzheimer's disease. We consider a resource management problem in a multi-cell downlink OFDMA network whereby the goal is to find the optimal combination of (i) assignment of users to base stations and (ii) resource allocation strategies at each base station. Efficient resource management protocols must rely on users truthfully reporting privately held information such as downlink channel states. However, individual users can manipulate the resulting resource allocation (by misreporting their private information) if by doing so they can improve their payoff. Therefore, it is of interest to design efficient resource management protocols that are strategy-proof, i.e. it is in the users' best interests to truthfully report their private information. Unfortunately, we show that the implementation of any protocol that is efficient and strategy-proof is NP-hard. Thus, we propose a computationally tractable strategy-proof mechanism that is approximately efficient, i.e. the solution obtained yields at least 1 2 of the optimal throughput. Simulations are provided to illustrate the effectiveness of the proposed mechanism.