prize-extraction
🎯 Fair Draw - Introduction
Fair Draw is an intelligent random selection method that uses a dynamic weight algorithm to ensure each member's chance of being selected is inversely proportional to their past selection frequency, thus achieving true fairness.
It is suitable for scenarios that require fair random selection, such as classroom questioning, task assignment, and activity participation.
Key Advantages
- Smart Balancing: Prevents frequent selection of the same student.
- Dynamic Adjustment: Weights change in real-time based on historical data.
- Multi-dimensional Consideration: Factors such as total times, group, and gender are all considered.
⚙️ Dynamic Weight System
The Dynamic Weight System is the core engine of SecRandom for fair draws. It calculates the real-time weight of each member based on 5 key dimensions:
| Dimension | Purpose | Weight Impact |
|---|---|---|
| 📊 Total Draw Count | Prevent frequent selection of the same person | More draws result in lower weight |
| 👥 Group Balance | Ensure equal opportunities across groups | Group draw frequency impacts weight |
| ⚧️ Gender Balance | Maintain gender proportion balance | Gender draw frequency impacts weight |
| 🎯 Base Weight | Provide baseline fairness | Fixed baseline value |
| 🆕 Cold Start Protection | Protect new members | First 10 draws have weight protection |
🔍 Algorithm Logic Explanation
📈 Weight Calculation Formula
The system calculates the final weight based on historical data through the following 5 steps:
1️⃣ Frequency Penalty Factor
Weight adjustment based on the total number of draws for a person:
frequency_factor = 1.0 / math.sqrt(student_history["total_number_of_times"] * 2 + 1)Example Calculation:
- Student A was drawn 5 times →
1/√(5*2+1) = 1/√11 ≈ 0.302 - Weight value: 0.302 (smaller values mean lower probability of being selected)
2️⃣ Group Balance Factor
Ensures equal opportunities for all groups:
group_factor = 1.0 / (group_history * 0.2 + 1)Trigger Condition: At least 3 groups have recorded draws.
3️⃣ Gender Balance Factor
Maintains gender ratio balance:
gender_factor = 1.0 / (gender_history * 0.2 + 1)Trigger Condition: At least 2 genders have recorded draws.
4️⃣ Cold Start Protection Mechanism
Protects newly joined students:
if current_round < COLD_START_ROUNDS: # COLD_START_ROUNDS = 10
frequency_factor = min(0.8, frequency_factor)Protection Effect: New students enjoy a minimum weight protection of 0.8 for the first 10 draws.
5️⃣ Final Weight Synthesis
The final weight is derived by combining all factors:
student_weights = {
'base': BASE_WEIGHT * 0.2, # Base Weight (20%)
'frequency': frequency_factor * 3.0, # Frequency Penalty (60%)
'group': group_factor * 0.8, # Group Balance (10%)
'gender': gender_factor * 0.8 # Gender Balance (10%)
}Weight Range
The final weight is normalized to a reasonable range to prevent extreme values from impacting fairness.
📊 Practical Application Effects
Scenario Example
Assume a class of 30 students, where:
- Xiao Ming has been drawn 15 times (high frequency)
- Xiao Hong has been drawn 3 times (medium frequency)
- Xiao Gang is a new student (cold start)
Weight Comparison:
- Xiao Ming: Low weight (significant frequency penalty)
- Xiao Hong: Medium weight (normal level)
- Xiao Gang: Protected weight (cold start mechanism)
🎲 Draw Probability
The system calculates the draw probability based on real-time weight, ensuring long-term fairness in the statistics.
