We Both Win: Non-zero sum relationships

Hi! We’re Boots and the Brain. Alan is professor who often talks about brains (but not today) and Sarah is the boots on the ground (esoteric translating into useful). We basically just like each other a lot and talk to each other a lot and that’s why our substack has back and forth, too. Without further ado, here’s a piece by Alan…

Photo by Michał Parzuchowski on Unsplash

Disclaimer: The original post encased two complementary but contradictory thoughts. One, that relationships follow the rules of non-zero sum game play and the other, you guessed it, relationships are zero sum. So, I decided to split it in half. The next is soon to follow…

When anyone in the family comes home, they are met by our ecstatic dog. He jumps, he whines, he wiggles, and he wags. It’s not just that he’s pleased to see us, it’s more like he’s welcoming a soldier-returning-from-war-heart-busting happy.

Sarah: Even if it’s only been 2-3 minutes.

It’s cute, it’s charming, and everyone wins.

However, the cats, the cats just don’t care.

Conversely, if a guest enters the house, then he growls, he snarls, and he barks. It’s annoying, it’s a pain, and everyone is, well, just not happy.

Sarah: And the cats, the cats still just don’t care.

This got me thinking about social interactions and how they can be classified into two or three basic types:

1) Zero-sum: The sum benefit at end of the exchange is equal to the sum at beginning. For example, when the gains of person 1 are equal to the losses of person 2. Think: poker.

2) Positive-sum [type of non-zero-sum]: The sum benefit at the end of the exchange is greater than the sum at the beginning. For example, when both person 1 and person 2 gain. Think: love.

3) Negative-sum [type of non-zero-sum]: The sum benefit at the end of the exchange is less than the sum at the beginning. For example, when the losses of person 1 are more than what person 2 gains. Think: war.

Sarah: And the other negative-sum where both lose, like divorce.

Zero-sum games are very familiar to us. In most zero-sum games, a quantity of something of value exists at the beginning of the game and the players compete to maximize ownership. Poker is a great example both on the microscale and the macroscale. On a given hand, the total sum of money in the game stays the same and the distribution is changed through play. Over a series of games players dropout as their funds zero out and, given time, a single individual can eventually accumulate the entirety of the cash. This macroscale zero-sum feature is true of most sports (where the thing of value is winning).

A popular non-zero-sum example is the prisoner’s dilemma. It’s a classic. So, remember the last time you and your buddy were arrested?

Sarah: I do! We were playing poker in an underground gambling den…

You were put in two different rooms and the cops offer to go easy on you if you spill the beans. These are the outcomes:
1) you and your friend keep quiet and walk
2) you spill the beans, get a slap on the wrist and your buddy gets the chair
3) you keep quiet but your bud turns you in and you fry

Sarah: Also, 4) you both spill the beans and both of you end up sizzled.

Interesting that you dropped the “both lose” option above and here. Was that by design? Or is the “every one loses” option too gloomy and against your personal view on life?

But, that aside, I see where you’re going with this. In poker, one’s loss is another’s gain. Here both can win and both can lose—nothing is being divvied up.

Also, if I get hit on the head while playing poker in an underground gambling casino and it raises a bump, it is a lump sum? If there’s yummy Asian food, is it dim sum?

Often in the real world we experience things that are non-zero-sum interactions. Much like dealing with our dog, Titan, it seems like usually everyone wins or everyone loses.

We often talk about the chemistry of social interactions. Chemistry has a nice way of classifying these interactions:

1) Endothermic: absorbs heat
2) Exothermic: releases heat
3) Adiabatic: neither releases nor absorbs heat

In this case the cats — when someone enters the house — the cats are functionally adiabatic.

Sarah: Um, sweets, hate to break it to you but although people say “that couple has chemistry,” characterizing social relationships into chemical process generally isn’t a thing…

The reason these chemical reactions are exothermic or endothermic is because they interact with their external environment.

Sarah: Hold the phone. Exothermic and endothermic reactions are really, really neat and I…can’t…stop…myself…from…jumping…in <gritted teeth, trying to resist>

Endothermic reactions pull energy/heat from the outside world (system enthalpy > 0) to build energy rich bonds and leave the outside world feeling cooler. You know those instant ice packs where you squish them and they get cold? They’re not pushing cold at your swelling, injured ankle; they’re sucking heat away from your swelling, injured ankle to form energy rich products inside the bag—they’re energy vampires.

The opposite is true for exothermic reactions. When their chemical bonds break, energy is released (system enthalpy <0) and the products are more stable. Heat is actually radiating from those instant hot packs much to the joy of your freezing hands/toes when you’re standing in the snow.

This is where we bump up on the first law of thermodynamics: heat energy cannot be created or destroyed.

This would imply that there are no true exothermic or endothermic interactions. By the rules of chemistry and physics, the first law of thermodynamics implies that there are only zero-sum interactions. I honestly don’t know if this holds true or not for social interactions. This is why I am writing two posts.

Sarah: First, true exothermic and endothermic interactions DO exist in a system. The ice pack system is endothermic—its energy is increasing. But, if the system is “the swollen, injured ankle + the ice pack”, yes, the energy is balancing out and is zero sum.

And second. Okay. <long look at the reader; breaking the fourth wall>

Sometimes when I say to Alan, “I love you” he gets a perplexed look on his face. An insecure person might wonder if he’s mulling over whether he in fact loves me back. But I know he’s actually thinking “What is love?” (This happens so often that it’s a comedy bit in the family where the kids break out in robotic voices and arm movements and ask “What…is…love?”). That he’s trying to understand and dissect love here through the laws of physics, chemistry, and I suspect later through neurochemical and biostructural brain science gives you a pretty good insight on what it’s like to live with Alan. And I love him for it.

In this post I will make the argument for the non-zero-sum social model. The one where we ignore the first law of thermodynamics.

Sarah: Um, yeah. Because, love….

This argument is frankly an easier argument to make (not more correct, just easier).

Sarah: not more correct????

I’ll handle the zero-sum model next post.

Robert Wright wrote a very fun book “Nonzero: The logic of human destiny.” It makes the strong case for the importance of nonzero sum interactions whether social, emotional, or financial. In the case for trade and collaboration, if we allow for nonzero sum interactions, we can enter into engagements (think the prisoner’s dilemma) and, through trust and collaboration, we optimize our interactions and our decisions to maximize benefits.

In this calculation, viewing relationships as zero-sum means that we leave on the table all of the benefits of non-zero-sum thinking. Zero-sum becomes a cautionary tale of selfishness.

To prepare for next post and the contingent argument, we should think over when we say sum what do we mean:

Are we summing money, happiness, safety? Do the aspects of Maslow’s hierarchy of need get included?

Sarah—As an aside, Maslow’s Hierarchy of Needs is a 5 level pyramid where more basic needs are met before we pursue higher level needs. They are:
1. Physiological needs (food/water)
2. Safety
3. Love
4. Esteem
5. Personal Growth

Are each of these dimensions bi-directional?

If you trade your spare orange for my spare apple it’s easy to say that we have both gained. Once money is involved as a proxy then the equation becomes potentially more complicated. If your orange is not really a spare then the trade can become less equal or less beneficial for you. You may be willing to experience a short-term loss for long-term gains.

To have non-zero-sum, we need to summate the gains/losses in the entirety of the interaction. We need to give a value to each aspect of the interaction: financial, spiritual, intellectual, emotional, and social gains. Money can provide a universal unit of value, but much like when you name the bird you no longer see the true bird, once things are reduced to monetary value you can no longer see true value.

If I’m going to believe in a non-zero-sum theory of social interaction then it is important to see value as more than just financial. It’s important to gain value in each interaction. It’s for me to be like Titan, and spread joy, and not like Titan and be a jerk.

Or maybe this is all complete bunk, a reasonable hypothesis we will explore next time on Boots and the Brain.

Sarah: A lot to unpack here. Not least of which is that my husband is trying to coax friendship, love, and business relationships into various potato sacks and stack them on a giant cosmic scale to see if the universe’s energy remains balanced. The next post will be where he shows relationships abide by the rules of zero sum and, I got to admit, I’m kind of intrgiued…because, well, they’re just not. So, this is going to get good.

But let’s talk about relationships. When I see couples, so much of the tension and hurt feelings boils down to viewing love as a zero sum relationship. The “They are winning, so I must be losing mentality.” Or conversely, that sly satisfaction of winning an argument and knowing your partner has lost. In actuality, however, both scenarios are non-zero sum and in the grand scheme of the system, both partners have lost. Too many losses on both sides ends in separation and divorce.

Too many times, we get lost in the minutiae of tit for tat or bean counting. It’s easy to get annoyed at the partner who rarely packs the dishwasher while also forgetting that maybe they take on the lion share of scrubbing toilets. But, this too is an oversimplification of zero sum—we get sucked into seeing family responsibilities as the pot in poker, the only currency, and we can get caught up in making sure “the currency” is equitably distributed.

Many couples try to account for other currencies— one person does the housekeeping and paying the bills, the other works outside of the home and tackles bedtime routines— in a way to approximate equal responsibility in a relationship. Again, this is trying to force a relationship into a zero sum mentality which gives it a certain vulnerability when the equitable distribution of labor stops feeling so equitable.

Relationships are messy and they can’t be captured by equations (cough, cough, Alan). What zero sum mentality fails to capture is rapport, trust, and connection. At the end of the day, it’s not whether a partner has picked up the dog poop three times and taken out the trash once— it’s “Do I trust them?” “Am I connected to them?” “Do they hold the essence of our relationship sacred?”

My mum perfectly captures the non zero sum vs zero sum relationship with her always sagely advice: “Do you want to be happy or do you want to be right?”

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