How satisfied should you expect to be with your partner?

I replicated this review, which you can check out in this colab notebook (I get much higher performance running it locally on my 20-core CPU).

There is only one cluster of discrepancies I found between my analysis and Vaniver's: in my analysis, mating is even more assortative than in the original work:

• Pearson R of the sum of partner stats is 0.973 instead of the previous 0.857
• 99.6% of partners have an absolute sum of stats difference < 6, instead of the previous 83.3%.
• I wasn't completely sure if Vaniver's "net satisfaction" was the difference of self-satisfaction and satisfaction with partner or perhaps the log average ratio. I used the difference (since theoretically self-satisfaction could be zero, which would make the ratio undefined). Average net satisfaction was downshifted from Vaniver's result. The range I found was $[-.4,1]$, while Vaniver's was $[-.2,1.2]$.

In Vaniver's analysis, $corr$ represents an adjustable correlation between a person's preferences and their own traits. Higher values of $corr$ result in a higher correspondence between one's own preferences and one's own traits.

One important impact of this discrepancy is that the transition between being on average more self-satisfied than satisfied with one's partner occurs at around $corr=0.5$ rather than $corr=0.75$, which intuitively makes sense to me, given the highly assortative result and the fact that the analysis directly mixture an initial set of preferences with some random data to form the final preferences as a function of $corr$.

Can we ground these results in empirical data, even though we can't observe preferences and stats with the same clarity and comprehensiveness in real-world data?

One way we can try is to consider the "self-satisfaction" metric we are producing in our simulation to be essentially the same thing as "self-esteem." There is a literature relating self-esteem to partner satisfaction in diverse cultures longitudinally over substantial periods of time. As we might expect, self-esteem, partner satisfaction, and marital satisfaction all seem to be interrelated.

• Predicting Marital Satisfaction From Self, Partner, and Couple Characteristics: Is It Me, You, or Us?
  • Men and women had similar scores in personality traits of social potency, dependability, accommodation, and interpersonal relatedness.
  • Broadly, self-satisfaction, partner-satisfaction, and having traits in common are all positively associated with marital satisfaction.
• Partner Appraisal and Marital Satisfaction: The Role of Self-Esteem and Depression
  • "Regardless of self-esteem and depression level, and across trait categories, targets were more maritally satisfied when their partners viewed them positively and less satisfied when their partners viewed them negatively."
• The Dynamics of Self–Esteem in Partner Relationships
  • "[S]elf–esteem and all three aspects of relationship quality are dynamically intertwined in such a way that both previous levels and changes in one domain predict later changes in the other domain."
• Relationships between self-esteem and marital satisfaction among women
  • "Marital satisfaction was found to be positively correlated with self-esteem in both cities, so that higher self-esteem was associated with greater satisfaction."
• Development of self-esteem and relationship satisfaction in couples: Two longitudinal studies.
  • "Second, initial level of self-esteem of each partner predicted the initial level of the partners’ common relationship satisfaction, and change in self-esteem of each partner predicted change in the partners’ common relationship satisfaction. Third, these effects did not differ by gender and held when controlling for participants’ age, length of relationship, health, and employment status. Fourth, self-esteem similarity among partners did not influence the development of their relationship satisfaction. The findings suggest that the development of self-esteem in both partners of a couple contributes in a meaningful way to the development of the partners’ common satisfaction with their relationship."
• A Mediation Role of Self-Esteem in the Relationship between Marital Satisfaction and Life Satisfaction in Married Individuals
  • "According to the findings of the study, the mediation self-esteem between the marital satisfaction and life satisfaction was statistically significant (p<.001). The whole model was significant (F(5-288)= 36.71, p<.001) and it was observed that it explained 39% of the total variance in the life satisfaction. Self-esteem was positively associated with marital satisfaction and considered one of the most important determinants of life satisfaction."

Finally, I wonder what the value of $corr$ is likely to be for participants of rationalist culture? A culture that promotes individual agency and self-improvement, that acknowledges serious challenges in our dating culture, our culture's egalitarian values, the far larger degree of control we have over ourselves than our partners, and the tendency for people to seek a self-justifying, optimistic narrative, all seem to me to point in the direction of $corr$ being high. That would suggest a rationalist culture with perhaps higher levels of self-esteem than partner-esteem. Fortunately, that says nothing at all about the absolute level of self- and partner-esteem, which I hope are on average high.

I can't disagree with Vaniver's conclusion that people are "mostly being serious" when they describe their partner as their better half. But I think the results of my reanalysis and my speculation on the value of `corr` (at least in rationalist-type culture) make me think this isn't because people are accurately appraising their partner as satisfying their own preferences better than they do themselves.

I looked around a bit more on Google Scholar (to be honest, just starting with the phrase "my better half"), and found a couple studies.

• My Better Half: Strengths Endorsement and Deployment in Married Couples
  • "The present study focuses on married partners’ strengths endorsement and on their opportunities to deploy their strengths in the relationship, and explores the associations between these variables and both partners’ relationship satisfaction. The results reveal significant associations of strengths endorsement and deployment with relationship satisfaction, as expected. However, unexpectedly, men’s idealization of their wives’ character strengths was negatively associated with relationship satisfaction."
  • 
  • This is on a scale from 1-5 (p < .05).

 Is it me or you? An actor-partner examination of the relationship between partners' character strengths and marital quality

• "[W]e examined the effects of three strengths factors (caring, self-control, and inquisitiveness) of both the individual and the partner on marital quality, evaluated by indices measuring marital satisfaction, intimacy, and burnout. Our findings revealed that the individual’s three strengths factors were related to all of his or her marital quality indices (actor effects). Moreover, women’s caring, inquisitiveness and self-control factors were associated with men’s marital quality, and men’s inquisitiveness and self-control factors were associated with women’s marital quality (partner effects)."

So idealizing your partner looks like a neutral-to-negative behavior. Inquisitiveness looks like a trait that both genders value. It strikes me that there are many things that you can do for your partner that they can't do for themselves - positive and negative. They can't praise or idealize themselves (or it won't come off the same way, anyway). They can't ask themselves "how was your day?" They can't give themselves a hug in a difficult moment, or if they do, it doesn't feel the same as when their partner does it.

No matter how effective you are at operating in the world, there are certain things that you just cannot do for yourself. In many areas of life, only your partner can. That seems like good reason to call them your better half.

Congratulations on getting married!

In the Gale-Shapley algorithm, there is an asymmetry between the two genders. One gender (typically the male) is proposing while the other is choosing. The resulting matching is the optimal stable matching for each member of the proposing gender, so I would think it makes a huge difference for your expected level of satisfaction if you belong to the proposing gender or the choosing gender. 

Are your statistics about both genders or just one of them? In either case, I would love to see separate statistics for the two genders. 

Congratulations! I enjoyed reading this, it makes me slightly more optimistic towards towards dating.

This post is very cute. I also reference it all the time to explain the 'inverse cat tax.' you You can ask my colleagues, I definitely talk about that model a bunch. So, perhaps strangely, this is my most-referenced post of 2022. 🙃

My explanation of a model tax: this forum (and the EA Forum) really like models, so to get a post to be popular, you gotta put in a model.

Great post! Intuitively, it feels like allowing for negative preferences (i.e. disliking something that other people like, like chattiness or introversion) would actually increase equitableness and maybe allow for increased other-satisfaction. (Depending on what distribution we draw people from)