Imperfect Matching in the World of Matchmaking
Everyone wants to find their soul mate and for many college-educated professionals in China, the preferred method of finding a partner is through hiring a matchmaker. Traditionally, there are expectations for young Chinese, single professionals to seek significant others that are well-off financially and physically attractive. However, according to a recent SCMP article- today’s Chinese young adults are judging potential spouses primarily by a different criterion: education.
Many clients of matchmakers desire more than a basic certification in a field of study; instead, educational degrees from some of the most elite universities in the world are expected. At first glance, this seems understandable. If a person values a potential partner that is highly skilled, then subsequently this person would want to meet someone that has been educated at a prestigious university. However, this emphasis on education seems to cause a new problem in the world of dating in China.
China’s gender imbalance means there are millions of unmarried men, according to the New York Times. Compound this fact with the rising standards tied to a person’s “value” as a potential partner and there’s no wonder that millions of men, especially those of low-income, feel shut out from the dating world. And where there are so many unmatched men, there are imperfect matchings.
A perfect matching is a configuration of a bipartite graph such that each node on one side of the graph is assigned to a unique node on the other side of the graph. Just like in a perfect matching, a matchmaker would want to “assign” their clients to potential matches in such a way that each client will be matched with someone. However, since a person has some “value” that they are judged by, this assigned value and the gender imbalance creates many constricted sets since many people may be interested in more educated partners, leaving the less educated unmatched.
Suppose a matchmaker is trying to pair three clients with three potential matches. One would think that since the number of people on each side of the bipartite graph is even, there would be a perfect matching. However, suppose one potential match is a rural farmer, another is a college educated office worker at Tencent, and the last one is a lawyer that attended Peking University. The three clients will probably all value the lawyer very highly. One client may rank the office worker lower than the lawyer, but more than likely the farmer will be given the lowest valuation from all three clients. So even if the matchmaker is able to match each client such that the clients’ valuations are maximized and they get a date (meaning the matchmaker has made an optimal assignment), there’s going to be at least one person unhappy with their match. Therefore, there’s a balance that must always be considered when attempting to optimize a variable in a situation and an individual’s satisfaction with an outcome that results from that optimization.
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