Parity Argument Research Articles

Parity, Poverty, and Physician Aid in Dying: Policy Recommendations for PAD in Light of Social Injustices.

In light of the proposed expansion of eligibility for physician aid in dying (PAD) in Canada to people with psychiatric disorders, there is a new subset of individuals seeking PAD-those with poverty-induced depression. The dominant account defending the expansion is known as the "parity argument." Defenders of the parity argument maintain that the expansion of PAD to those with psychiatric conditions is needed to reflect that the seriousness of a patient's suffering does not depend on the cause of that suffering. Parity accounts, as they stand, would allow cases of poverty-induced depression to qualify. I raise a moral dilemma that the parity theorist must face considering this new subset of cases-expanding access to PAD, without adequate social protections, could produce more social inequality by aiming to reduce it. I propose six recommendations that policy-makers should consider before expanding PAD given these cases, social injustice, and the social determinants of mental health.

Recovering Differential Forces From the GRACE‐D Accelerometer

AbstractThe reduction of non‐gravitational accelerations through an onboard accelerometer is a vital part of accurately estimating gravity fields for Gravity Recovery and Climate Experiment (GRACE) Follow‐On (GRACE‐FO). Current accelerometer quality, specifically a defect on the GRACE‐D accelerometer, necessitates the use of extensive calibration techniques to optimally utilize the accelerometer measurements. This paper describes these techniques and correction algorithms as they are used for the official GRACE‐FO accelerometer products, which rest on the information present in the partially functional GRACE‐D accelerometer. First, transplanted data from GRACE‐C is used to remove common effects between the spacecraft. Then, GRACE‐D data is utilized to compute a correction to the transplanted data to account for solar radiation pressure (SRP) and albedo using a parity argument and to account for non‐common drag and thruster leaks in the attitude control system. The SRP and albedo term predominantly improves C3,0 while the drag and leaky thruster term improves the gravity field across the entire spectrum. Finally, some comments on alternative data usage, initial modifications to the algorithms to account for other spacecraft operational modes, and future outlook are provided.

Newman and Quasi‐Fideism: A Reply to Duncan Pritchard

Abstract: In recent years, Duncan Pritchard has developed a position in religious epistemology called quasi‐fideism that he claims traces back to John Henry Newman's treatment of the rationality of religious belief. In this paper, we give three reasons to think that Pritchard's reading of Newman as a quasi‐fideist is mistaken. First, Newman's parity argument does not claim that religious and non‐religious beliefs are on a par because both are groundless; instead, for Newman, they are on a par because both often stem from implicit rather than explicit reasoning. Second, pace Pritchard, Newman's distinction between simple and complex assent does not map onto the Wittgensteinian distinction between groundless hinge commitments and beliefs that flow from these hinges. For Newman, simple and complex assent differ in terms of the believer's level of awareness of their grounds. Third, and finally, Newman does not reject Locke's evidentialism in toto. Instead, he argues that certitude is not restricted to beliefs stemming from intuition and demonstration but often rightly includes probabilistically supported (or fallibly evidenced) beliefs.

Satiation in Fisher Markets and Approximation of Nash Social Welfare

We study linear Fisher markets with satiation. In these markets, sellers have earning limits, and buyers have utility limits. Beyond applications in economics, they arise in the context of maximizing Nash social welfare when allocating indivisible items to agents. In contrast to markets with either earning or utility limits, markets with both limits have not been studied before. They turn out to have fundamentally different properties. In general, the existence of competitive equilibria is not guaranteed. We identify a natural property of markets (termed money clearing) that implies existence. We show that the set of equilibria is not always convex, answering a question posed in the literature. We design an FPTAS to compute an approximate equilibrium and prove that the problem of computing an exact equilibrium lies in the complexity class continuous local search ([Formula: see text]; i.e., the intersection of polynomial local search ([Formula: see text]) and polynomial parity arguments on directed graphs ([Formula: see text])). For a constant number of buyers or goods, we give a polynomial-time algorithm to compute an exact equilibrium. We show how (approximate) equilibria can be rounded and provide the first constant-factor approximation algorithm (with a factor of 2.404) for maximizing Nash social welfare when agents have capped linear (also known as budget-additive) valuations. Finally, we significantly improve the approximation hardness for additive valuations to [Formula: see text]. Funding: J. Garg was supported by the National Science Foundation [Grant CCF-1942321 (CAREER)]. M. Hoefer was supported by Deutsche Forschungsgemeinschaft [Grants Ho 3831/5-1, Ho 3831/6-1, and Ho 3831/7-1].

A lower bound for constant-size local certification

Given a network property or a data structure, a local certification is a labeling that allows to efficiently check that the property is satisfied, or that the structure is correct. The quality of a certification is measured by the size of its labels: the smaller, the better. This notion plays a central role in self-stabilization, because the size of the certification is a lower bound (and often an upper bound) on the memory needed for silent self-stabilizing construction of distributed data structures.When it comes to the size of the certification labels, one can identify three important regimes: the properties for which the optimal size is polynomial in the number of vertices of the graph, the ones that require only polylogarithmic size, and the ones that can be certified with a constant number of bits. The first two regimes are well studied, with several upper and lower bounds, specific techniques, and active research questions. On the other hand, the constant regime has never been really explored.The main contribution of this paper is the first non-trivial lower bound for this constant regime. More precisely, we show that by using certification on just one bit (a binary certification), one cannot certify k-colorability for k≥3. To do so, we develop a new technique, based on the notion of score, and both local symmetry arguments and a global parity argument. We hope that this technique will be useful for establishing stronger results.We complement this result with an upper bound for a related problem, illustrating that in some cases one can do better than the natural upper bound.

Mental Health Parity Arguments for Accessing Gender Affirmation Surgery.

Many insurers exclude coverage for transgender individuals. Litigation challenging these exclusions has increased. Most of these cases successfully advance equality claims by arguing that trans exclusions discriminate based on sex. That is, procedures performed on patients for reasons unrelated to gender affirming care are being denied to transgender individuals. There are, however, limitations to this argument. First, some courts may construe care narrowly and hold that some procedures are unique to gender affirming care that have no analog in other contexts. Second, a court that is hostile to the sex discrimination argument might hold that the denial does not arise from sex discrimination, but rather, because of the kind of diagnosis at issue. Further, the sex discrimination argument might force transgender individuals into making claims based on a binarized gender identity which may not conform with their lived experience.Claims based on the Mental Health Parity and Addiction Equity Act of 2008 (MHPAEA) can address these shortcomings. This Act prohibits insurers from discriminating against mental health diagnoses-for example, procedures that insurers cover because of medical or surgical diagnoses should alsobe covered if indicated for mental health diagnoses. Gender dysphoria is a recognized mental health diagnosis. Transgender individuals seeking gender affirming care arising from gender dysphoria can thus claim that exclusions of coverage violate the MHPAEA. Some transgender individuals might raise concerns that such an approach would lead to increased medicalization of trans identity. However, an MHPAEA claim would only appear in cases where a transgender individual is voluntarily submitting themselves to medical assistance in order to advance their own autonomy.

The Perils of Rejecting the Parity Argument

AbstractMany moral error theorists reject moral realism on the grounds that moral realism implies the existence of categorical normativity, yet categorical normativity does not exist. Call this the Metaphysical Argument. In response, some moral realists have emphasized a parity between moral normativity and epistemic normativity. They argue that if one kind of normativity is rejected, then both must be rejected. Therefore, one cannot be a moral error theorist without also being an epistemic error theorist. Call this the Parity Argument. In this paper, we address three possible responses to the Parity Argument from moral error theorists: (1) accept the parity but still reject epistemic error theory, (2) reject the parity, (3) accept the parity and defend epistemic error theory. We argue that there are problems with each of these responses, so the Parity Argument stands as a strong counterargument to the Metaphysical Argument. We conclude by drawing some lessons for any future challenges to the Parity Argument.

Eating in Isolation: A Normative Comparison of Force Feeding and Solitary Confinement.

The practice of solitary confinement (SC) is established within the literature as a common occurrence of torture within the prison system, and many international and national human rights organizations have called for its abolition. A somewhat more contentious topic in the literature is the practice of force feeding (FF) of hunger-striking prisoners. The paper aims to make a case against FF by establishing a parity argument that states the following: If SC is considered an immoral practice (and indeed it should be), it should follow that FF is morally impermissible as well. In conclusion, this paper will argue that FF of hunger-striking prisoners is a violation of their fundamental moral rights and constitutes cruel and inhumane treatment and, therefore, should be abolished.

Properties, Collections, and the Successive Addition Argument: A Reply to Malpass

The Successive Addition Argument (SAA) is one of the key arguments espoused by William Lane Craig for the thesis that the universe began to exist. Recently, Malpass, Mind, 131(523), 786–804 (2021) has developed a challenge to the SAA by way of constructing a counterexample that originates in the work of Fred Dretske. In this paper, I show that the Malpass-Dretske counterexample is in fact no counterexample to the argument. Utilizing a distinction between properties of members and properties of collections, I argue that Malpass’ counterexample has no bearing on the soundness of the SAA. I also develop a novel parity argument against Malpass’ argument that I demonstrate can only be resolved by way of the aforementioned analysis.

Mereology is not a Guide to (In)conceivability

A sophisticated version of the zombie argument due to David Chalmers runs roughly as follows: a zombie world is ideally primarily conceivable, and whatever is ideally primarily conceivable is primarily possible. Thus, a zombie world is primarily possible, which implies, in turn, that either physicalism is false or Russellian monism is true. Appealing to some plausible mereological considerations, Daniel Giberman presents a novel argument to the effect that zombies are not ideally primarily conceivable. I shall argue, firstly, that a main premise of Giberman's argument is ill-supported, as it trades on a confusion between the primary and the secondary intensions of the "actually" operator. I then consider two lines of reasoning, which might be extracted from Giberman's text, in favour of another chief premise of his argument. I shall argue that the first line of reasoning is flawed, and the second one, in effect, will transform Giberman's argument into a kind of "parity argument" in which his mereological considerations play no role.

Rydberg atomic antenna in strongly driven multielectron atoms

We study the role of intermediate excitations of Rydberg states as an example of Kuchiev's ``atomic antenna'' in above-threshold ionization of xenon, in particular their effect on the coherence between the spin-orbit-split states of the ion. We focus on the case of a laser frequency close to resonant with the spin-orbit splitting, where a symmetry (parity) argument would preclude any coherence being directly generated by strong-field ionization. Using ab initio simulations of coupled multielectron spin-orbit dynamics in strong laser fields, we show how field-driven rescattering of the trapped Rydberg electrons introduces efficient coupling between the spin-orbit-split channels, leading to substantial coherences, exceeding 10% for some photon energies.

Complete dynamical evaluation of the characteristic polynomial of binary quantum graphs

We evaluate the variance of coefficients of the characteristic polynomial for binary quantum graphs using a dynamical approach. This is the first example where a spectral statistic can be evaluated in terms of periodic orbits for a system with chaotic classical dynamics without taking the semiclassical limit, which here is the limit of large graphs. The variance depends on the sizes of particular sets of primitive pseudo orbits (sets of distinct primitive periodic orbits): the set of primitive pseudo orbits without self-intersections and the sets of primitive pseudo orbits with a fixed number of self-intersections, all of which consist of two arcs of the pseudo orbit crossing at a single vertex. To show other pseudo orbits do not contribute we give two arguments. The first is based on a reduction of the variance formula from a sum over pairs of primitive pseudo orbits to a sum over pseudo orbits where no bonds are repeated. The second employs a parity argument for the Lyndon decomposition of words. For families of binary graphs, in the semiclassical limit, we show the pseudo orbit formula approaches a universal constant independent of the coefficient of the polynomial. This is obtained by counting the total number of primitive pseudo orbits of a given length.

Fully Polynomial-Time Approximation Schemes for Fair Rent Division

We study the problem of fair rent division that entails splitting the rent and allocating the rooms of an apartment among agents in a fair manner (i.e., under the imposed rents, no agent has a strictly stronger preference for any other agent’s room). The utility functions specify the cardinal preferences of the agents for the rooms for every possible room rent. Although envy-free solutions are guaranteed to exist under reasonably general utility functions, efficient algorithms for finding them were known only for quasilinear utilities. This work addresses this notable gap and develops a fully polynomial-time approximation scheme for fair rent division with minimal assumptions on the utility functions. Envy-free solutions correspond to equilibria of a two-sided matching market with monetary transfers; hence, this work also provides efficient algorithms for finding approximate equilibria in such markets. We complement the algorithmic results by proving that the fair rent division problem lies in the intersection of the complexity classes polynomial parity arguments on directed graphs and polynomial local search.

Phenomenal transparency, cognitive extension, and predictive processing

I discuss Clark’s predictive processing/extended mind hybrid, diagnosing a problem: Clark’s hybrid suggests that, when we use them, we pay attention to mind-extending external resources. This clashes with a commonly accepted necessary condition of cognitive extension; namely, that mind-extending resources must be phenomenally transparent when used. I then propose a solution to this problem claiming that the phenomenal transparency condition should be rejected. To do so, I put forth a parity argument to the effect that phenomenal transparency cannot be a necessary condition on cognitive extension: roughly, since internal cognitive resources can fail to be transparent when used, by parity, external resources can fail to be phenomenally transparent too. Further, I argue that phenomenal transparency is not even a reliable indicator of cognitive extension; hence its absence should not be considered a problem for Clark’s extended mind-predictive processing hybrid. Lastly, I consider and allay a number of worries my proposal might raise, and conclude the paper.

Detecting Unsolvability Based on Separating Functions

While the unsolvability IPC sparked a multitude of planners proficient in detecting unsolvable planning tasks, there are gaps where concise unsolvability arguments are known but no existing planner can capture them without prohibitive computational effort. One such example is the sliding tiles puzzle, where solvability can be decided in polynomial time with a parity argument. We introduce separating functions, which can prove that one state is unreachable from another, and show under what conditions a potential function over any nonzero ring is a separating function. We prove that we can compactly encode these conditions for potential functions over features that are pairs, and show in which cases we can efficiently synthesize functions satisfying these conditions. We experimentally evaluate a domain-independent algorithm that successfully synthesizes such separating functions from PDDL representations of the sliding tiles puzzle, the Lights Out puzzle, and Peg Solitaire.

Progressions in young learners’ understandings of parity arguments

ABSTRACT Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characterizes empirically developed progressions in Grades K–1 students’ thinking about parity arguments for sums of evens and odds, as well as underlying concepts of pair and parity of a number. Data are drawn from classroom lessons of a Grades K–1 early algebra instructional sequence, as well as task-based interviews conducted at four timepoints during the implementation of the sequence. While most students at the beginning of the study (Grade K) did not know the concepts of even or odd and could not make any viable arguments regarding parity, by the end of Grade 1 students were largely constructing representation-based arguments to justify number parity and claims about sums of evens and odds. Results of this study align with other research that shows young learners can develop viable arguments to justify mathematical generalizations. Results also provide preliminary evidence that the instructional sequence used here can foster students’ practice of argumentation from the start of formal schooling.

Consensus Halving for Sets of Items

Consensus halving refers to the problem of dividing a resource into two parts so that every agent values both parts equally. Prior work shows that, when the resource is represented by an interval, a consensus halving with at most n cuts always exists but is hard to compute even for agents with simple valuation functions. In this paper, we study consensus halving in a natural setting in which the resource consists of a set of items without a linear ordering. For agents with linear and additively separable utilities, we present a polynomial-time algorithm that computes a consensus halving with at most n cuts and show that n cuts are almost surely necessary when the agents’ utilities are randomly generated. On the other hand, we show that, for a simple class of monotonic utilities, the problem already becomes polynomial parity argument, directed version–hard. Furthermore, we compare and contrast consensus halving with the more general problem of consensus k-splitting, with which we wish to divide the resource into k parts in possibly unequal ratios and provide some consequences of our results on the problem of computing small agreeable sets.

Spectral stability of pattern-forming fronts in the complex Ginzburg–Landau equation with a quenching mechanism

We consider pattern-forming fronts in the complex Ginzburg–Landau equation with a traveling spatial heterogeneity which destabilises, or quenches, the trivial ground state while progressing through the domain. We consider the regime where the heterogeneity propagates with speed c just below the linear invasion speed of the pattern-forming front in the associated homogeneous system. In this situation, the front locks to the interface of the heterogeneity leaving a long intermediate state lying near the unstable ground state, possibly allowing for growth of perturbations. This manifests itself in the spectrum of the linearisation about the front through the accumulation of eigenvalues onto the absolute spectrum associated with the unstable ground state. As the quench speed c increases towards the linear invasion speed, the absolute spectrum stabilises with the same rate at which eigenvalues accumulate onto it allowing us to rigorously establish spectral stability of the front in . The presence of unstable absolute spectrum poses a technical challenge as spatial eigenvalues along the intermediate state no longer admit a hyperbolic splitting and standard tools such as exponential dichotomies are unavailable. Instead, we projectivise the linear flow, and use Riemann surface unfolding in combination with a superposition principle to study the evolution of subspaces as solutions to the associated matrix Riccati differential equation on the Grassmannian manifold. Eigenvalues can then be identified as the roots of the meromorphic Riccati–Evans function, and can be located using winding number and parity arguments.

The complexity of the parity argument with potential

The parity argument principle states that every finite graph has an even number of odd degree vertices. We consider the problem whose totality is guaranteed by the parity argument on a graph with potential. In this paper, we show that the problem of finding an unknown odd-degree vertex or a local optimum vertex on a graph with potential is polynomially equivalent to EndOfPotentialLine if the maximum degree is at most three. However, even if the maximum degree is 4, such a problem is PPA∩PLS-complete. To show the complexity of this problem, we provide new results on multiple-source variants of EndOfPotentialLine, which is the canonical problem for EOPL. This result extends the work by Goldberg and Hollender; they studied similar variants of EndOfLine.

A formação dos ministros da educação no Brasil e o recorte de gênero - 1930 a 2020: políticas públicas de gestão

The problems that come from the current crisis of representation go back to the process of creating the notions and institutions of representative democracy. Through historical analysis we can better comprehend this complexity. This article aims to analyze the link between representation, participation and decentralization by focusing on the 1789 debates on the Municipality of Paris and Condorcet’s constitutional model, which still stands as a theoretical point of reference. The continuity in practical and theoretical issues concerning representation is also explored with regard to Condorcet’s claims in favor of women’s political rights intrinsically linked to his concept of representation. They are compared to the current gender parity arguments, which led in 1999 to the revision of art. IIII of the French Constitution encouraging the equal access to representative institutions. Stemmed from different contexts both these sets of arguments maintain that only parity between men and women renders the representation of national sovereignty effective.