A Theory of Tournament Representations

Authors: Arun Rajkumar, Vishnu Veerathu, Abdul Bakey Mir

ICLR 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We conducted simple experiments on real world data sets. Specifically, we considered 114 real world tournaments that arise in several applications including election candidate preferences, Sushi preferences, cars preferences, etc (source: www.preflib.org). The number of nodes in these tournaments varied from 5 to 23. Out of the 114 tournaments considered, 76(66.67%) were in fact locally transitive. For these tournaments, the upper bounds and lower bounds given by our theorems matched and was equal to 2. Interestingly, even for the non-locally transitive tournaments, the lower bound still turned out to be 2. We computed the upper bound for tournaments of size at most 9 (we did not do it for larger tournaments as this involves a brute force search) and found the value to be either 4 or 6.
Researcher Affiliation Collaboration Arun Rajkumar Indian Institute of Technology RBCDSAI, IITM Abdul Bakey Mir Indian Institute of Technology Vishnu Veerathu Cohesity Inc
Pseudocode No The paper describes algorithms (e.g., a Quicksort-based algorithm), but it does not present them in a structured pseudocode block or a clearly labeled algorithm figure.
Open Source Code Yes The code for the filtration can be found here. [link removed]
Open Datasets Yes Specifically, we considered 114 real world tournaments that arise in several applications including election candidate preferences, Sushi preferences, cars preferences, etc (source: www.preflib.org).
Dataset Splits No The paper mentions using 114 real-world tournaments for experiments but does not provide any specific details about training, validation, or test dataset splits or how the data was partitioned for analysis.
Hardware Specification No The paper does not provide any specific details about the hardware (e.g., CPU, GPU models, memory, or cloud resources) used to run its experiments.
Software Dependencies No The paper mentions that "The code for the filtration can be found here" but does not specify any software dependencies (e.g., programming languages, libraries, frameworks) with version numbers that would be needed to replicate the experimental setup.
Experiment Setup No The paper describes the datasets used and the findings of its real-world experiments but provides no specific details regarding the experimental setup, such as hyperparameters, training configurations, or system-level settings.