The Assumptions are the environment in which the system operates. Example: "$N < 100"
The Requirements are the things the system must enforce/provide. Example: "No user shall vote more than once."
By grouping both, you make it sound as if "No user shall vote more than once." is an Assumption and is not a property (supposed to be) protected by the scheme.
You may even go further and split Assumptions in Environmental Assumptions and Entities, where Entities describes the participants of the system (S1-S3, the Users) and their properties (Keys etc.).
Is $RANDOMNAME always the same name for a given vote? If so, the association between votes/$RANDOMNAME and the signed confirmations/$RANDOMNAME breaks the anonymity completely. That should be clarified in the text.
[Section] "what can be achieved" parts (trust, anonymity, etc.) need to be a bit more focused and explained. Most systems will not be able to fulfill all requirements (availability?), so it's likely you'll need to make some concessions.