Because preferences naturally arise and play an important role in many real-life decisions, they are at the backbone of various fields. In particular preferences are increasingly used in almost all matching procedures-based applications. In this work we highlight the benefit of using AI insights on preferences in a large scale application, namely the French Admission Post-Baccalaureat Platform (APB). Each year APB allocates hundreds of thousands first year applicants to universities. This is done automatically by matching applicants preferences to university seats. In practice, APB can be unable to distinguish between applicants which leads to the introduction of random selection. This has created frustration in the French public since randomness, even used as a last mean does not fare well with the republican egalitarian principle. In this work, we provide a solution to this problem. We take advantage of recent AI Preferences Theory results to show how to enhance APB in order to improve expressiveness of applicants preferences and reduce their exposure to random decisions.
In the domain of Constraint Programming, @cite_21 explores stability in different problems variations including cases where men women can rank members of their own genders, etc. A constraint encoding of the SM problem with ties and incomplete lists is presented and empirically evaluated in @cite_22 .
@cite_21 @cite_22
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We present the first complete algorithm for the SMTI problem, the stable marriage problem with ties and incomplete lists. We do this in the form of a constraint programming encoding of the problem. With this we are able to carry out the first empirical study of the complete solution of SMTI instances. In the stable marriage problem (SM) [5] we have n men and n women. Each man ranks the women, giving himself a preference list. Similarly each woman ranks the men, giving herself a preference list. The problem is then to marry men and women such that they are stable i.e. such that there is no incentive for individuals to divorce and elope. This problem is polynomial time solvable. However, when preference lists contain ties and are incomplete (SMTI) the problem of determining if there is a stable matching of size n is then NP-complete, as is the optimisation problem of finding the largest or smallest stable matching [6, 10]. In this paper we present constraint programming solutions for the SMTI decision and optimisation problems, a problem generator for random instances of SMTI, and an empirical study of this problem. In the stable roommates (SR) problem we have n agents, where each agent ranks all other agents in strict order of preference. The problem is then to match agents into pairs such that no two agents prefer each other to their matched partners, and this is a stable matching. The stable marriage (SM) problem is a special case of SR, where we have two equal sized sets of agents, men and women, where men rank only women and women rank only men. Every instance of SM admits at least one stable matching, whereas for SR as the number of agents increases the number of instances with stable matchings decreases. So, what will happen if in SM we allow men to rank men and women to rank women, i.e. we relax gender separation? Will stability abruptly disappear? And what happens in a stable roommates scenario if agents do not rank all other agents? Again, is stability uncommon? And finally, what happens if there are an odd number of agents? We present empirical evidence to answer these questions. The stable marriage (SM) 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 formulation, n men and n women express their preferences (via a strict total order) over the members of the other sex. Solving an SM problem means finding a stable marriage where stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. We consider both the classical stable marriage problem and one of its useful variations (denoted SMTI (Stable Marriage with Ties and Incomplete lists)) where the men and women express their preferences in the form of an incomplete preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these preference lists, and we try to find a stable matching that marries as many people as possible. Whilst the SM problem is polynomial to solve, the SMTI problem is NP-hard. We propose to tackle both problems via a local search approach, which exploits properties of the problems to reduce the size of the neighborhood and to make local moves efficiently. We empirically evaluate our algorithm for SM problems by measuring its runtime behavior and its ability to sample the lattice of all possible stable marriages. We evaluate our algorithm for SMTI problems in terms of both its runtime behavior and its ability to find a maximum cardinality stable marriage. Experimental results suggest that for SM problems, the number of steps of our algorithm grows only as O(n log(n)), and that it samples very well the set of all stable marriages. It is thus a fair and efficient approach to generate stable marriages. Furthermore, our approach for SMTI problems is able to solve large problems, quickly returning stable matchings of large and often optimal size, despite the NP-hardness of this problem. The original stable marriage problem requires all men and women to submit a complete and strictly ordered preference list. This is obviously often unrealistic in practice, and several relaxations have been proposed, including the following two common ones: one is to allow an incomplete list, i.e., a man is permitted to accept only a subset of the women and vice versa. The other is to allow a preference list including ties. Fortunately, it is known that both relaxed problems can still be solved in polynomial time. In this paper, we show that the situation changes substantially if we allow both relaxations (incomplete lists and ties) at the same time: the problem not only becomes NP-hard, but also the optimal cost version has no approximation algorithm achieving the approximation ratio of N1-Ɛ, where N is the instance size, unless P=NP. The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed. It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially we can obtain a 2-approximation algorithm. In this article, we give the first nontrivial result for approximation of factor less than two. Our algorithm achieves an approximation ratio of 2 (1 p L−2) for instances in which only men have ties of length at most L. When both men and women are allowed to have ties but the lengths are limited to two, then we show a ratio of 13 7( 1.1052). We consider Stable Marriage with Covering Constraints (SMC): in this variant of Stable Marriage, we distinguish a subset of women as well as a subset of men, and we seek a matching with fewest number of blocking pairs that matches all of the distinguished people. We investigate how a set of natural parameters, namely the maximum length of preference lists for men and women, the number of distinguished men and women, and the number of blocking pairs allowed determine the computational tractability of this problem. This research compares and analyzes the verbal commentary of televised coverage of two women's and men's athletic events: the “final four” of the women's and men's 1989 National Collegiate Athletic Association (NCAA) basketball tournaments and the women's and men's singles, women's and men's doubles, and the mixed-doubles matches of the 1989 U.S. Open tennis tournament. Although we found less overtly sexist commentary than has been observed in past research, we did find two categories of difference: (1) gender marking and (2) a “hierarchy of naming” by gender and, to a certain extent, by race. These differences are described and analyzed in light of feminist analyses of gendered language. It is concluded that televised sports commentary contributes to the construction of gender and racial hierarchies by marking women's sports and women athletes as “other,” by infantilizing women athletes (and, to a certain extent, male athletes of color), and by framing the accomplishments of women athletes ambivalently. The stable marriage problem is that of matching n men and n women, each of whom has ranked the members of the opposite sex in order of preference, so that no unmatched couple both prefer each other to their partners under the matching. At least one stable matching exists for every stable marriage instance, and efficient algorithms for finding such a matching are well known. The stable roommates problem involves a single set of even cardinality n, each member of which ranks all the others in order of preference. A stable matching is now a partition of this single set into n2 pairs so that no two unmatched members both prefer each other to their partners under the matching. In this case, there are problem instances for which no stable matching exists. However, the present paper describes an O(n2) algorithm that will determine, for any instance of the problem, whether a stable matching exists, and if so, will find such a matching. 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. Given an instance I of the classical Stable Marriage problem with Incomplete preference lists (smi), a maximum cardinality matching can be larger than a stable matching. In many large-scale applications of smi, we seek to match as many agents as possible. This motivates the problem of finding a maximum cardinality matching in I that admits the smallest number of blocking pairs (so is ''as stable as possible''). We show that this problem is NP-hard and not approximable within n^1^-^@e, for any @e>0, unless P=NP, where n is the number of men in I. Further, even if all preference lists are of length at most 3, we show that the problem remains NP-hard and not approximable within @d, for some @d>1. By contrast, we give a polynomial-time algorithm for the case where the preference lists of one sex are of length at most 2. We also extend these results to the cases where (i) preference lists may include ties, and (ii) we seek to minimize the number of agents involved in a blocking pair. T his document is the report of a workshop that convened a group of experts to discuss the recruitment and retention of women in Computer Science and Engineering (CSE) Graduate Programs. (1) Participants included long-time members of the CSE academic and research communities, social scientists engaged in relevant research, and directors of successful retention efforts. (2) The report is a compendium of the experience and expertise of workshop participants, rather than the result of a full-scale, scholarly study into the range of issues. Its goal is to provide departments with practical advice on recruitment and retention in the form of a set of specific recommendations. Women are significantly underrepresented in CSE academic departments [5][40]. As computing technology becomes increasingly pervasive, this underrepresentation translates into a loss of opportunity for individuals, a loss of talent to the workforce, and a loss of creativity in shaping the future of society. While there are many causes of this underrepresentation some rooted in early socialization and primary educational experiences academic departments at the university level nevertheless can have an effect [6][7]. In particular, an improvement at the graduate level in recruitment and retention (and thus in graduation rates) would enable more women to move into visible and influential positions in the CSE community. The increasing presence of these women would provide positive role models and mentors. In order to treat all students fairly, educators must pay attention to gender-based traits. Although in characterizing behaviors one must be careful to acknowledge the existence of individual differences and to avoid stereotyping, there is a large body of information on gender traits. There is strong evidence, for example, that women, even though they perform at the same levels, have less confidence in their abilities and individual accomplishments than men [2][17][36][39][43]. Women are often less aggressive than male students in promoting themselves, attempting new or challenging activities, and pursuing awards or fellowships. There is evidence that females come to computing as only one interest among many, and are thus less single-minded than their male counterparts [27]. Often women report feeling "out of place" in the male-dominated, hacker culture [3] [22] [28]. In light of such differences, some of our recommendations are gender-specific. Most, however, are not. The adoption of our recommendations would improve the educational environment for all students. The recommendations are given in two sections, the first Historically, papers have been physically bound to the journal in which they were published; but in the digital age papers are available individually, no longer tied to their respective journals. Hence, papers now can be read and cited based on their own merits, independently of the journal's physical availability, reputation, or impact factor (IF). We compare the strength of the relationship between journals' IFs and the actual citations received by their respective papers from 1902 to 2009. Throughout most of the 20th century, papers' citation rates were increasingly linked to their respective journals' IFs. However, since 1990, the advent of the digital age, the relation between IFs and paper citations has been weakening. This began first in physics, a field that was quick to make the transition into the electronic domain. Furthermore, since 1990 the overall proportion of highly cited papers coming from highly cited journals has been decreasing and, of these highly cited papers, the proportion not coming from highly cited journals has been increasing. Should this pattern continue, it might bring an end to the use of the IF as a way to evaluate the quality of journals, papers, and researchers. © 2012 Wiley Periodicals, Inc. We study the behavior of random walks along the edges of the stable marriage lattice for various restricted families of allowable preference sets. In the "k-attribute model," each man is valued in each of k attributes, and each woman's ranking of the men is determined by a linear function, representing her relative ranking of those attributes; men's rankings of the women are determined similarly. We show that sampling with a random walk on the marriage lattice can take exponential time, even when k = 2. Moreover, we show that the marriage lattices arising in the k-attribute model are more restrictive than in the general setting; previously such a restriction had only been shown for the sets of preference lists. The second model we consider is the "k-range model," where each person lies in a position in [i, i + k - 1], for some i, on every preference list of the opposite sex. When k = 1 there is a unique stable marriage. When k = 2 there already can be an exponential number of stable marriages, but we show that a random walk on the stable marriage lattice always converges quickly to equilibrium. However, when k ≥ 5, there are preference sets such that the random walk on the lattice will require exponential time to converge. Lastly, we show that in the extreme case where each gender's rankings of the other are restricted to one of just a constant k possible preference lists, there are still instances for which the Markov chain mixes exponentially slowly, even when k = 4. This oversimplification of the general model helps elucidate why Markov chains based on spouse-swapping are not good approaches to sampling, even in specialized scenarios. This article examines how men and women differ in both their perceptions of the risks associated with shopping online and the effect of receiving a site recommendation from a friend. The first study examines how gender affects the perceptions of the probability of negative outcomes and the severity of such negative outcomes should they occur for five risks associated with buying online (i.e., credit card misuse, fraudulent sites, loss of privacy, shipping problems, and product failure). The second study examines gender differences in the effect of receiving a recommendation from a friend on perceptions of online purchase risk. The third study experimentally tests whether, compared to men, women will be more likely to increase their willingness to purchase online if they receive a site recommendation from a friend. The results suggest that, even when controlling for differences in Internet usage, women perceive a higher level of risk in online purchasing than do men. In addition, having a site recommended by a friend leads to both a greater reduction in perceived risk and a stronger increase in willingness to buy online among women than among men. Ranked lists are encountered in research and daily life and it is often of interest to compare these lists even when they are incomplete or have only some members in common. An example is document rankings returned for the same query by different search engines. A measure of the similarity between incomplete rankings should handle nonconjointness, weight high ranks more heavily than low, and be monotonic with increasing depth of evaluation; but no measure satisfying all these criteria currently exists. In this article, we propose a new measure having these qualities, namely rank-biased overlap (RBO). The RBO measure is based on a simple probabilistic user model. It provides monotonicity by calculating, at a given depth of evaluation, a base score that is non-decreasing with additional evaluation, and a maximum score that is nonincreasing. An extrapolated score can be calculated between these bounds if a point estimate is required. RBO has a parameter which determines the strength of the weighting to top ranks. We extend RBO to handle tied ranks and rankings of different lengths. Finally, we give examples of the use of the measure in comparing the results produced by public search engines and in assessing retrieval systems in the laboratory. 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). Such problems are more expressive than the classical stable marriage problems. Moreover, in some real-life situations it is more natural to express scores (to model, for example, profits or costs) rather than a qualitative preference ordering. In this context, we define new notions of stability and optimality, and we provide algorithms to find marriages which are stable and or optimal according to these notions. While expressivity greatly increases by adopting weighted preferences, we show that in most cases the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem. Basow continues to present a balanced view of the literature on both men and womens gender roles, with thorough attention to the empirical research. In a field that is generating research at an amazing pace, Basow provides the most comprehensive, most up-to-date and most research-oriented book available, presenting all the current findings in psychology and sociology, as well as biology, political science, and anthropology. She covers both the "old" topics related to gender as well as new concerns in the field, such as AIDS and data on changing families. Our science, technology, engineering and math (STEM) workforce is crucial to America’s innovative capacity and global competitiveness. Yet women are vastly underrepresented in STEM jobs and among STEM degree holders despite making up nearly half of the U.S. workforce and half of the college-educated workforce. That leaves an untapped opportunity to expand STEM employment in the United States, even as there is wide agreement that the nation must do more to improve its competitiveness.Although women fill close to half of all jobs in the U.S. economy, they hold less than 25 percent of STEM jobs. This has been the case throughout the past decade, even as college-educated women have increased their share of the overall workforce.Women with STEM jobs earned 33 percent more than comparable women in non-STEM jobs – considerably higher than the STEM premium for men. As a result, the gender wage gap is smaller in STEM jobs than in non-STEM jobs.Women hold a disproportionately low share of STEM undergraduate degrees, particularly in engineering.Women with a STEM degree are less likely than their male counterparts to work in a STEM occupation; they are more likely to work in education or healthcare.There are many possible factors contributing to the discrepancy of women and men in STEM jobs, including: a lack of female role models, gender stereotyping, and less family-friendly flexibility in the STEM fields. Regardless of the causes, the findings of this report provide evidence of a need to encourage and support women in STEM. This paper studies the gender compensation gap among high-level executives in US corpora- tions. We use the ExecuComp data set that contains information on total compensation for the top five highest paid executives of a large group of US firms over the period 1992-1997. About 2.5 of the executives in the sample are women. These women earn about 45 less than their male counterparts. As much as 75 of this gap can be accounted for by the fact that women manage smaller companies and are less likely to be CEO; Chair, or President of their company. The unexplained gender gap can be reduced to less than 5 when one further accounts for the fact that female executives are younger and have less seniority than male executives. Over the period under study, women have nearly tripled their participation in the top executive ranks and have also strongly improved their relative compensation, mostly by gaining representation into the larger corporations. While the absence of a significant conditional gender gap implies that women and men who hold similar jobs in firms of similar size receive fairly equal treatment in terms of compensation, it does not rule out the possibility of discrimination in terms of gender segregation or promotion. We consider a two-sided market under incomplete preference lists with ties, where the goal is to find a maximum size stable matching. The problem is APX-hard, and a 3 2-approximation was given by McDermid [1]. This algorithm has a non-linear running time, and, more importantly needs global knowledge of all preference lists. We present a very natural, economically reasonable, local, linear time algorithm with the same ratio, using some ideas of Paluch [2]. In this algorithm every person make decisions using only their own list, and some information asked from members of these lists (as in the case of the famous algorithm of Gale and Shapley). Some consequences to the Hospitals Residents problem are also discussed.