Symmetric Choice Research Articles

Exploring reference-dependency in route switching behavior on intercity travel: Endowment effect and disparities between willingness to pay and willingness to accept

This study explores asymmetric preferences in route switching behavior on intercity travel. A reference-dependent travel choice model reflecting the endowment effect is empirically compared with the classical symmetric travel choice model to investigate the significance of the reference-dependency. Based on the application to stated preference data, our results reveal that the reference-dependent travel choice model outperforms the classical symmetric travel choice model in route switching decision, indicating the significant disparities between WTA and WTP. It implies that policy making based on the results of the classical symmetric model assuming equivalent WTA and WTP could lead to the overestimation of switching demand. Furthermore, our results show that drivers are more heterogeneous in terms of WTA than WTP. Moreover, our applications of the latent class mixed logit structure indicate that most of the responded drivers show reference-dependency in route switching decision. Our findings in this study are essential in transport network policy making.

Choiceless Polynomial Time with Witnessed Symmetric Choice

We extend Choiceless Polynomial Time (CPT), the currently only remaining promising candidate in the quest for a logic capturing Ptime , so that this extended logic has the following property: for every class of structures for which isomorphism is definable, the logic automatically captures Ptime . For the construction of this logic, we extend CPT by a witnessed symmetric choice operator. This operator allows for choices from definable orbits. But, to ensure polynomial-time evaluation, automorphisms have to be provided to certify that the choice set is indeed an orbit. We argue that, in this logic, definable isomorphism implies definable canonization. Thereby, our construction removes the non-trivial step of extending isomorphism definability results to canonization. This step was a part of proofs that show that CPT or other logics capture Ptime on a particular class of structures. The step typically required substantial extra effort.

Manipulations in Democracy?

Democracy is upheld through the principle of majority rule. To validate the application of democracy, it is imperative to assess the sincerity of voter decisions. When voter sincerity is compromised, manipulation may occur, thereby undermining the legitimacy of democratic processes. This paper presents a general version of a symmetric dichotomous choice model. Using simple majority rule, we show that when a voter receives one or more private signals, sincere voting is an equilibrium behavior. A slight change to this basic model may create an incentive to vote insincerely. We show that even in a more restricted model where every voter receives only one private signal whose level of precision is the same for all the voters but depends on the state of nature, voters may have an incentive to vote insincerely.

Construction of symmetric paired choice experiments: minimising runs and maximising efficiency

Discrete choice experiments (DCEs) are popular in various fields such as health resources, marketing, transport, economics, and many others for identifying the factors that influence an individual’s choice behaviour. Selecting the DCE design is crucial in determining the observable effects. In this paper, the optimal form of the information matrix is introduced for attributes at two levels, main effect models, and equal choice probabilities for paired choice experiments. Additionally, the construction of D-optimal designs is modified to obtain DCEs when the number of attributes equals the number of runs, including designs with choice sets of sizes that are not necessarily multiples of 4, i.e. N ≢ 0mod4. The designs suggested in this paper have the same or higher D-efficiencies than existing efficient designs for the same number of choice sets. Moreover, the proposed design techniques can be extended to be applied to situations where the attributes of DCEs have a higher number of levels (ℓ > 2), resulting in designs with the same improved D-efficiencies and sufficiently small sample sizes. The designs proposed in this paper offer a notable advantage by allowing a reduction of 33% in the number of choice pairs with only a marginal loss of 11% in D-efficiency when compared to an optimal design. In comparison, the design suggested by other researchers incurs a higher loss in D-efficiency.

Wide-angle and relativistic effects in Fourier-space clustering statistics

Galaxy power spectrum and bispectrum signals are distorted by peculiar velocities and other relativistic effects arising from a perturbed spacetime background. In addition, study of correlation functions of tracers in Fourier space is often done in the plane-parallel approximation under which it is assumed that line-of-sight (LOS) vectors are parallel. In this work we show that a simple perturbative procedure can be employed for a fast evaluation of beyond plane-parallel (wide-angle) corrections to the power spectrum and bispectrum. We also show that evolution of linear matter density fluctuations in a relativistic context can be found from a simple method. For the power spectrum at linear level, we compare leading order wide-angle contributions to multipoles of the galaxy power spectrum with those from non-integrated and integrated relativistic corrections and estimate their possible contamination on local fNL measurements to be of order a few. We also compute wide-angle corrections in the presence of nonlinear terms at one-loop order. For the bispectrum, we show that wide-angle effects alone, even with fully symmetric choices of LOS, give rise to imaginary, odd-parity multipoles of the galaxy bispectrum (dipole, octupole, etc.) which are in many cases larger than previously known ones of relativistic origin. We calculate these contributions and provide an estimator for measuring the leading order bispectrum dipole from data, using a symmetric LOS definition. Finally, we calculate the leading order corrections to multipoles of real plane-parallel bispectrum multipoles and estimate the apparent local fNL induced to be of order unity.

Necessary and sufficient conditions for pairwise majority decisions on path-connected domains

In this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked domain on a tree if and only if it is the pairwise majority rule (also known as the tree-median rule) and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even.

Capacity choice game in a multiserver queue: Existence of a Nash equilibrium

AbstractIn many congestion‐prone services, front‐line employees have discretion over the rate at which they serve customers. To evaluate the impact of queue pooling on their decisions, we model the situation as a two‐server, single‐queue symmetric capacity choice game. Gopalakrishnan et al. (2016) characterize the existence of a Nash equilibrium in this game under a requirement on the servers' capacity cost functions, that is, where servers have limited discretion. Without that requirement and when servers are free to choose any service rate, the servers' cost function is ill‐behaved and standard tools for establishing the existence of an equilibrium cannot be applied. We consider a general power capacity cost function with no restriction on the servers' choice of capacity, and rely on a lesser‐known result, namely Tarski's intersection theorem, to establish the existence of a symmetric pure‐strategy Nash equilibrium. Comparing settings where queue stability is enforceable versus not, we show that there always exists a Nash equilibrium in the former case, unlike in the latter, and that some of the capacity choices that are equilibria in the former case are no longer equilibria in the latter. Our analysis highlights the criticality of the enforceability of system stability on equilibrium outcomes.

Effects of cyclic allele dominance rules and spatial structure on the dynamics of cyclic competition models.

Barreto et al. (2017) showed that the genotypic cyclic competition model with three phenotypes appearing as three morphs of male lizards' throats had the same equilibrium but a wider stability region as the corresponding phenotypic model. In this paper we re-examine stability conditions under the symmetric choice of parameters for the phenotypic model so we can set the same internal equilibrium densities for all three phenotypes. In this setting we compare the stability regions of cyclic allele dominance rule. Next we consider the dynamics on a two-dimensional square lattice space and then show the effect of this spatial structure on the stability of phenotypic model. We obtain the following results: (i) Cyclic allele dominance rule in a genotypic model gives a wider stable region of internal equilibrium than the allele dominance rule observed in lizards; and (ii) spatial structure drastically changes dynamical behavior, especially when all three phenotypes coexist in almost all the parameter spaces when both competition and dispersal occur locally.

Capacity Choice Game in a Multi-Server Queue: Existence of a Nash Equilibrium

In a multi-server, single-queue symmetric capacity choice game, Gopalakrishnan et al. (2016) characterize the existence of a Nash equilibrium under a requirement on the servers’ capacity cost functions, which excludes some highly relevant cases where servers have ample discretion over their choice of service rates. Without that requirement and when servers are free to choose any service rate, potentially leading to an unstable queueing system, the servers’ cost function is ill-behaved and standard tools for establishing the existence of an equilibrium cannot be applied. In this note, we consider a general power capacity cost function in a two-server capacity choice game with no restriction on the servers’ choice of capacity. Relying on a lesser-known result, namely Tarski's intersection theorem, we establish the existence of a Nash equilibrium, thus extending the result by Gopalakrishnan et al. (2016) to our setting. Comparing settings where queue stability is enforceable versus not, we show that there always exists a Nash equilibrium in the former case, unlike in the latter, and that some of the capacity choices that are equilibria in the former case are no longer equilibria in the latter. Our analysis highlights the criticality of the enforceability of system stability on equilibrium outcomes.

Effect of different nuclear density approximations on fusion dynamics within Skyrme Energy Density Formalism

The role of different density approximations such as frozen, sudden and modified sudden, investigated within the Skyrme Energy Density Formalism (SEDF), is compared with the phenomenological relaxed-density approach for Ni-based reactions. These approximations give different ways in which individual densities of projectile and target can be added for obtaining compound nucleus density. For the 58Ni + 58Ni reaction, unlike sudden, the frozen density approximation is known to give the realistic barrier parameters (Nucl. Phys. A 870-871, 42 (2011)) and addresses the experimental data with the use of the extended $ \ell$ -summed Wong model. In view of this, the barrier parameters within the sudden approximation are obtained, by modifying the central density term as an independent function of the surface thickness factor, which in turn, fits the data nicely at sub barrier energies. In comparison to this, the largest barrier height of the phenomenological potential of relaxed-density advocates the possibility of fusion hindrance. Additionally, for the 18O and 40Ca + 58Ni reactions, the frozen and modified sudden approximations address the data at below barrier-energies. For the case of a heavier-mass system, the barrier parameters cannot be extracted due to the disappeared pocket for the case of sudden and modified sudden density approximations. In such situation, the frozen and relaxed-density approaches behave in a similar manner and show a better fit to the data using the extended $ \ell$ -summed Wong formula. The $ \ell$-values are extracted using the sharp cut-off model for above-barrier energies and extrapolated at lower energies. Among the chosen approximations, the frozen approximation seems to provide a better option for the reactions considered from different mass regions. Further, on the basis of frozen and phenomenological approaches, the reduced cross-sections are calculated and compared with the Universal Fusion Function (UFF) for symmetric and asymmetric choices of nuclear partners.

Asymmetry in initial cluster size favors symmetry in a network of oscillators.

Counterintuitive to the common notion of symmetry breaking, asymmetry favors synchrony in a network of oscillators. Our observations on an ensemble of identical Stuart-Landau systems under a symmetry breaking coupling support our conjecture. As usual, for a complete deterministic and the symmetric choice of initial clusters, a variety of asymptotic states, namely, multicluster oscillation death (1-OD, 3-OD, and -OD), chimera states, and traveling waves emerge. Alternatively, multiple chimera death (1-CD, 3-CD, and -CD) and completely synchronous states emerge in the network whenever some randomness is added to the symmetric initial states. However, in both the cases, an increasing asymmetry in the initial cluster size restores symmetry in the network, leading to the most favorable complete synchronization state for a broad range of coupling parameters. We are able to reduce the network model using the mean-field approximation that reproduces the dynamical features of the original network.

Asymmetric, closed-form, finite-parameter models of multinomial choice

Class imbalance, where there are great differences between the number of observations associated with particular discrete outcomes, is common within transportation and other fields. In the statistics literature, one explanation for class imbalance that has been hypothesized is an asymmetric (rather than the typically symmetric) choice probability function. Unfortunately, few relatively simple models exist for testing this hypothesis in transportation settings—settings that are inherently multinomial. Our paper fills this gap.In particular, we address the following questions: “how can one construct asymmetric, closed-form, finite-parameter models of multinomial choice” and “how do such models compare against commonly used symmetric models?” Methodologically, we introduce (1) a new class of closed-form, finite-parameter, multinomial choice models, (2) a procedure for using these models to extend existing binary choice models to the multinomial setting, and (3) a procedure for creating new binary choice models (both symmetric and asymmetric). Together, our contributions allow us to create new asymmetric, closed-form, finite-parameter multinomial choice models. We demonstrate our methods by developing four new asymmetric, multinomial choice models. Empirically, most of our models strongly dominate the multinomial logit (MNL) model in terms of in-sample and out-of-sample log-likelihoods. Moreover, analyzing two policy applications, we find practical differences between the MNL and our new asymmetric models. Our results suggest that while asymmetric models may not always outperform symmetric ones, asymmetric choice models are worth testing because they might have better statistical performance and entail substantively different policy and financial implications when compared with traditional symmetric models, such as the MNL.

Logit and Probit application for the prediction of bankruptcy in Slovak companies

Research background: Prediction of bankruptcy is an issue of interest of various researchers and practitioners since the first study dedicated to this topic was published in 1932. Finding the suitable bankruptcy prediction model is the task for economists and analysts from all over the world. forecasting model using. Despite a large number of various models, which have been created by using different methods with the aim to achieve the best results, it is still challenging to predict bankruptcy risk, as corporations have become more global and more complex.
 Purpose of the article: The aim of the presented study is to construct, via an empirical study of relevant literature and application of suitable chosen mathematical statistical methods, models for bankruptcy prediction of Slovak companies and provide the comparison of overall prediction ability of the two developed models.
 Methods: The research was conducted on the data set of Slovak corporations covering the period of the year 2015, and two mathematical statistical methods were applied. The methods are logit and probit, which are both symmetric binary choice models, also known as conditional probability models. On the other hand, these methods show some significant differences in process of model formation, as well as in achieved results.
 Findings & Value added: Given the fact that mostly discriminant analysis and logistic regression are used for the construction of bankruptcy prediction models, we have focused our attention on the development bankruptcy prediction model in the Slovak Republic via logistic regression and probit. The results of the study suggest that the model based on a logit functions slightly outperforms the classification accuracy of probit model. Differences were obtained also in the detection of the most significant predictors of bankruptcy prediction in these types of models constructed in Slovak companies.

Symmetric mechanism design

Designers of economic mechanisms can often benefit by using discriminatory mechanisms which treat agents asymmetrically. This paper studies the extent to which a policy prohibiting biased mechanisms is effective in achieving fair outcomes. Our main result is a characterization of the class of social choice functions that can be implemented by symmetric mechanisms. When the solution concept used is Bayes–Nash equilibrium, symmetry is typically not very restrictive and discriminatory social choice functions can be implemented by symmetric mechanisms. Our characterization in this case is based on a ‘revelation principle’ type of result, where we show that a social choice function can be symmetrically implemented if and only if a particular kind of (indirect) symmetric mechanism implements it. When implementation in dominant strategies is considered, only symmetric social choice functions can be implemented by symmetric mechanisms. We illustrate our results in environments of voting with private values, voting with a common value, and assignment of indivisible goods.

Most incompatible measurements for robust steering tests

We address the problem of characterizing the steerability of quantum states under restrictive measurement scenarios, i.e., the problem of determining whether a quantum state can demonstrate steering when subjected to $N$ measurements of $k$ outcomes. We consider the cases of either general positive operator-valued measures (POVMs) or specific kinds of measurements (e.g., projective or symmetric). We propose general methods to calculate lower and upper bounds for the white-noise robustness of a $d$-dimensional quantum state under different measurement scenarios that are also applicable to the study of the noise robustness of the incompatibility of sets of unknown qudit measurements. We show that some mutually unbiased bases, symmetric informationally complete measurements, and other symmetric choices of measurements are not optimal for steering isotropic states and provide candidates to the most incompatible sets of measurements in each case. Finally, we provide numerical evidence that nonprojective POVMs do not improve over projective ones for this task.

Algebro-geometric approach for a centrally extended Uq[sl(2|2)] R-matrix

In this paper we investigate the algebraic geometric nature of a solution of the Yang–Baxter equation based on the quantum deformation of the centrally extended sl(2|2) superalgebra proposed by Beisert and Koroteev [1]. We derive an alternative representation for the R-matrix in which the matrix elements are given in terms of rational functions depending on weights sited on a degree six surface. For generic gauge the weights geometry are governed by a genus one ruled surface while for a symmetric gauge choice the weights lie instead on a genus five curve. We have written down the polynomial identities satisfied by the R-matrix entries needed to uncover the corresponding geometric properties. For arbitrary gauge the R-matrix geometry is argued to be birational to the direct product CP1×CP1×A where A is an Abelian surface. For the symmetric gauge we present evidences that the geometric content is that of a surface of general type lying on the so-called Severi line with irregularity two and geometric genus nine. We discuss potential geometric degenerations when the two free couplings are restricted to certain one-dimensional subspaces.

Play It Again: Partner Choice, Reputation Building and Learning From Finitely Repeated Dilemma Games

Often the fuller the reputational record people’s actions generate, the greater their incentive to earn a reputation for cooperation. However, inability to ‘wipe clean’ one’s past record might trap some agents who initially underappreciate reputation’s value in a cycle of bad behaviour, whereas a clean slate could have been followed by their ‘reforming’ themselves. In a laboratory experiment, we investigate what subjects learn from playing a finitely repeated dilemma game with endogenous, symmetric partner choice. We find that with a high cooperation premium and good information, investment in cooperative reputation grows following exogenous restarts, although earlier end‐game behaviour is observed.

Analysis of Pivot Sampling in Dual-Pivot Quicksort: A Holistic Analysis of Yaroslavskiy’s Partitioning Scheme

The new dual-pivot Quicksort by Vladimir Yaroslavskiy - used in Oracle's Java runtime library since version 7 - features intriguing asymmetries. They make a basic variant of this algorithm use less comparisons than classic single-pivot Quicksort. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order statistics of a random sample. Surprisingly, dual-pivot Quicksort then needs more comparisons than a corresponding version of classic Quicksort, so it is clear that counting comparisons is not sufficient to explain the running time advantages observed for Yaroslavskiy's algorithm in practice. Consequently, we take a more holistic approach and give also the precise leading term of the average number of swaps, the number of executed Java Bytecode instructions and the number of scanned elements, a new simple cost measure that approximates I/O costs in the memory hierarchy. We determine optimal order statistics for each of the cost measures. It turns out that the asymmetries in Yaroslavskiy's algorithm render pivots with a systematic skew more efficient than the symmetric choice. Moreover, we finally have a convincing explanation for the success of Yaroslavskiy's algorithm in practice: Compared with corresponding versions of classic single-pivot Quicksort, dual-pivot Quicksort needs significantly less I/Os, both with and without pivot sampling.

Existence of symmetric central configurations

Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific symmetry properties, using slightly different techniques in each. The aim here is to describe a uniform approach by adapting to the symmetric case the well-known variational argument showing the existence of central configurations. The principal conclusion is that there is a central configuration for every possible symmetry type, and for any symmetric choice of masses. Finally the same argument is applied to the class of balanced configurations introduced by Albouy and Chenciner.

Sequential Search and Learning from Rank Feedback: Theory and Experimental Evidence

This paper studies the effect of limited information in a sequential search setting where a single selection is to be made from a set of random potential options. We consider both a full-information problem, where the decision maker observes the exact value of each option as she searches, and a partial-information problem, in which the decision maker only learns the rank of the current option relative to the options that have already been observed. We develop a model that allows for a sharp contrast between search behavior in the two information settings, both theoretically and empirically. We present the results of an experiment that tests, and supports, the key prediction of our model analysis—limited information induces longer search. Our data further suggest systematic deviations from the theoretical benchmarks in both informational settings. Importantly, subjects in our partial-information conditions are prone to stop prematurely during early stages of the search process and to suboptimally continue the search during late stages. We propose a simple model that succinctly captures the interplay of two symmetric choice and judgment biases that have asymmetric (but opposing) effects on the length of search. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2014.1902 . This paper was accepted by Teck-Hua Ho, behavioral economics.