
Given the following reason that explains which contestant is the winner, rewrite the reason to REPLACE all contestant names with their real names.

The contestant names are wrapped in $name$ format (e.g., $Alice$, $Bob$, $Charlie$).

Use the provided dummy-to-real names mapping to convert each $dummy_name$ to its corresponding real name.

Dummy-to-real mapping:
{{ dummy_to_real_names }}

Reason:
{{ reason }}

**Instructions:**
1. Find all instances of $name$ in the reason text
2. Look up each name in the dummy_to_real_names mapping
3. Replace $name$ with the corresponding real name
4. Keep all other text unchanged

**Example:**
If mapping is {"Alice": "gpt-4", "Bob": "claude-3"} and reason contains "$Alice$ provided better answers than $Bob$", 
the result should be "gpt-4 provided better answers than claude-3"

Return only the rewritten reason as JSON.

---
**Example JSON:**
{
  "rewritten_reason": <your-rewritten-reason-here>
}

JSON:
