Needless to say, this response is not satisfactory to people who believe that without states, there will be more war. They are using a broader definition of war than just conflict between states.
The broadest possible definition of war would be any conflict between two individuals. Then the question of whether statism or anarchism will have less war becomes the question of what system will minimize conflicts.
The question of what ultimately causes conflicts lies largely outside the realm of political philosophy and economics (and in psychology), but we can ask:
- Will conflict prevention industries be more effective in a free market or under state control?
- Will conflict resolution industries be more effective in a free market or under state control?
Before thinking about how the security and law industries might be structured in a free market (which is difficult because we are all personally familiar only with how states structure these industries), we can say, using general economic principles, that we can expect greater quality, efficiency and service, lower prices, more dynamism, diversity and choice, and less corruption, with a free market arrangement than with a state monopoly.
All this means that we have every reason to believe that there would be fewer conflicts if the security and law industries were provided by a free market, i.e. libertarian anarchy. That is, in the broadest sense, war would be minimized by anarchy.
For an examination of how free markets in security and law might be structured, see the writings of Murray Rothbard, Hans-Hermann Hoppe and David Friedman.