Democratic countries do not fight wars against each other. This is true today, was true in all of the twentieth century, and was true in the nineteenth century in that countries with then democratic institutions and with a substantial part of the male population enfranchised, did not fight wars with each other. Hence, a more democratic world would promise to be also a more peaceful world.
The observation that countries in which governments are under some form of popular check are less likely to be warring, was first made by the German philosopher Immanuel Kant in a publication of 1795 entitled Perpetual Peace (Zum ewigen Frieden). Here he not only proposed the equivalent of a UN Charter in which countries commit themselves to peaceful coexistence. He also recommended that countries should adopt republican constitutions since that would make them less prone to war.
The peaceful inclination in democratic governments is due partly to the distribution of power in the population. Since the glories of war accrue mainly to élites and the costs of war fall disproportionately on the populace, élites may incline to war where they are not answerable to the populace and be more constrained from war where they are under popular control. Other reasons may be a high level of trade between democratic countries, that democratic leaders and citizens learn the art of compromise, that they see people in other democratic countries as similar to themselves, and that their communality encourages a habit of peaceful negotiations and treaties.
Regrettably, democratic countries have not in the same way been able or willing to avoid war with non-democratic countries. They have fought wars of more or less defence against non-democratic aggressors, as in the Second World War, and then with uninhibited brutality. And they have fought wars of aggression in self-interest, as for example the many and violent colonial wars that for example Britain and France engaged in during the nineteenth and twentieth centuries.
Democracy, then, is good for peace in the world – but does not guarantee peace.