Apportionment with Parity Constraints
- URL: http://arxiv.org/abs/2108.04137v1
- Date: Mon, 9 Aug 2021 16:08:12 GMT
- Title: Apportionment with Parity Constraints
- Authors: Claire Mathieu, Victor Verdugo
- Abstract summary: We consider the question of how to allocate seats of a parliament under parity constraints between candidate types.
A typical benchmark used in the context of two-dimensional apportionment is the fair share, which corresponds to an ideal fractional biproportional solution.
- Score: 1.52292571922932
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In the classic apportionment problem the goal is to decide how many seats of
a parliament should be allocated to each party as a result of an election. The
divisor methods provide a way of solving this problem by defining a notion of
proportionality guided by some rounding rule. Motivated by recent challenges in
the context of electoral apportionment, we consider the question of how to
allocate the seats of a parliament under parity constraints between candidate
types (e.g. equal number of men and women elected) while at the same time
satisfying party proportionality.
We consider two different approaches for this problem. The first mechanism,
that follows a greedy approach, corresponds to a recent mechanism used in the
Chilean Constitutional Convention 2021 election. We analyze this mechanism from
a theoretical point of view. The second mechanism follows the idea of
biproportionality introduced by Balinski and Demange [Math. Program. 1989,
Math. Oper. Res. 1989]. In contrast with the classic biproportional method by
Balinski and Demange, this mechanism is ruled by two levels of proportionality:
Proportionality is satisfied at the level of parties by means of a divisor
method, and then biproportionality is used to decide the number of candidates
allocated to each type and party. We provide a theoretical analysis of this
mechanism, making progress on the theoretical understanding of methods with two
levels of proportionality. A typical benchmark used in the context of
two-dimensional apportionment is the fair share (a.k.a matrix scaling), which
corresponds to an ideal fractional biproportional solution. We provide lower
bounds on the distance between these two types of solutions, and we explore
their consequences in the context of two-dimensional apportionment.
Related papers
- Multipartite entanglement theory with entanglement-nonincreasing
operations [91.3755431537592]
We extend the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication.
We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states.
arXiv Detail & Related papers (2023-05-30T12:53:56Z) - Efficient Alternating Minimization Solvers for Wyner Multi-View
Unsupervised Learning [0.0]
We propose two novel formulations that enable the development of computational efficient solvers based the alternating principle.
The proposed solvers offer computational efficiency, theoretical convergence guarantees, local minima complexity with the number of views, and exceptional accuracy as compared with the state-of-the-art techniques.
arXiv Detail & Related papers (2023-03-28T10:17:51Z) - Fairly Allocating Utility in Constrained Multiwinner Elections [0.0]
A common denominator to ensure fairness across all such contexts is the use of constraints.
Across these contexts, the candidates selected to satisfy the given constraints may systematically lead to unfair outcomes for historically disadvantaged voter populations.
We develop a model to select candidates that satisfy the constraints fairly across voter populations.
arXiv Detail & Related papers (2022-11-23T10:04:26Z) - Individualized Decision-Making Under Partial Identification: Three
Perspectives, Two Optimality Results, and One Paradox [0.0]
We argue that when faced with unmeasured confounding, one should pursue individualized decision-making using partial identification.
We establish a formal link between individualized decision-making under partial identification and classical decision theory.
arXiv Detail & Related papers (2021-10-21T08:15:35Z) - Fairmandering: A column generation heuristic for fairness-optimized
political districting [0.0]
American winner-take-all congressional district system empowers politicians to engineer electoral outcomes by manipulating district boundaries.
Existing computational solutions mostly focus on drawing unbiased maps by ignoring political and demographic input, and instead simply optimize for compactness.
We claim that this is a flawed approach because compactness and fairness are qualities, and introduce a scalable two-stage method to explicitly optimize for arbitrary piecewise-linear definitions of fairness.
arXiv Detail & Related papers (2021-03-21T19:22:42Z) - NLP-CIC @ DIACR-Ita: POS and Neighbor Based Distributional Models for
Lexical Semantic Change in Diachronic Italian Corpora [62.997667081978825]
We present our systems and findings on unsupervised lexical semantic change for the Italian language.
The task is to determine whether a target word has evolved its meaning with time, only relying on raw-text from two time-specific datasets.
We propose two models representing the target words across the periods to predict the changing words using threshold and voting schemes.
arXiv Detail & Related papers (2020-11-07T11:27:18Z) - Double Robust Representation Learning for Counterfactual Prediction [68.78210173955001]
We propose a novel scalable method to learn double-robust representations for counterfactual predictions.
We make robust and efficient counterfactual predictions for both individual and average treatment effects.
The algorithm shows competitive performance with the state-of-the-art on real world and synthetic data.
arXiv Detail & Related papers (2020-10-15T16:39:26Z) - Dealing with Incompatibilities among Procedural Goals under Uncertainty [1.2599533416395763]
We represent agent's plans by means of structured arguments whose premises are pervaded with uncertainty.
We measure the strength of these arguments in order to determine the set of compatible goals.
Considering our novel approach for measuring the strength of structured arguments, we propose a semantics for the selection of plans and goals.
arXiv Detail & Related papers (2020-09-17T00:56:45Z) - Modeling Voting for System Combination in Machine Translation [92.09572642019145]
We propose an approach to modeling voting for system combination in machine translation.
Our approach combines the advantages of statistical and neural methods since it can not only analyze the relations between hypotheses but also allow for end-to-end training.
arXiv Detail & Related papers (2020-07-14T09:59:38Z) - Rethink Maximum Mean Discrepancy for Domain Adaptation [77.2560592127872]
This paper theoretically proves two essential facts: 1) minimizing the Maximum Mean Discrepancy equals to maximize the source and target intra-class distances respectively but jointly minimize their variance with some implicit weights, so that the feature discriminability degrades.
Experiments on several benchmark datasets not only prove the validity of theoretical results but also demonstrate that our approach could perform better than the comparative state-of-art methods substantially.
arXiv Detail & Related papers (2020-07-01T18:25:10Z) - Pseudo-Convolutional Policy Gradient for Sequence-to-Sequence
Lip-Reading [96.48553941812366]
Lip-reading aims to infer the speech content from the lip movement sequence.
Traditional learning process of seq2seq models suffers from two problems.
We propose a novel pseudo-convolutional policy gradient (PCPG) based method to address these two problems.
arXiv Detail & Related papers (2020-03-09T09:12:26Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.