Extending Tournament Solutions
Authors: Felix Brandt, Markus Brill, Paul Harrenstein
AAAI 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Tournaments have a rich mathematical theory and many formal results for majoritarian functions assume that the majority relation constitutes a tournament. In this paper, we propose a generic way to extend any tournament solution to the class of weak tournaments. This so-called conservative extension of a tournament solution S returns all alternatives that are chosen by S in some orientation of the weak tournament at hand. We show that many of the most common axiomatic properties of tournament solutions are inherited from S to its conservative extension (see Table 1 for an overview). Due to the space constraint, most proofs are omitted. They can be found in the full version of this paper. We argue that these results provide a justiļ¬cation for restricting attention to tournaments when studying majoritarian functions. The conservative extension also leads to interesting computational problems that are strongly related to the possible winner problem (Lang et al. 2012). |
| Researcher Affiliation | Academia | Felix Brandt Institut f ur Informatik Technische Universit at M unchen 85748 Garching, Germany brandtf@in.tum.de Markus Brill Department of Computer Science Duke University Durham, NC 27708, USA brill@cs.duke.edu Paul Harrenstein Department of Computer Science University of Oxford Oxford OX1 3QD, UK paul.harrenstein@cs.ox.ac.uk |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide any statements about releasing open-source code or links to a code repository. |
| Open Datasets | No | This paper is theoretical and does not involve the use of datasets for training or evaluation. |
| Dataset Splits | No | This paper is theoretical and does not involve dataset splits (training, validation, test). |
| Hardware Specification | No | This is a theoretical paper and does not describe any experiments that would require specific hardware specifications. |
| Software Dependencies | No | This paper is theoretical and does not list any specific software dependencies with version numbers. |
| Experiment Setup | No | This is a theoretical paper and does not describe any experimental setup details such as hyperparameters or training configurations. |