Final answer:
Promotions based on proven skills and not personal attributes or favoritism in an idealized bureaucratic hierarchy are referred to as a merit system.
Step-by-step explanation:
The concept of promotions to higher levels within an idealized bureaucratic hierarchy based on a cheese mat rather than personal attributes or favoritism refers to a merit system.
In bureaucracies, meritocracies are based on proven and documented skills, rather than on nepotism or random choice. These systems aim to ensure that those most likely to succeed are the ones who are promoted. Merit-based selection is intended to protect employees from managerial abuse and make the bureaucracy more efficient.
However, the merit system also has drawbacks. It can result in bureaucracies that are insufficiently responsive to political change, as permanent employees become too independent of elected leaders. Additionally, the expertise of individual bureaucrats may sometimes hide their own biases and preferences.