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Tuesday, 16 February 2016


Steven Pinker's famous book The Better Angels of our Nature posits four reasons for the decline in violence that has happened and is happening in the world: empathy, self-control, our moral sense, and reason.  He explicitly (though only partially) rejects the idea that we are evolving to become more peaceful.

I am not sure (particularly given meme as well as gene copying) that evolution can be discounted as an explanation for the decline in violence.

Recall John Maynard Smith's hawks-and-doves example of an evolutionarily stable strategy. Suppose the payout or utility matrix is

hawk dove
hawk -1, -1 +0.5, -0.5
dove -0.5, +0.5 +0.25, +0.25

What this says in English is that when two hawks meet they fight and each loses 1 unit of utility (the -1s top left) because of energy wastage, injury or death.   When a hawk meets a dove the hawk gains +0.5 units of utility because the hawk can easily steal from the dove (the +0.5 top right) and the dove loses 0.5 (the -0.5).  When a dove meets a hawk the reverse happens (bottom left).  And when two doves meet they each gain 0.25 units because they don't fight and can cooperate (bottom right).

The resulting utility graph looks like this:

The horizontal axis is the proportion of doves (the proportion of hawks is one minus the proportion of doves) and the vertical axis is utility .  The blue line is what hawks get for any given proportion of doves, and the orange line is what doves get.  To the left of the crossing point the orange line is higher, so there it makes more sense to be a dove than a hawk.  To the right the blue line is higher so there it makes more sense to be a hawk than a dove.  This means that the crossing point is the point where the population is evolutionarily stable - at that point it makes no sense for either doves or hawks to change their behaviour.  The crossing point is where the population has 33% of hawks and 67% of doves.

(I have chosen numbers that make the Nash equilibrium occur at zero utility for simplicity; this is not necessary for the argument that follows.)

Now suppose that one thing changes: technological advance makes weapons more deadly.

Note very carefully that better weapons is not the same thing as more weapons.  The number of weapons always goes as the proportion of hawks (33% above) and is an output from, not an input to, the model.

With better weapons, when a dove meets a dove nothing is different because they didn't fight before and they don't now.  When a hawk meets a dove the hawk gets the same profit as before because the dove surrendered all that it had before.  So the numbers in the right hand column stay the same except for...

When a dove meets a hawk the dove may lose more (maybe it dies instead of merely being injured: the -0.75s). And when a hawk meets a hawk both lose disastrously because their better weapons mean greater injury and more death (the -1.5s).  So the numbers in the left hand column get more negative:

hawk-1.5,-1.5+0.5, -0.75
dove-0.75, +0.5+0.25, +0.25

and the utility graph changes:

Now the population is stable when there are fewer hawks (25%) - and thus also fewer weapons - and more doves (75%).

Making weapons better at killing gives a society with fewer of them; a society that is more peaceful.

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