Optimized and Arbitrary

This is one of a series of posts about math and morality.  I’ll be getting back to the series soon, but I’m currently pausing to answer some of the questions that have been accumulating.

In comments on “On What Evidence?” Crowhill and Charles got into a disagreement about human morality and evolution that I exerpt below.


Does there have to be some sort of “objective morality” for a dog to know how he’s supposed to behave towards other dogs? Isn’t it entirely possible that dogs simply developed some set of arbitrary social rules that happened to work decently well for them?

Why can’t something similar be true of humans? Why couldn’t we have developed some set of social rules that helped our species survive?


You a fatal flaw when you discuss social behavior evolving or ‘developing’ – first you use the word ‘develop’ as if to make it insignificant, second you repeatedly say that they are arbitrary, etc…

If rules exist within a social group because they helped the survival of a social species – they are ANYTHING but arbitrary!

I think it’s actually both reasonable and important to use the term arbitrary to describe evolutionarily guided social systems, but to explain why, I need to switch mathematical subfields to game theory.  Game theory can be loosely summarized as the study of how to make choices.  Researchers talk about strategies to adopt to try and get the best payoff possible and also characterize common snarls and situations.

A Nash equilibrium occurs when, for each player, the current outcome is optimal assuming that no other player changes his/her strategy. This means that no player has an incentive to change their behavior. A Nash Equilibrium is absolutely not a guarantee that the current state is actually the best for all concerned.

The best known example of a game where the Nash Equilibrium solution sucks and the best solution is unstable is the Prisoner’s Dilemma (click the link for explanation if you’re not familiar). If both players keep mum, either benefits from changing strategy. In the case that they both rat, neither benefits from changing strategy. Even though both being silent is clearly preferable to both snitching, there’s no way to escape from a Nash Equilibrium without finding a way to coordinate action.*

I think it’s reasonable to assume that social behavior represents, if not a perfect Nash Equilibrium, at least something close to one. In that respect, it certainly is not arbitrary. However, I would bet that there are a variety of sets of social norms that are stable enough to be close-enough Nash Equilibria, just like our current situation. This certainly seems to be the case in other aspects of evolution. Think of Darwin’s finches. Each beak configuration is advantageous and distinct, but the choice of which stable configuration prevailed was pretty much arbitrary.

If we thought the structure of our society carried as little moral weight as the structure of a bird’s beak, there would be no reason to be troubled by the fact that some of the values or practices of our society was arbitrary. However, it’s easy to imagine plenty of stable societies that could be construed as Nash Equilibria but which we find to be abhorrent. This is another nail in the coffin of the idea that evolutionary fitness is a valid way to defend our actions.  We need to be aware of our social system as arbitrary at least in part and be attentive to ways it ought to be reformed.

*Unrelated to larger point about morality but still interesting:

A lot of effort is put into finding ways to pull people out of unpleasant Nash Equilibria. One of my favorites is the National Popular Vote campaign which aims to do away with the Electoral College. Although each state can decide to apportion it’s electoral votes however it wants, no state has an impetus to deviate if it will mean less attention from politicians. What NPV does is get states to sign on to legislation that promises their electoral votes to the winner of the national popular vote provided enough states have also passed the legislation (it goes into effect when states with electoral votes totaling 270 sign on). The current tally is 6 states and 73 electoral votes.

Of Morality and Mandelbrot [Pope Francis Bookclub]
Contemplation and Comment Moderation for Lent
Books that Change the Way You Think [Radio Readings]
The Story of Shmuel and Tailoring Support [Guest Post]
About Leah Libresco

Leah Anthony Libresco graduated from Yale in 2011. She works as a statistician for a school in Washington D.C. by day, and by night writes for Patheos about theology, philosophy, and math at www.patheos.com/blogs/unequallyyoked. She was received into the Catholic Church in November 2012."

  • http://www.blogger.com/profile/00096273666451765269 Stephen Marsh

    //but the choice of which stable configuration prevailed was pretty much arbitrary.//Not really:http://en.wikipedia.org/wiki/Evolutionarily_stable_strategy#Nash_equilibria_and_ESSESS is almost but not quite the same thing as a Nash Equilibrium. We're dealing with more than two actors and we're dealing with base material that doesn't have to be rational (different alleles and mutations), so you have to take into account the possibility of a neutral invasion of a different strategy in determining what prevails.Based on my admittedly limited knowledge, this can affect your contention that amorality or a bizarre totalitarian system can be a Nash Equilibrium. Maybe it can (I haven't read We so I don't know if this applies), but when you can have an influx of information, or foreign assistance, or when your society can get attacked by a different one, or a foreign / differently-educated revolutionary (Che) comes in, then it might not necessarily be stable.

  • http://www.blogger.com/profile/03615608336736450543 Hendy

    " This is another nail in the coffin of the idea that evolutionary fitness is a valid way to defend our actions."I don't know that anyone is particularly advocating defending actions by saying, "What do you expect? I was just increasing my evolutionary fitness!" It's more a question of whether what we value has stemmed from evolution, is simply being defined by humans, or whether these values exist in immaterial time-space to be discovered just like mathematical truths.Also, relative values don't mean nothing matters. This is the whole point of society. Many people wish to respond to relativism by slapping the relativist in the face and saying, "So, I don't believe in not slapping people in the face. What are you going to do about it?" But that's not how it works. We gather as intelligent beings to decide what best supports the society and enact prohibitions for violations of these rules.As a thought experiment, other than being aware of morality, what actions do you see that are literally unseen anywhere else in the animal kingdom. They surely exist, I'm just looking for some things to ponder.Does it really only boil down to our reactions and the fact that we think about morality itself rather than just seeming to do that which we are "programmed" to do what makes us look to the existence of real values?

  • David B.

    Except that evolution isn't about the advantage to the individual, it is about the advantage to the gene itself. If a lot of offspring get genes for cooperation and together they are hard-wired build an equilibrium better for all (i.e. what morality does), that would in fact out compete another population without those genes.

  • http://www.blogger.com/profile/02327655974517447377 Crowhill

    Hendy is right. My point is not that evolutionary explanations defend our actions. They clearly don't. My point is that they could explain the fact that we have moral intuitions. IOW, if the question is "why do we have these moral feelings?," the evolutionary explanation seems completely adequate. If the question is, "what is the justification for the rightness of some set of moral statements?," then the evolutionary explanation doesn't do any good at all. The hard thing to face is the possibility that there may be no justification for our moral statements.

  • http://www.blogger.com/profile/16496144988509668275 Leah

    @StephenI guess the disclaimer I should add is: sufficiently stable/resilient societies are indistinguishable from equilibria. Totalitarian societies aren’t perfectly adamant Nash equilibria, nor are liberal democracies or any other societal frame we’re familiar with. My point was, for an arbitrary threshold of stability/resilience, there are likely to exist n>1 societies above that threshold and it is not necessarily the case that all n are equally morally acceptable. Given that fact, we should apply a higher standard to our society than stability/persistence.@Everyone elseAnother response post goes up tomorrow morning.

  • http://www.blogger.com/profile/11174257204278139704 Charles

    I would liek to point out that I wasn't dismissing Crowhill's point, and I am certainly not dismissing your point.I was simply saying that evolution is not arbitrary. And if you have multiple equilibriums, none of them are arbitrary. It really was an issue of semantics, and ironically it plays into the "no morality without god" crowd, despite the fact that you think I was arguing the other side.The common pedestrian way to dismiss evolution, other than pointing out the idiot evolutionary psychology theories that hold as much weight as Deepak Chopra's understanding of quantum physics, is to point out just how arbitrary it is. Typically this is done with a flippant comment like: "You are saying we are just the result of some RANDOM events?" – All I am trying to say is that this is a dangerous slope. While the events may have been 'random' – and the successful mutations may have been 'arbitrary', it is fundamentally important to get across that the end result IS NOT 'arbitrary randomness'. You may get this, and all the commenters here may but it is a point that is not understood by the VAST majority of anti-evolution folks I personally encounter.Now this is off topic to the issue at hand, whether there is an absolute morality, but this issue often gets clouded by the fact that it is VERY VERY difficult to separate out what you mean is absolute from what is cultural baggage. Just because a 'bad' society could reach a nash-style equilibrium doesn't mean that they aren't objectively immoral. But who is to say all totalitarian societies are immoral? Are we saying that democracy is an objective good? This line also ignores the issues that sometimes things that are objectively good for society may not be on a case by case basis for members of that society.

  • http://www.blogger.com/profile/16496144988509668275 Leah

    Bang on target, Charles. As I said in one of today’s posts, if I could wave a magic wand and give everyone a better understanding of one topic, it would probably be randomness and probability. One of my pet peeves is when people discuss something being ‘random’ without mentioning what kind of distribution they are randomly drawing from. There’s a pervasive idea that ‘randomness’ is only a description of the uniform distribution. A random drawing will produce some values much more frequently if I’m randomly sampling from a normal distribution.The TV show Numb3rs (the crime solving adventures of an FBI agent and his mathematician brother) did a great job debunking a commonly held misunderstanding of randomness in the pilot episode. Just watch the first scene of this clip as Charlie (the mathematician) asks the workers in the FBI office to scatter themselves at random through the room.

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