From wikipedia, I saw the explanation for "audience cost"
The term was popularized in a 1994 academic article by James Fearon where he argued that democracies carry greater audience costs than authoritarian states, which makes them better at signaling their intentions in interstate disputes. It is one of the mechanisms for democratic peace theory
In international relations theory, an audience cost is the electoral penalty a leader incurs from his or her constituency if they escalate a foreign policy crisis and are then seen as backing down. It is one of the mechanisms for democratic peace theory. It is associated with rational choice scholarship in international relations.
The implication of audience costs is that threats issued by leaders (who incur audience costs) against other states are more likely to be seen as credible and thus lead those states to meet the demands of the leader making threats
From this definition, I have some curiosities:
I can not understand why the leader need to resign or step down if they escalate the foreign policy crisis (I also try to find the meaning of "foreign policy crisis" but there is no clear definition so far)