Does it Pay to Divide and Conquer?

4 September 2013, 1009 EDT

duckThe intuition behind the maxim divide et impera is clear.  If they’re busy fighting each other, they not fighting you.  And that’s obviously in your interest (assuming, that is, you are some sort of occupier or metropole seeking to extract rents from a local population.)  Devious and underhanded?  Sure.  Morally repugnant?  If you’re inclined to view politics through such a lens.  But effective?  Self-evidently.

Or so you might think.

Brenton Kenkel, a University of Rochester doctoral student currently on fellowship at Princeton, argues otherwise in this fascinating working paper.

To evaluate the logic behind divide and conquer, Brenton analyzes a game-theoretic model wherein a conqueror demands tribute from a population consisting of an arbitrary number of groups, each of which chooses how much effort to devote to economically productive activity, resistance against the conqueror, and conflict with other groups.  He derives a number of interesting results, most of which I’ll briefly discuss, but the basic argument is straightforward—the more time groups spend fighting each other, the less time they spend fighting the conqueror, which means a larger share of the total resources can be demanded; but time spent fighting anyone is time that isn’t spent on economically productive activities, and so there’s less available to demand.  Fostering internal conflict ensures that the conqueror gets a larger slice of a smaller pie.  And while you might think that means the net effect is ambiguous, Brenton’s model indicates that the latter effect always trumps the former.

That’s not to say that fostering internal conflict is never optimal.  Conditional on there being pre-existing divisions in society, it is better to turn the groups against one another.  But that doesn’t quite validate the logic of divide and conquer, because Brenton further shows that the conqueror is generally better off if population is unified than if they are divided.  As he aptly puts it, divide and conquer is a second best strategy—an optimal response to a situation the conqueror would just as soon alter if at all possible.

In other words, whether it pays to divide and conquer depends on what you think that strategy entails.  According to the ultimate arbiter of everything on the internet, Wikipedia“elements of this technique involve:

  • creating or encouraging divisions among the subjects to prevent alliances that could challenge the sovereign

  • aiding and promoting those who are willing to cooperate with the sovereign

  • fostering distrust and enmity between local rulers

  • encouraging meaningless expenditures that reduce the capability for political and military spending.”

Brenton’s analysis indicates that conquerors do not generally have an incentive to create or encourage divisions among the population.  They often have an incentive to ruthlessly exploit those divisions that already exist, but that doesn’t mean they profit from creating new divisions.

Yet his paper does indeed indicate that it can be beneficial to promote some groups over others, as one would expect.  As an example, he points to China’s effort to increase the Han population in the Xinjiang province.  This has had the effect of reducing violence against the Chinese government—at least in part because it has reduced the attractiveness of independence to the Uyghurs by reducing their ability to dominate a new state—as well as increasing economic productivity.

There is one condition under which conquerors potentially do prefer the population to be fragmented—when no group is particularly productive and there is abundant natural resource wealth.  In such cases, the fact that intergroup conflict not only siphons away resistance but also economic productivity has little impact on the size of the pie.  This may explain, for example, why colonial powers adopted different policies in different places, and why the legacy of colonialism differs so widely across the world.  But this is the exception that proves the rule.  It is important to consider not just who has the upper hand in whatever military engagements take place, but how much value is destroyed (or not created) by said violence.

Note that this is a work in progress.  Brenton would welcome any comments you might have.  His email address is bkenkel<at>