Manipulation and gender neutrality in stable marriage procedures
نویسندگان
چکیده
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.
منابع مشابه
Stability, Optimality and Manipulation in Matching Problems with Weighted Preferences
The stable matching problem (also known as 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....
متن کاملWhere are the hard manipulation problems?
One possible escape from the Gibbard-Satterthwaite theorem is computational complexity. For example, it is NP-hard to compute if the STV rule can be manipulated. However, there is increasing concern that such results may not reflect the difficulty of manipulation in practice. In this tutorial, I survey recent results in this area. The Gibbard Satterthwaite theorem proves that, under some simple...
متن کاملStability and Optimality in Matching Problems with Weighted Preferences
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...
متن کاملMale optimal and unique stable marriages with partially ordered preferences
The stable marriage problem has a wide variety of practical applications, including matching resident doctors to hospitals, and students to schools. In the classical stable marriage problem, both men and women express a strict order over the members of the other sex. Here we consider a more realistic case, where both men and women can express their preferences via partial orders, i.e., by allow...
متن کاملMarriage Formation in Context: Four Decades in Comparative Perspective
Marriage formation is deeply embedded in societal context. This study documents trends towards lower marriage rates and delayed marriage in Europe and the US. Using time series analyses, it shows the relevance of economic and gender context in understanding marriage formation. The study extends previous work by including more countries, a longer time period, and by examining changes in predicto...
متن کامل