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Register a new userInstability in Stable Marriage Problem: Matching Unequally Numbered Men and Women
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The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of questions have been extensively studied in this field. This article considers a generalized form of stable marriage problem, where different numbers of men and women need to be matched pairwise and the emergence of single is inevitable. Theoretical analysis and numerical simulations confirm that even small deviations from equal number of two sides can have a large impact on matching solution of Gale-Shapley Algorithm. These results provide insights to many of the real-world applications when matching two sides with unequal number.
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Are you having trouble getting married? These days, there are lots of products on the market for dating, from apps to websites and matchmakers, but we know a simpler way! Thats right -- your path to coupled life isnt through Tinder: its through Sudoku! Read our fabulous paper where we explore the Stable Marriage Problem to help you find happiness and stability in marriage through math. As a bonus, you get two Sudoku puzzles with a new flavor.
Cultural products are a source to acquire individual values and behaviours. Therefore, the differences in the content of the magazines aimed specifically at women or men are a means to create and reproduce gender stereotypes. In this study, we compare the content of a women-oriented magazine with that of a men-oriented one, both produced by the same editorial group, over a decade (2008-2018). With Topic Modelling techniques we identify the main themes discussed in the magazines and quantify how much the presence of these topics differs between magazines over time. Then, we performed a word-frequency analysis to validate this methodology and extend the analysis to other subjects that did not emerge automatically. Our results show that the frequency of appearance of the topics Family, Business and Women as sex objects, present an initial bias that tends to disappear over time. Conversely, in Fashion and Science topics, the initial differences between both magazines are maintained. Besides, we show that in 2012, the content associated with horoscope increased in the women-oriented magazine, generating a new gap that remained open over time. Also, we show a strong increase in the use of words associated with feminism since 2015 and specifically the word abortion in 2018. Overall, these computational tools allowed us to analyse more than 24,000 articles. Up to our knowledge, this is the first study to compare magazines in such a large dataset, a task that would have been prohibitive using manual content analysis methodologies.
The matching hypothesis in social psychology claims that people are more likely to form a committed relationship with someone equally attractive. Previous works on stochastic models of human mate choice process indicate that patterns supporting the matching hypothesis could occur even when similarity is not the primary consideration in seeking partners. Yet, most if not all of these works concentrate on fully-connected systems. Here we extend the analysis to networks. Our results indicate that the correlation of the couples attractiveness grows monotonically with the increased average degree and decreased degree diversity of the network. This correlation is lower in sparse networks than in fully-connected systems, because in the former less attractive individuals who find partners are likely to be coupled with ones who are more attractive than them. The chance of failing to be matched decreases exponentially with both the attractiveness and the degree. The matching hypothesis may not hold when the degree-attractiveness correlation is present, which can give rise to negative attractiveness correlation. Finally, we find that the ratio between the number of matched couples and the size of the maximum matching varies non-monotonically with the average degree of the network. Our results reveal the role of network topology in the process of human mate choice and bring insights into future investigations of different matching processes in networks.
In human society, a lot of social phenomena can be concluded into a mathematical problem called the bipartite matching, one of the most well known model is the marriage problem proposed by Gale and Shapley. In this article, we try to find out some intrinsic properties of the ground state of this model and thus gain more insights and ideas about the matching problem. We apply Kuhn-Munkres Algorithm to find out the numerical ground state solution of the system. The simulation result proves the previous theoretical analysis using replica method. In the result, we also find out the amount of blocking pairs which can be regarded as a representative of the system stability. Furthermore, we discover that the connectivity in the bipartite matching problem has a great impact on the stability of the ground state, and the system will become more unstable if there were more connections between men and women.
In this paper, we investigate stable matching in structured networks. Consider case of matching in social networks where candidates are not fully connected. A candidate on one side of the market gets acquaintance with which one on the heterogeneous side depends on the structured network. We explore four well-used structures of networks and define the social circle by the distance between each candidate. When matching within social circle, we have equilibrium distinguishes from each other since each social networks topology differs. Equilibrium changes with the change on topology of each network and it always converges to the same stable outcome as complete information algorithm if there is no block to reach anyone in agents social circle.
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