Picking Sequences and Monotonicity in Weighted Fair Division
Authors: Mithun Chakraborty, Ulrike Schmidt-Kraepelin, Warut Suksompong
IJCAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we conduct a thorough investigation of picking sequences based on common apportionment methods, as well as the maximum (weighted) Nash welfare solution, in relation to fairness and monotonicity properties. ... We begin in Section 3 by establishing fundamental results on our properties in the context of picking sequences. ... With this groundwork laid, we proceed to determine the properties satisfied by each allocation rule in Section 4. First, we consider the picking sequences derived from five traditional divisor methods... Next, in Section 5, we address the picking sequence derived from another important apportionment method: the quota method. Finally, in Section 6, we examine the maximum weighted Nash welfare (MWNW) solution... Our results are summarized in Table 1. Theorem 3.1. A picking sequence π satisfies WEF1 if and only if for every prefix of π and every pair of agents i, j with tj ≥ 2, we have ti+1/wi ≥ tj/wj and ti/wi ≥ (tj−1)/wj if wi ≤ wj; or ti+1/wi ≥ (tj−1)/wj and ti/wi ≥ tj/wj if wi ≥ wj, where ti and tj denote the number of agent i’s and agent j’s picks in the prefix, respectively. |
| Researcher Affiliation | Academia | Mithun Chakraborty1 , Ulrike Schmidt-Kraepelin2 and Warut Suksompong3 1Department of Electrical Engineering and Computer Science, University of Michigan, USA 2Efficient Algorithms Research Group, TU Berlin, Germany 3School of Computing, National University of Singapore, Singapore dcsmc@umich.edu, u.schmidt-kraepelin@tu-berlin.de, warut@comp.nus.edu.sg |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | The paper is theoretical and does not use or refer to any datasets, public or otherwise. |
| Dataset Splits | No | The paper is theoretical and does not involve dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe any computational experiments, thus no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not mention any specific ancillary software or library names with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup details such as hyperparameters or training configurations. |