With regard to methodology, mixed approaches that combine both quantitative and qualitative methods are particularly welcome in our department.
If you intend to examine more than one case, you will also be asked to justify the selection of your geographical and temporal span, even though you can do this more briefly when they have chosen a “large N” design.
Elaborate on the logic and strategy behind case selection and comment on the inherent disadvantages (if any).
Organise your proposal should around a small set of ideas or hypotheses that you would like to investigate.
Provide some evidence of relevant background reading if possible.
Avoid sending a purely generic statement of purpose that fails to identify why the EUI is a good fit for your training.
Discuss any research skills such as language training or methods/data familiarity that could be useful in the completion of your thesis.
Remember that a research gap is not yet a research puzzle that is worth answering).
The comparison of units is particularly appreciated in our department, be it sub-national or cross-national.
Highlighting paradoxes and unexpected results can also be a powerful tool to motivate readers whose research interests are far from yours.
Try to keep the spotlight on the main idea(s) of your project along the whole text while clearly spelling out your concrete plans.