The other “Indian Matchmaking”
How an important concept explains Indian realities
If you’re Indian, you probably don’t need another introduction to Sima Aunty, and she is doing an important job of “matchmaking”. This can nicely be described using graphs, where “matchings” are essentially “one-one” mappings between two sets of nodes.
So in Figure 1, X and Y correspond to the men and women in the show, with the edges depicting possible matches and the ones in blue representing a “matching”. If nobody is left out in X, then we call that a “perfect matching” with respect to X.
For perfect matches to exist, there is a very well-known result called Hall’s theorem, that gives a simple condition to evaluate. For every subset of one side |S|, the number of its neighbours |N(S)| on the other side is at least as large as the size of the subset (|N(S)| ≥ |S|)
This straightaway gives many situations where perfect matchings are not possible and would entail interesting social situations. For example:
- If the men outnumber the women
- Even when there is a surplus of women and if a set of men are hellbent on matching with one person
In the above situations, a perfect matching would not exist as a direct result of Hall’s theorem.
But this is just one such situation where there is a lack of perfect matching. In fact, there are many real-life situations where there is “imbalance” and these matching situations are known for interesting dynamics.
Imbalance and its Effects
Imbalanced matching markets [1] occur when there is a significant disparity between the number of seekers (those seeking a match) and providers (those offering the match). This discrepancy often leads to inefficiencies, disparities in outcomes, and some cases, unethical practices due to the huge incentives offered by it.
Under the effects of competition, it is not just sufficient to have perfect matchings, but “stable matchings”, where each side has preferences. Also, there are no pairs of elements, one from each side, who both prefer each other over their current partners. These have very interesting properties, particularly in situations where there is an imbalance.
Consider the experiment where there are varying numbers of men but a fixed number of women and preferences are random. Then, as shown in Figure 3, even a slight imbalance causes the average preference obtained to shoot up and it also grows with an increase in the magnitude of imbalance. Note that the side that is in shortage gets roughly their first preference irrespective of the imbalance and who is proposing.
The Indian Context
What is interesting to note is Indians have to encounter multiple extremely “imbalanced matching markets” over the course of their lives. Some of those (in roughly chronological order include):
- Education — School and College Admission
- Transportation — Ticket Reservations, Rush Hour Chaos
- Matchmaking — Gender Imbalance
- Employment — Job Search
- Real Estate — Land for Purchase, Rental Availability
- Healthcare — Bed Availability
As mentioned in the previous section, more than the high population, it is the imbalance that causes the extremes of competition. For education and employment, the imbalance ratio is of the order of hundreds or even thousands. This is one of the driving factors for immigration where people prefer moving to countries with more favourable markets and not have to repeatedly encounter such highly competitive situations. However, immigration itself is an option available only to a select few, and for some pathways, as a lottery, thus creating a “pressure cooker” situation for the current generation.
Also, when the ranking is very close and slight advantages would bring one to the top of the preference list, there would be significant pressure to use unfair means and get ahead, thus giving rise to corruption.
Summary
This article discusses the concept of matching markets. First, the ideas of perfect matchings and Hall’s theorem are introduced. Then, stable matchings are presented and how they are more reflective of real-life situations, particularly when there is imbalance along with interesting dynamics. Various real-life examples are provided in the Indian context and how the imbalance contributes to intense competition. Additionally, it touches on the potential rise of unethical practices and corruption in highly competitive scenarios. Thus, efforts must be directed towards reducing the occurrence and imbalance of matching markets in various facets of life in India for better standard of living.
References
[1] Ashlagi, I., Kanoria, Y., & Leshno, J. D. (2017). Unbalanced random matching markets: The stark effect of competition. Journal of Political Economy, 125(1), 69–98.
