What do heaps, jail, and cows have to do with your marriage and your friends or your workmates, roommates, and family?
Heaps, going to jail, grazing cows, and bad roommates are the subject of four famous dilemmas and paradoxes, known as the Sorites Paradox (from ancient Greek philosophy); The Prisoner’s Dilemma (from game theory); and The Tragedy of the Commons and The Free-Rider Problem (both from economics). They’ve been endlessly discussed and argued about. But paradoxes and dilemmas are not just the playpens of philosophers, economists, and game theorists. They apply in all sorts of ways to public policy and ordinary life. Since this is a blog about philosophy and personal life, I’m going to talk about how they apply to personal life, like dealing with a credit hog on a business team, an abusive spouse, a bad roommate, or a sibling who doesn’t keep promises. (I talk a bit about how the Prisoner’s Dilemma and Tragedy of the Commons apply to engineering in Ethical Engineering.)
The Sorites Paradox: When Is Enough Enough?
The Sorites Paradox might be named the paradox of fuzzy limits. Fill a wheelbarrow with sand and dump it on the patio. That’s definitely a heap of sand. Now take away a grain of sand. Still a heap, right? Take away another grain of sand (but don’t put it in your brother’s Kool Aid). Still a heap. But if you keep doing this, you will eventually be left with one grain of sand, which is clearly not a heap. So when did the heap of sand become not a heap? Which grain of sand was the last before the heap was gone? There is no answer, of course. Yet we all know the difference between a heap of sand and a single grain. The Sorites Paradox is not just a verbal game. The problem of how much is enough comes up often in life.
Here is an example. Suppose I am standing in front of a vending machine about to buy a pack of gum. I have only a dollar on me. A starving person comes by, on the verge of death. I can save his life, at least temporarily, by buying him food from the machine and foregoing my gum. (Assume the gum and a small sandwich both cost two dollars). Almost everyone would agree it is abominably selfish to say “you die, I want my gum.” The sacrifice of the gum is trivial, after all. But the thing is, we all do the equivalent thing every day. Right now, I am writing in a Starbucks, drinking iced coffee. The price of the iced coffee could keep a starving family alive for a day if, instead, I donated the money to Oxfam. So I am in effect saying to that family “you all die, I want my coffee.” Maybe I should do both—buy my coffee and also contribute to Oxfam. I can afford that. But here is where the Sorites Paradox comes in. Subtract the cost of one coffee from my wallet and I am fine. But there are millions of hungry people in the world. At what point is it ok to say “that’s enough—the rest of you die.” Which donation to Oxfam is, metaphorically, the last grain of sand? Because no single $4 donation reduces me to poverty. When can I stop giving and not be abominably selfish? When is it no longer a heap? In reverse, my keeping my thermostat at 79 in the summer makes no difference to climate change. If enough of us do, it does make a difference (it becomes a heap).
The Sorites Paradox is especially relevant to troubled relationships. In a marriage, no one snide remark is abuse. Anyone at whom you’ve never taken even a tiny dig is probably not very important to you (no dig, no treasure). But unremitting put-downs, snide remarks, and digs can become abuse. How many does it take to make a heap? When does a spouse’s behavior cross the line into abuse, and when is it time to call it quits?
One way to deal with these issues in life is something some philosophers have suggested as a solution—pick an arbitrary cutoff. Just lop the head off the dragon. 2000 grains of sand is a heap, 1999 is not. For example, you can decide to donate to charity exactly 10% of your take home pay. Another way is to use a psychological cutoff: “I’ll leave when I find I want to hit him” or “I’ll leave when she makes me actually cry.” Much of the time, however, we find we can’t really draw a line in the sand, whether arbitrary or psychological. Here is one way to deal with those cases, which I’ll call the fuzzy boundary zone method. We can divide the issue into three zones with fuzzy boundaries: the clearly-not-bad-enough zone, the gray area zone, and the definitely-bad-enough zone. When firmly in the clearly-not-bad-enough zone, you might take some steps to make things better, but you normally won’t take drastic action. Less than perfect is not the same as abusive. If you’re well past the boundary into the definitely-bad-enough, take decisive action. If you’re not physically safe in a relationship, get out now. When in the fuzzy boundary areas or the gray areas, you have to decide on a case-by-case basis, depending on many factors, like how much is at stake and whether you owe the person a debt of gratitude, to name just two of the many considerations you might need to weigh.
Trust: Prisoner’s Dilemma and Tragedy of the Commmons
The Prisoner’s Dilemma and Tragedy of the Commons are problems of trust. In both cases, the best overall outcome is for everyone to cooperate. But if one person doesn’t co-operate, that person gets an advantage while others suffer. If you can’t risk someone deciding not to cooperate, then you can’t afford to co-operate. So everyone loses.
Here is the Prisoner’s Dilemma: Prisoners A and B are both offered a deal. If neither confesses to a crime (if they “co-operate” with each other), both receive a six-month jail sentence. If one “defects” by confessing, that one goes free while the other gets a ten-year jail sentence. If both confess, they both get 5 years in jail. So, they should both refuse to confess (they should co-operate). But the most likely outcome is that both confess and get 5 years, out of fear of a 10 year sentence because the other will confess (defect), hoping to go free.
The Tragedy of the Commons is about an unregulated common grazing pasture, open to everyone. The commons can support 5 animals per person. If everyone else keeps to the five-animal limit, everything is fine. If you alone bring 10 animals on the commons to graze, the harm will be minimal. (Five extra animals does only minimal harm to the commons.) But if a significant number of people bring more than 5 animals, the ecosystem will collapse. Everyone starves. Can you rely on others to keep to the five-animal limit, or do you need to bring more animals before the ecosystem collapses, giving you a “buffer” to stave off starvation?
These may seem like artificial and implausible scenarios, but they capture many real-life situations. For example, air pollution increases a company’s costs by damaging machinery and increasing insurance premiums and down-time, since employees get sick. The cost of scrubbers often pays for itself. However, air pollution doesn’t just stay around the polluting factory. If factory A installs scrubbers and its rival B doesn’t, they both suffer the same costs, since B’s pollution spreads out in the air and affects both factories. But, other things being equal, B can produce the same product more cheaply (they aren’t paying for scrubbers), thus putting A out of business. The logic of the Prisoner’s Dilemma forces both A and B to forego scrubbers: you can’t trust the other guy not to defect. Everyone loses.
This problem of trust also arises in personal relationships. If both people do the “right” thing, like compromise, be honest, do their fair share, and so on, both are generally better off. But if A does these things and B doesn’t, B gets an advantage at A’s expense. For example, Geoffrey and his sister Melinda both promise to help each other out. If Geoffrey keeps his promise and Melinda doesn’t, Melinda gets Geoffrey’s help without having to sacrifice anything, while Geoffrey is out what he gave Melissa without getting anything in return. But they both lose if neither keeps promises because they can’t trust each other to do the right thing.
Of course, the Prisoner’s Dilemma is a one-time choice: there is no next time. Relationships are not like that: with families, romances, and workmates there is a next time. The winning strategy in tournaments with a next time (called an “Iterated Prisoner’s Dilemma”), where players could not communicate, was “Tit-for-Tat,” developed by Anatol Rapoport. In Tit-for-Tat, you begin by co-operating, then do whatever the other person did last time. This strategy starts with generosity, then is nice when the other person is nice and tough when they’re not nice, but is also quick to forgive when the other person changes.
Real relationships are different from these game theory situations in three important ways. First, in real relationships there are side benefits to a co-operative relationship. Feeling good about your spouse can be more important than who washes the dishes more often. A friendly and supportive workplace environment is of great value. So you might prefer a “tit-for-two-tat” strategy, where you give them two chances before defecting. (You get a second chance, but not a third). If the relationship is important enough, a tit-for-three (or more) strategy might work best. Or we might abandon strict strategies and, looking at the overall picture, balance generosity and forgiveness with sending a message and not being a doormat (“not this time”). In a business team, you might cherish a reliable partner but wish to avoid one you can’t trust. So, in situations where one person can “grab” the credit for what the team did, a good strategy might be what’s called “Grim Trigger”: co-operate once, then continue to co-operate if the other does, but, if the other person defects once, you defect forever. After all, if the other team member shares credit, you have a reliable partner, and the partnership is worth protecting. But once they hog the credit, they show they’re not trustworthy.
Second, people do communicate. Third, people are often mutually interested. I care about my brother and spouse, and we talk. If we care about each other and explain our needs, we will both try to compromise and help each other, instead of just trying to get the best deal for ourselves. So the tit-for-tat or tit-for-two-tat strategies can be your first draft, a place to start. Judgment and affection will also help shape your response. And communication is a powerful tool.
The Free-Rider Problem
These three dilemmas raise what is called the “Free-Rider” problem. In the Tragedy of the Commons, the commons survives even if one family doesn’t do it’s part, but collapses if enough families don’t (it becomes a heap). The one family who defects while others co-operate becomes a Free-Rider on others doing their share. The company that doesn’t install scrubbers is a Free-Rider on other companies who do, since they get the same benefit of cleaner air without paying the cost. A group of roommates share a kitchen. If one person doesn’t do their share to stock and clean the kitchen (which is a commons), nothing catastrophic happens. The others’ efforts are enough. But if two or three people decide to become a Free-Rider, the commons collapses: the mess and shortages build up.
In public life, the state deals with Free-Rider Problems in one of four ways: by imposing penalties, imposing costs, excluding access, or bearing the cost (carrying the Free-Rider). Polluters are fined (penalties) and drivers pay taxes (imposed costs) to maintain the roads. Toll roads exclude those who don’t pay (they don’t get to ride). Taxpayers absorb the costs for those who can’t afford to pay taxes. In private life, the same four remedies are available. Renters can kick out the roommate who won’t clean, “fine” them in other ways, direct or indirect (playing loud music while they try to sleep), or they can decide not to fight this battle and absorb the cost (carry the Free-Rider). The more intimate the relationship, the bigger role mutual concern and communication play. A marriage of tit-for-tat is not an ideal relationship, but neither is a marriage where one partner takes advantage of the other. If you find that consistently, in many ways, your partner is free-riding on you, despite your attempts to have constructive and supportive conversations about it, you may want to re-think the relationship. Keep in mind, though, what they do bring to the relationship. You’re not perfect either. If you look at the whole relationship, not just one issue, good is good enough.
In general, there is no algorithm for dealing with these problems in your personal relationships. Life is complicated. Judgment about your particular case is indispensable. But recognizing “oh, this is a Free-Rider problem” or “this is a Prisoner’s Dilemma situation” can help you to think clearly about how to handle it and suggest some possible strategies (exclude the Free-Rider, use Tit-for Two-Tat, etc.).
Further Exploration
More paradoxes: The Liar Paradox https://iep.utm.edu/liar-paradox/; Russell’s Paradox https://iep.utm.edu/par-russ/; Zeno’s Paradoxes https://iep.utm.edu/zenos-paradoxes/; Hilbert’s Infinite Hotel (or Grand Hotel) Paradox https://www.scienceabc.com/pure-sciences/what-is-the-infinite-hotel-paradox-definition-examples.html; and the Grandfather Paradox https://www.livescience.com/grandfather-paradox.
The Sorites Paradox is pertinent to discussions of world famine https://rintintin.colorado.edu/~vancecd/phil308/Singer2.pdf and whether utilitarianism is too demanding https://utilitarianism.net/objections-to-utilitarianism/demandingness/#:~:text=Many%20critics%20argue%20that%20utilitarianism,bring%20about%20the%20best%20consequences. The Free-Rider problem comes up in political philosophy and public policy. To read more about the prisoner’s dilemma, visit https://heritage.umich.edu/stories/the-prisoners-dilemma/. The tragedy of the commons, described by Garrett Hardin https://math.uchicago.edu/~shmuel/Modeling/Hardin,%20Tragedy%20of%20the%20Commons.pdf , features in conversations about the work of Robert Nozick and liberalism as well as population control. To read more about the tragedy of the commons, visit https://online.hbs.edu/blog/post/tragedy-of-the-commons-impact-on-sustainability-issues. For an in-depth look at the free rider problem, there is a Stanford Encyclopedia of Philosophy article on the topic: https://plato.stanford.edu/entries/free-rider/.
Disclaimer
Nothing that appears on this blog is meant to replace legal advice, therapy, or medical treatment. I am not providing legal, medical, or mental health advice. Always seek the advice of your own attorney or medical or mental health provider about specific questions concerning your specific health or legal issues.
