Leo Tolstoy, a human dove par execellence.
So, let's play a game of hawks and doves. The way that it works is that we shall model a society, which for mathematical simplicity I shall assume it has an infinite population (curious how that would make things simpler rather than more difficult, but I digress), and within that society there are two types of people: hawks and doves. For this game, people in this society will interact with others within this society randomly and when they do they will interact according to the behavior determined by their type.
One one hand, we have the doves, who keep Tolstoy and Gandhi on their nightstand and who believe in the natural goodness of cooperating with their fellow brothers and sister. When doves will cooperate with everyone that they meet up with. On the other, we have the hawks, who have a worn copy of The Leviathan on their nightstand and who believe that they need to do anything in their power to get the resources they need to live their short and brutish lives. Hawks will use violence on whomever they meet in order to secure a marginally higher payoff from the encounter than the doves would have. Everything does well when doves meet other doves, they cooperate with each other in good will and then go on with their lives. However, when a dove meets a hawk, the hawk will commence the use of force against the dove and the dove, not wanting to violate their pacifist beliefs, will flee. When two hawks meet each other, though, the two will fight leading to a large loss for both of them.
The payoffs for each meeting are as follow. When two doves meet, they each cooperate together and receive a payoff of 5, quite the reward. When a hawk meets a dove, the hawk gets a payoff of 7, marginally better than the payoff for a dove, whereas the dove absconds empty-handed. There are disastrous consequences when two hawks meet, and they will both leave worse off than when they meet, each receiving a payoff of -3. This is explained in this handy table with the payoff for the column players being on the left and for the row players on the left:
What determines members of these two populations are not determined by the genes within people's bodies, but the ideas in their minds. We shall assume that over the time leading up to the start of our thought-experiment, the angelic nature of the human being has been in ascent and the arguments for pacifism have been victorious. Now everyone has got a copy of Tolstoy in their coat pocket and the idea of pacifism in their minds. Everyone is a dove. Can this situation last, though?
That is what we are interested in and after paragraphs of exposition its finally time to get down to answering that question. Without assuming that all men are angels would everyone in this fictional society remain a dove. I contend that they would not. There are now incentives to be a hawk that I now argue we must accept will lead this population back towards a mixed population.
That incentive is that there is now a higher pay-off to being a hawk than a dove. How do we know this? With some math. Let “P” be the percent of the population that is doves (this will mean that 1-P is the percent of hawks in the population), the expected payoff for being a dove can be expressed:
D=5P+(1-P)0
=5P
For those who have never seen this before, the expected payoff is the pay-off that the person in question would get for meeting a dove multiplied by the ratio of doves in the population add the pay-off for meeting a hawk multiplied by the ratio of doves in the population (this is where the assumptions of infinite population and random sampling are important, but they're not important enough to go on about here). The expected payoff for being a hawk can be expressed as:
H=7P+(1-P)(-3)
=10P-3
When the population is all doves (i.e. P=1), this leaves us with expected payoffs of:
D=5
H=7
So, once a dove picks up a copy of Hobbes and mutates into a hawk, the society will be ripe for more hawks to follow. After all, under these circumstances, the hawks will flourish getting higher expected payoffs each time they meet someone than the doves. If we assume that people can willfully change the memes in their mind, then the change will be even quicker as doves have their fidelity to pacifism tested by the temptation of a higher payoff. Doves on the margins will then convert to a new creed and follow new strategies.
When will this process end? It will end when there are no more incentives to be a hawk, when the expected payoffs of the two strategies are equal and when there are no more incentives to concert. We can calculate what the population will look like:
D=H
5P=10P-3
P=3/5
Ergo, once the population is 3/5 dove and 2/5 hawk, the payoffs that the two classes can expect equalize. Since there is no longer any difference between the two classes' payoffs, there is no longer any incentive for people to change their strategy. What this means is that the population will settle into an equilibrium at those population ratios with no force for change present until an external force acts upon it.
One aspect of that point of equilibrium of interest here is the question of what creates the environment of incentives that holds the population of hawks in balance. It certainly isn't the doves. They simply retreat whenever they meet a hawk lest they break their oath of non-violence. Instead, the only factor within this population that holds the hawks at bey is the ratio of hawks within the population. It is the danger of meeting another hawk and the negative payoff such an event yields that provides a disincentive for being a hawk. As the ratio of hawks in the population increase, the payoff for being a hawk increases until individuals are better off switching to non-violence.
The moral of our fictional game? Violence is only held in check by violence. If man were an angel upon this earth, then our approach here would be useless since no human being would be tempted to give up her moral convictions by a worldly payoff. However, the timber of humanity is crooked and so to expect an edifice to be built of it that perfectly corresponds to the moral laws of the world is to drink deeply from the font of naïveté.
If society is to maintained and cooperation preserved, then there must be a way of holding violence in check. The doves cannot do that. A population of Doves cannot protect itself against the mutation of hawkish ideas within it and it cannot hold those who hold those ideas in check. Only a population of mixed hawks and doves within this model can. To once again quote Orwell: "Those who 'abjure' violence can only do so because others are committing violence on their behalf." The Doves free ride on the mechanism that the Hawks provide to keep other Hawks in check. They keep their hands clean, but it is only because others commit violence that they are able to do so.
The pacifist errs by asserting that peace and violence are contraries; instead, they are more often two heads of the same coin. The threat of violence, and its occasional use keeps the incentive towards the more devilish features of human nature in check thereby allowing the more angelic to flourish in human cooperation. There are even times when even the most dovish of human beings must be roused to violence in order to preserve the hope for peace and prosperity in the future:
Declare this among the nations
proclaim a war,
rouse the warriors to arms!
Let all the soldiers
report and march!
Beat your plowshares into swords
and your pruning hooks into spears
let the weak man say, “I am a warrior!”
(Joel 4:9-10)
"The moral of our fictional game? Violence is only held in check by violence."
I agree with this conclusion though I don't think the game necessarily confirms it. There is no reason that the payoffs proposed should be the correct (even in proportions to the) real-world amounts. Certainly, some payoff structures would make it always preferable to be a Dove, rather than requiring Hawks to deter others from being Hawks. The realism of such structures where the payoff of (D,D) exceeds the Hawk payoff of (H,D) and (D,H) may be contested; though I am not entirely convinced that such an arrangement is even unusual, particularly with moral incentives being considered.
Though my major criticism must hinge on the notion of a division between Hawks and Doves as sorts of people, who never act in other manners until they definitively change their mind. Indeed, if the proposed payoffs are correct, we can conceive of "hawk" and "dove" being actions rather than mentalities with which one's actions always accord; with this, we come to rather startling conclusions. (I do not feel this complicates the model much as most of the games we consider have real choice each time they are played.) If approaching someone we know will Dove, we should Hawk. If approached by a Hawk, we should Dove. The equilibria for the game are (H,D) and (D,H). While still indicating that violence is going to exist in a society, this seems counter-intuitively to argue that when faced with violence in a particular situation the best strategy is to retreat. (This is likely true for those cases as suggested by the payoff matrix where violent response will escalate the situation, presumably minor theft, but it is certainly not true for cases where violent response will not likely make the situation any worse, e.g. assault, kidnapping, attempted murder). Though I think this would go further to support the argument that the proposed payoffs are not realistic, as it would required all interactions in equilibrium to have one party use force against the other.
Just my two cents on the model, which I think definitely could be used to confirm this conclusion with reasonable assumptions explicitly developed. This is certainly an interesting approach, nonetheless.
Posted by: Thomas Choate | 09/12/2012 at 07:15 PM
Here's what I said on Facebook:
A nice analysis, but I do believe that any remotely thoughtful pacifist is aware of this fact. In a world where violence is inevitable, true pacifism amounts to a transcendence of the will to live. Of course, the knights of righteous bloodshed will claim that pacifists are "free riders," but how is this any better than the "you use roads, therefore you owe your living to the state" argument?
Also, since at no point in history has the world been full of doves, and such a world would likely look very different from a private-property based economy, I doubt your psychological predictions are necessarily valid.
You replied:
I have no doubt that a thoughtful pacifist is aware of this argument. It is a very common argument that I thought could be improved upon with a little mathematical formalism.
Also, that the pacifists are free riders doesn't necessitate the sort of argument I think you're hinting at where the knights of righteous bloodshed claim that their violence is a public good and that therefore they can take an amount of resources from the pacifists to pay for their provision of that public good. Whether the knights would be just in demanding that sum is a question I'll leave untouched here. Perhaps the pacifist would prefer a world in which no one used violence in self-defense.
(I think the road argument steps beyond what it's premises can reasonably argue. Yes, I think that one could reasonably argue that anyone who uses a public road owes a sum approximating the marginal benefit they get from using that road to the government.
However, to argue that all of society depends of government infrastructure would necessitate the premise that private entrepreneurs would not be able to provide (perhaps less efficiently than the government) those services if the government were not to. Ronald Coase showed that private entrepreneurs provided lighthouses without the state, so I don't think it is at all unreasonable to argue that they would be able to provide highways as well.)
I completely admit that no society of Earth has even been all-dove. (That would falsify my model since I'm trying to provide a means of understanding why no society can even achieve that population ratio of doves.) I'm not at all as convinced as you are that a system of private property titles would not emerge in a society of doves since property titles lead to efficient economic systems (see Mises and Hayek on socialist calculation). Also all of my psychological premises may not be valid, but I think they are reasonable and I challenge anyone who does not think they are to prove my moral/psychological premises wrong.
I reply:
-My reference to the roads argument was just an example of someone giving you something you didn't ask for, and acting like they did you a favor, e.g. Orwell talking about all the favors he does for the pacifists. I didn't really mean it as a deeper criticism than that.
-I wouldn't be surprised if something resembling property emerged in a pacifist society, but it would be different from private property as we know it because it would not be based on a threat of violence. As you say in your blog, organized violence does have a strong influence on the actions of individuals.
-As for psychological predictions, I believe violence might decrease if the people who condemned it unilaterally actually consistently and authentically applied that principle. If someone tells me not to watch tv, I am more likely to listen to them if they themselves do not watch tv--even if they say it's "necessary tv-watching," they are still contradicting their premise that tv is evil.
Is violence evil? Then don't do it. Is it good when filtered through a religious, economic, or political ideal? Then don't condemn it generally.
Posted by: Benny | 09/12/2012 at 10:40 PM