Related papers: The Smoothed Likelihood of Doctrinal Paradox

The Smoothed Likelihood of Doctrinal Paradox

URL: http://arxiv.org/abs/2105.05138v2
Date: Fri, 4 Jun 2021 16:39:25 GMT
Title: The Smoothed Likelihood of Doctrinal Paradox
Authors: Ao Liu, Lirong Xia
Abstract summary: We show that under mild conditions, the smoothed likelihood of the doctrinal paradox is either $0$, $exp(-Theta(n))$, $Theta(n-1/2)$ or $Theta(1)$. Our main theorem states that under mild conditions, the smoothed likelihood of the doctrinal paradox is either $0$, $exp(-Theta(n))$, $Theta(n-1/2)$ or $Theta(1)$.
Score: 34.534516291695155
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: When aggregating logically interconnected judgments from $n$ agents, the result might be inconsistent with the logical connection. This inconsistency is known as the doctrinal paradox, which plays a central role in the field of judgment aggregation. Despite a large body of literature on the worst-case analysis of the doctrinal paradox, little is known about its likelihood under natural statistical models, except for a few i.i.d. distributions [List, 2005]. In this paper, we characterize the likelihood of the doctrinal paradox under a much more general and realistic model called the smoothed social choice framework [Xia, 2020b], where agents' ground truth judgments are arbitrarily correlated while the noises are independent. Our main theorem states that under mild conditions, the smoothed likelihood of the doctrinal paradox is either $0$, $\exp(-\Theta(n))$, $\Theta(n^{-1/2})$ or $\Theta(1)$. This not only answers open questions by List [2005] for i.i.d. distributions but also draws clear lines between situations with frequent and with vanishing paradoxes.

Related papers

A refined Frauchiger--Renner paradox based on strong contextuality [0.0]
We observe that logical contextuality is the key ingredient of the FR paradox. We propose a natural extension of Peres's dictum to resolve these extended Wigner's friend paradoxes.
arXiv Detail & Related papers (2024-09-09T10:36:47Z)
Variance-Aware Regret Bounds for Stochastic Contextual Dueling Bandits [53.281230333364505]
This paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM) We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound $tilde Obig(dsqrtsum_t=1Tsigma_t2 + dbig)$. Our regret bound naturally aligns with the intuitive expectation in scenarios where the comparison is deterministic, the algorithm only suffers from an $tilde O(d)$ regret.
arXiv Detail & Related papers (2023-10-02T08:15:52Z)
Logic meets Wigner's Friend (and their Friends) [49.1574468325115]
We take a fresh look at Wigner's Friend thought-experiment and some of its more recent variants and extensions. We discuss various solutions proposed in the literature, focusing on a few questions.
arXiv Detail & Related papers (2023-07-04T13:31:56Z)
Wigner's Friend paradoxes: consistency with weak-contextual and weak-macroscopic realism models [0.0]
Wigner's friend paradoxes highlight contradictions between measurements made by Friends inside a laboratory and superobservers outside a laboratory. The contradictions lead to no-go theorems for observer-independent facts, thus challenging concepts of objectivity. We demonstrate consistency with a contextual weak form of macroscopic realism.
arXiv Detail & Related papers (2022-11-05T11:13:12Z)
A possibilistic no-go theorem on the Wigner's friend paradox [0.0]
We present a probability-free version of the Local Friendliness theorem. It builds upon Hardy's no-go theorem for local hidden variables.
arXiv Detail & Related papers (2022-05-24T17:31:54Z)
Causal Expectation-Maximisation [70.45873402967297]
We show that causal inference is NP-hard even in models characterised by polytree-shaped graphs. We introduce the causal EM algorithm to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. We argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
arXiv Detail & Related papers (2020-11-04T10:25:13Z)
A Weaker Faithfulness Assumption based on Triple Interactions [89.59955143854556]
We propose a weaker assumption that we call $2$-adjacency faithfulness. We propose a sound orientation rule for causal discovery that applies under weaker assumptions.
arXiv Detail & Related papers (2020-10-27T13:04:08Z)
Contextuality scenarios arising from networks of stochastic processes [68.8204255655161]
An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X. We present a different and classical source of contextual empirical models: the interaction among many processes. The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.
arXiv Detail & Related papers (2020-06-22T16:57:52Z)
On abstract F-systems. A graph-theoretic model for paradoxes involving a falsity predicate and its application to argumentation frameworks [0.0]
F-systems are digraphs that enable to model sentences that predicate the falsity of other sentences. In this paper we present the F-systems model abstracting from all the features of the language in which the represented sentences are expressed.
arXiv Detail & Related papers (2020-05-14T15:07:11Z)
Unitary-Only Quantum Theory Cannot Consistently Describe the Use of Itself: On the Frauchiger-Renner Paradox [0.0]
The Frauchiger-Renner Paradox is an extension of paradoxes based on the 'Problem of Measurement,' such as Schrodinger's Cat and Wigner's Friend. This paper discusses a basic inconsistency arising in the FR scenario at a much earlier point than the derived contradiction.
arXiv Detail & Related papers (2020-02-04T18:34:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.