Martin Indyk and Robert Kagan write:

Strengthening the liberal political order will require increased efforts to enlist the support of emerging democracies. Nations like Brazil, Indonesia, South Africa, Turkey and Mexico have become increasingly influential economically. But they are struggling to find their identity as democratic powers on the international stage. Some are drifting toward a worldview that actually undermines the liberal nature of the global order.

This is very vague stuff, but if this complaint is anything like a lot of other Western criticisms of rising democratic powers it is mostly nonsense. The standard criticism of rising democratic powers is that they are unwilling to back Western governments’ policies of regime change and armed intervention in other nations’ conflicts. This is not necessarily because these democracies are “drifting” toward an illiberal worldview, nor is it because they favor undermining the current international order. Many of these governments have concluded that such policies are destructive and contrary to their understanding of what the international order is supposed to be like. According to this view, toppling other governments, attacking other governments, and trying to dictate political outcomes in internal conflicts have been very harmful to the affected regions and to international peace and security. These policies have also frequently resulted in the empowerment of illiberal political forces.

Indyk and Kagan don’t go into detail to describe what they mean by “finding” an identity as a democratic power, but if their past arguments are any guide this refers to the willingness of democratic states to imitate Western interventionist governments. It is particularly important for Kagan’s ideologically–defined division of states into “autocracies” and democracies that all of the latter pursue similar foreign policy goals, which is supposed to put them in opposition to the interests of the former. What bothers the authors about so many of the rising democratic powers is that their governments refuse to subordinate their respective national interests to a crusading democratist ideology.