Height-Balanced Tree Scoring for Preference Data
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Solution Overview
Problem
Existing systems for collecting crowd-based scoring of diverse choices are inefficient as they require exhaustive comparisons, leading to biased and sparse data, especially when the number of choices increases, resulting in computationally intensive and biased results.
Innovation Solution
The use of a height-balanced tree structure, such as a red-black tree, to reduce the number of comparisons needed to evaluate preferences among members of a set, by periodically rebalancing the tree and tracking both 'yes' and 'no' votes to assign scores based on relative preference data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exhaustive pairwise comparisons are conducted to score all choices, then complete preference data is obtained, but the computational complexity and time required increase dramatically with the number of choices
Solution Approach 1:
The patent segments the exhaustive comparison task by organizing choices into a tree structure where each node represents a subset of choices. Instead of comparing all pairs directly, the system divides the set into smaller subsets at each tree level, comparing only within those subsets. This segmentation reduces the total number of comparisons from O(n²) to O(n log n) while still capturing comprehensive preference information across all choices.
2Measurement precision
If the number of choices increases, then more comprehensive scoring is needed, but the time required for individuals to evaluate and vote increases, leading to biased and sparse data
Solution Approach 1:
The tree structure segments the evaluation task into manageable subsets. Individuals only need to evaluate choices within their assigned subset at each tree level, rather than evaluating all choices exhaustively. This reduces the time burden on individuals while maintaining comprehensive coverage across all choices through the aggregation of results from multiple subsets.
Solution Approach 2:
The system performs partial comparisons by only evaluating subsets of choices rather than all possible pairs. Each individual performs a partial evaluation of their assigned subset, and the results are aggregated to derive complete scoring. This partial action approach reduces individual time investment while achieving comprehensive scoring through mathematical aggregation of the partial results.
3Loss of information
If individuals vote on all possible choices, then complete preference data is collected, but the process becomes cumbersome and leads to biased voting patterns
Solution Approach 1:
The voting process is segmented into multiple rounds, with each round presenting a subset of choices derived from the tree structure. Individuals vote only on the choices within their assigned subset rather than all choices simultaneously. This segmentation makes the voting process more manageable and less cumbersome while ensuring complete preference data is collected through aggregation of results from all subsets.
4Measurement precision
If pairwise comparisons are conducted between all possible choices, then accurate relative scoring is achieved, but the number of comparisons becomes computationally intensive
Solution Approach 1:
The patent segments the comparison process by organizing choices into a tree structure where comparisons are performed locally within subsets at each tree level rather than globally across all pairs. This segmentation reduces the total number of comparisons required while maintaining accurate relative scoring through the hierarchical aggregation of local comparison results.
Solution Approach 2:
The patent introduces a hierarchical dimension to the comparison process by organizing choices into multiple tree levels. Instead of a flat two-dimensional pairwise comparison matrix, the system uses a three-dimensional hierarchical structure (tree level, subset position, choice position) to organize comparisons. This dimensional transformation reduces the computational burden while preserving scoring accuracy.
Data Source
AI summary
A software voting or prediction system iteratively solicits participant preferences between members of a set, with a binary tree built used to minimize the number of iterations required. As each member of the set is considered, it is pairwise-compared with select members represented by nodes already in the binary tree, with iterations beginning at a root node of the tree and continuing to a leaf node. The newly considered member is placed as a new leaf node, and the tree is height-rebalanced as appropriate. Red-black tree coloring and tree rotation rules are optionally used for this purpose. Yes/no preference tallies are kept for each member of the set throughout the tree-building process and are ultimately used for scoring. Height-rebalancing of the tree helps minimize the number of iterations needed to precisely score each member of the set relative to its alternatives.