The algorithm used is a form of Greedy Allocation or Preference-Based Fair Division, which is often related to Matching Theory and Discrete Optimization. More specifically, it follows the Maximal Matching in Bipartite Graphs approach, commonly used in Assignment Problems and Fair Division Problems.

Key Steps in the Algorithm:

1. Sort Items by Highest Preference: Prioritize assigning items to users with the highest (5) preference first.
2. Assign Items Uniquely: If an item has only one user with the highest preference, assign it to them.
3. Resolve Conflicts:
   • If multiple users want the same item, prioritize users who have no other high-preference choices.
   • If conflicts remain, consider secondary preferences (rating 3 or 4).
4. Ensure Each User Gets One Item (if possible): Distribute remaining items fairly among lower-preference users.

This resembles the Hungarian Algorithm (used for optimal matching in bipartite graphs) and Gale-Shapley Algorithm (used for stable marriage and fair allocation). However, the specific method applied here is more of a Greedy Preference Allocation technique.

There may be situations where a conflict does not have an automatic resolution, ex. five people all want a single item with highest preference and no other items. You can choose from a couple methods to resolve those conflicts:

1. First-Come-First-Served – the first user to reply wins the tie-breaker if all else is equal.
2. Random selection – The report will clearly indicate which items were distributed due a conflict and random resolution.
3. Manual Resolution – You (the administrator) can choose the winner of the tie-breaker, then calculations can proceed to distribute remaining items. (Not recommended due to possible accusation of bias)

When you create groups you assign the group to a tier then users in the group are assigned items based on tier, ex.: child tier users get priority allocation over grandchild tier users.

1. Sorting Order → Users are first sorted by tier (1 before 2), then by preference (higher first).
2. Higher-Tier Users Are Processed First → A Tier 1 user’s 4 will be assigned before a Tier 2 user’s 5.
3. Conflicts Are Resolved Automatically by ensuring higher-tier users get first pick.

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