Eric D. Widmer
Nguyen, Vi Cao, Fragnière, E., Gauthier, J.-A., Sapin, M., Widmer, E.D. (2010). Optimizing the marriage market: An application of the linear assignment model. European Journal of Operational Research, vol.202, n° 2, pp.547-553.

Research shows that success of marriages and other intimate partnerships depend on objective attributes such as differences of age, cultural background or educational levels between partners. This article proposes a mathematical approach of marriage which intends to optimally allocate spouses in order to reduce the likelihood of divorce within the set of structural constraints defining a marriage market. Based on a representative and longitudinal sample of 1074 cohabitating and married couples living in Switzerland, we estimate various objective functions corresponding to age, education, religion, devotion, ethnicity, psychological well-being and previous divorce experience concerning every possible combination of men and women. Our results show that the current state of marriages or partnerships is well below the social optimum. About 7 individuals over 10 (75%) are reallocated to a couple with a higher chance of survival than the actual couple that they belong to. This reallocation leads the initial non optimal situations to the final optimal situations with a reduction of the objective function by 15% of its initial value.

Love – the Swiss way: sociologists want to « optimize the marriage market »

Cao, N., Fragnière, E., Gauthier, J., Sapin, M., & Widmer, E.D. (2010). Optimizing the marriage market: An application of the linear assignment model. European Journal of Operational Research, 202 (2), 547-553 DOI: 10.1016/j.ejor.2009.06.009

A lifetime ago – when I was still a university student in Italy – I bumped into an old article discussing marital matters in what for me was a very unusual way: modelling the utility functions of two partners getting intimate in bed (an occupation evocatively referred to as “activity X”…hummm!). “When love exists”, the author maintained, “each spouse’s marginal utility from x depends on both one’s own and one’s spouse’s consumption of hours in bed” (Hoffman, 1977).

If I indulge in reminescence here, it’s only to suggest that, after having spent my formative years dealing with such weirdness, the article I deal with today, published by the European Journal of Operational Research, shouldn’t come as a surprise. And yet, I’m still a little startled when I read of someone adopting a mathematical approach to marriage. Don’t get me wrong. I’m not saying that all mathematical approaches to social phenomena should be rebuked. I’m not that kind of person. Please allow me to develop on this.

Eric D. Widmer, a professor at the department of Sociology of the University of Geneva, and his team have produced an interesting research about optimizing the chances of finding the right partner. Based on a representative and longitudinal sample of 1074 Swiss couples (cohabiting and married), they estimated various objective functions corresponding to age, education, ethnicity, and previous divorce experience.

To be more precise:

1.Evidence suggests that the soundest couples are those where the husband is 5 years older than his wife – the appeal of a mature man, I suppose. Or maybe, the charms of a younger woman to an older man, who knows…

2.Successful couples show also another feature: wives have a higher level of education than their husbands. Definitely the charms of a young and smart Swiss woman play a role there… Or maybe some rigidities of the Swiss labour market which doesn’t seem to encourage women’s labour force participation to the same level as other developed countries. Or at least, didn’t seem back in 1999, when the family survey data started to be collected.

3.Moreover, the couples less prone to divorce are those where both partners haven’t been through divorce before. The hypothesis is that those who never experienced divorce don’t know their ways around lawyers and paperwork, thus displaying a higher level of aversion for this uncertain course of action.

4.Last but not least, the most successful couples are those where both partners are of Swiss nationality. Cultural homogamy triumphs! In your face, neighbour who married a hot Brazilian woman that left you after two years of love and torrid sex because she could not stand eat fondue with your friends in a ski resort every goddamn weekend! (This last bit, might or might not actually be in the article…).
So far, so good. Despite the slight creepiness of that last result, it’s just classical correlation, logistic regressions and whatnot to assess the effects of homogamy on marital stability. Of course there’s nothing wrong with the idea of weighing up the chances of living “happily ever after” by minimizing the causes of divorce. After all, other researches have shown that this is the micro-motive behind the success of many a contemporary matchmaking service (Mazzarella, 2007).

But things get a little, well… peculiar when Swiss researchers discover that, according to their results, the current state of marriages or partnerships in their country is well below the social optimum. So they came up with a linear assignment mathematical model through which a “central agency” would reallocate partners in an optimal way. It is not clear who or what this central agency is. A bigbrotheresque online dating agency? A government agency? The optimization model, created using the General Algebraic Modeling System (GAMS), allows the researchers to reallocate the partners in more efficient ways. As a result, approximately 68% of individuals are “reallocated to a new couple” with a higher likelihood of survival. With a 21% reduction in the objective function, we get closer to “the final optimal solution”. (Just remove one the last two adjectives and you’ll appreciate the creepiness of it all…)

Of course the reason why I act all grumpy about this article is the political echo of the survey data plus the model revolving around a shadowy “central agency” supposed to put it to good use. I mean, the analysis is accurate, the model is sound, and the researchers are entitled to adopt whatever approach they deem appropriate to study homogamy. But the very way this article has been spinned by the media is questionable. Exemplary from this point of view is the right-wing French-speaking newspaper Le Matin which, on October 29th 2009, devoted an entire page to the study. The results where summarized as follows: “A Swiss man with a Swiss woman, that’s going to last. If one of the two partner is not of Western ethnicity, the marriage is four times more likely to end up in a divorce”. And the best part is this illustration where a guy with a caracteristic Hitler hairdo holds hands with an Aryan-type bimbo.

This kind of media manipulation is all the more disturbing in light of the fact that Eric Widmer has a proven track record as a brilliant sociologist who definitely cannot be accused of being a political reactionary. On the contrary, the bulk of his research can be regarded as fostering social progress and tolerance: he has deconstructed the social representations of the « feeling of insecurity » prevailing in several European countries and showed that it is more related to attitudes towards modernisation than to an actual rise in criminality figures (Widmer et al., 2004) and more recently he has fostered social recognition of non-standard family configurations by applying his FNM (Family Network Method) to several types of unrecognized partnerships (Widmer et al., 2007).

Emily P. Hoffman (1977). The Deeper Economics of Sleeping: Important Clues toward the Discovery of Activity X, Journal of Political Economy, 85 (3): 647-650.

Mazzarella, S. R. (. (2007). Cyberdating success stories and the mythic narrative of living « happily-ever-after with the one ». In M. Galician, & D. L. Merskin (Eds.), Critical thinking about sex, love, and romance in the mass media. Mahwah, NJ, Erlbaum: 23-37.

Widmer, E.D., Languin, N., Pattaroni, L., Kellerhals, J., Nills-Robert, C. (2004). Du sentiment d’insécurité aux représentations de la délinquance. Déviance et société. 28(2): 141-157.

Widmer, E.D., Robert-Tissot, C., Sapin, M. (2007). Intimités conjugales et configurations familiales. Une application du Family network method aux populations cliniques. In : Burton-Jeangros, C. Widmer, E.D., Lalive d’Epinay, C. (eds). Interactions familiales et constructions de l’intimité. Paris, L’Harmattan: 381-398.

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