Climbing out of the rabbit hole

After a long hiatus I have decided to add to this little blog some more. I stopped for so long because my previous posts sent me down an unexpected rabbit hole. What was supposed to be a simple question, “what are emotions?” which I was asking simply to lay the foundation for a different question, put me onto a mission to find and explore what I believe to be a better answer than what was available. I stopped blogging because I was initially hoping to publish these ideas and, for some academic journals, blogging constitutes publishing in another venue. Since then, though, my life plans have moved away from academia and racking up publications is no longer that important. I have other goals for my work so I am not ready to spell everything out (the model has come a long way since the previous posts on this blog) but thinking and learning about emotions has led me to enough tangential ideas that I think I can justify taking another crack at blogging. So, let me tell you about my adventures in Wonderland…

Tuesday 12 November 2013

The Love Equation

Love is a complicated thing and finding someone who you can love and who will love you back is the first step down that desirable but complicated path. Making a romantic match is like matching two puzzle pieces when each piece is a puzzle itself. We have to consider all the complexities of each person and then only once we have a good picture of the individuals can we consider how well they would fit as a couple. But what actually determines fit? Both old wisdom and new science tell us a lot about what makes a good fit and the list is pretty long. It includes similar social and economic class, similar intelligence and physical attractiveness, similar political and religious views, difference in dominant vs. submissive, etc. These factors are a jumble, though, they all seem to help but none of them appear necessary or sufficient. Dating services work by shoving all of these factors together and then rating partners on how well they match up. This works because that’s the best service they can offer since they have a limited pool. They match you with your first, second, third, etc. best match until enough of the unmeasured factors also match up. What dating services can’t do is identify that threshold point between success and failure. To do that we need a unified framework that considers all of the factors together. This is where ecology steps in [1].

Ecologists study how populations interact with themselves and other species and one of our key areas of focus is studying biodiversity: the number and types of species present in an area. To study how biodiversity is actually maintained, ecologists have devoted a lot of effort to understanding how species coexist, particularly how competitors (species which use similar resources and face similar threats) are able to coexist. The problem is that no species is actually trying to coexist with its competitors. If a species could kick out all of its competitors, all the better. So the only reason the best competitor in any environment doesn’t just kick out the less well adapted species is that it can’t. The rule ecologists have found is \[\frac{\text{Lesser species' effect on lesser species}}{\text{Better species' effect on lesser species}}>\frac{\text{Fitness of better species}}{\text{Fitness of lesser species}} \]
The right side of the equation says that coexistence gets harder as the stronger species gets better adapted than the lesser species. Basically, it’s easier to coexist when both species are more equally adapted to the environment. The left side of the equation says that coexistence gets easier if the species harm themselves more than they are harmed by the other species.

What do I mean by harm? Individuals harm their own species the same way you harm yourself by eating food in your house: the more food you eat the less you have to eat later. Species can harm themselves more than they harm other species if they interact with their environment differently. Imagine two roommates who share food and won’t buy groceries for a while. One roommate eats mostly meat in every meal while the other eats meals that are mostly veggies. Each time the meat-eater makes a meal, that is one less meal available for him but it has little effect on how many more meals the pseudo-vegetarian can make since very few veggies were eaten. Basically, the left side of the equation says that the more complimentary the two species are the easier it is to coexist.

So far we haven’t got anything new. Just like the common wisdom for dating, the more equal species are the more likely they will coexist and the more complimentary they are the more likely they will coexist.

The new contribution from ecology is putting the whole equation together. Species need to be as complimentary as they are unequal. The more equal they are the less complimentary they need to be, the less equal they are the more complimentary they need to be. For relationships, this means that partners only need to be as different in their type of needs and abilities (complementarity; e.g., skilled at making money, friends, or a household, good at dealing with big problems versus many small problems, good at making plans versus dealing with surprises, etc.) as they are different in their ability to meet their needs (quality [2]; e.g., career level, intelligence, wealth, attractiveness, charisma, etc.). Couples can have successful relationships even if they are quite different in quality provided they are very complimentary. Likewise, couples can have successful relationships even if they are very similar in their needs and abilities provided they are also very similar in their ability to meet those needs. Successful relationships can be found everywhere between these extremes, the two aspects just need to balance.

Translating from ecology, the Love Equation is as follows. For a romantic relationship to be successful, the following equation must be true for both partners: \[\frac{\text{Quality of partner}}{\text{Quality of self}}<\frac{\text{Value of my partner's abilities to myself}}{\text{value of my abilities to myself}} \]
where quality is judged objectively by society as a whole. The Love Equation nicely separates out the two key aspects of a successful relationship: equality and complementarity. To further justify this equation, if we remove objectivity and instead view the criterion from the perspective of those in the relationship it simplifies down to the intuitive \[\text{Percieved quality of partner}>\text{Percieved quality of self}\]
where quality is being perceived, subjectively,  by both partners in the relationship. This equation is just a formalization of common wisdom. Both partners should feel they are “lucky” to be in the relationship. More precisely, they should value their partner’s contributions to the relationship more than their own contributions. 

The Love Equation tells us the minimum requirement for a loving and complete romantic relationship. Unfortunately, relationships don’t exist in a vacuum so there are three external factors which can interfere: (1) changes in circumstances, (2) differences in goals and values, and (3) other potential partners. Changes in circumstances will happen over the course of a relationship and can disrupt the relationship by changing the values in the Love Equation. Differences in goals and values increase the vulnerability of the relationship to changes in circumstance by increasing the likelihood that one partner will be affected more than the other, reducing equality. Finally, if there are lots of alternative partners available it is more likely that a small reduction in equality or complementarity will make a different partner more attractive than the current one (better potential partners can also make a potentially loving relationship undesirable to begin with). Fortunately, the way to guard against these factors is simply to start with a relationship with more equality and complementarity. 

That’s the equation for love. A relationship can be built without meeting the Love Equation but it will not develop into a fully developed intimate relationship. A stable and loving partnership requires that individuals be complimentary enough to offset differences in quality. There are two things I would like you to take away from this equation. First, partners need to be similar and different, similar in their ability to achieve but different in their approach, but how they go about being similar and different can vary enormously. While rather cliché, it is entirely possible for a loving relationship to be built on one partner being wealthy or powerful while the other is physically attractive, it’s just a little more vulnerable to changing circumstances. The second thing is that partners only need to be as complimentary as they are different in quality. For example, a relationship can survive two very dominant personalities provided the couple are also very equal.

So, when looking for love keep the Love Equation in mind to keep you realistic about what will work, despite advice to the contrary, and what won’t work, despite you really wanting it (i.e., give up on that celebrity crush). That being said, one of your brain’s main jobs is figuring this all out behind the scenes so just trust your heart and make sure that you both feel lucky.




[1] This is a shortened and simplified version of a more technical and nuanced post available at http://evolutionandemotions.blogspot.ca/2013/11/LoveAndCoexistence.html
[2] As with species, a person’s quality is entirely conditional on the environment we are considering them in (including everything from broad geography and society to the specific social network). This has two main implications. First, while people are not inherently better or worse than others, people do vary in how successful they appear to be. This is contingent both on how much they are able to achieve in their given environment and how much their achievements matches what is considered successful by the people around them (money, family, athleticism, intellectual/artistic contributions, etc.). The second implication, which follows from the first, is that people will choose to be in an environment in which they have high value. This can be as subtle as choosing to spend time in places where people who value your skills also spend time (e.g., athletics individuals at gyms, intellectual individuals at universities, etc) or as major as moving to another city/country where your strengths and weaknesses are more appropriate. For relationships, this means that partners should be relatively well suited to the same environment such that they are not sacrificing a substantial amount of potential quality to be around each other (for most relationships this isn’t a big deal as future partners tend to only meet because they thrive in the same environment). 

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