Stochastic satisficing account of confidence in uncertain value-based decisions

Every day we make choices under uncertainty; choosing what route to work or which queue in a supermarket to take, for example. It is unclear how outcome variance, e.g. uncertainty about waiting time in a queue, affects decisions and confidence when outcome is stochastic and continuous. How does one evaluate and choose between an option with unreliable but high expected reward, and an option with more certain but lower expected reward? Here we used an experimental design where two choices’ payoffs took continuous values, to examine the effect of outcome variance on decision and confidence. We found that our participants’ probability of choosing the good (high expected reward) option decreased when the good or the bad options’ payoffs were more variable. Their confidence ratings were affected by outcome variability, but only when choosing the good option. Unlike perceptual detection tasks, confidence ratings correlated only weakly with decisions’ time, but correlated with the consistency of trial-by-trial choices. Inspired by the satisficing heuristic, we propose a “stochastic satisficing” (SSAT) model for evaluating options with continuous uncertain outcomes. In this model, options are evaluated by their probability of exceeding an acceptability threshold, and confidence reports scale with the chosen option’s thus-defined satisficing probability. Participants’ decisions were best explained by an expected reward model, while the SSAT model provided the best prediction of decision confidence. We further tested and verified the predictions of this model in a second experiment. Our model and experimental results generalize the models of metacognition from perceptual detection tasks to continuous-value based decisions. Finally, we discuss how the stochastic satisficing account of decision confidence serves psychological and social purposes associated with the evaluation, communication and justification of decision-making

Trusting and learning from others: immediate and long-term effects of learning from observation and advice

Social learning underpins our species's extraordinary success. Learning through observation has been investigated in several species, but learning from advice—where information is intentionally broadcast—is less understood. We used a pre-registered, online experiment (n = 1492) combined with computational modelling to examine learning through observation and advice. Participants were more likely to immediately follow advice than to copy an observed choice, but this was dependent upon trust in the adviser: highly paranoid participants were less likely to follow advice in the short term. Reinforcement learning modelling revealed two distinct patterns regarding the long-term effects of social information: some individuals relied fully on social information, whereas others reverted to trial-and-error learning. This variation may affect the prevalence and fidelity of socially transmitted information. Our results highlight the privileged status of advice relative to observation and how the assimilation of intentionally broadcast information is affected by trust in others

Dynamic mean-field and cavity methods for diluted Ising systems

We compare dynamic mean-field and dynamic cavity as methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks the dynamic cavity method generally predicts magnetizations of individual spins better than both first order ("naive") and second order ("TAP") dynamic mean field theory

P5-free augmenting graphs and the maximum stable set problem

AbstractThe complexity status of the maximum stable set problem in the class of P5-free graphs is unknown. In this paper, we first propose a characterization of all connected P5-free augmenting graphs. We then use this characterization to detect families of subclasses of P5-free graphs where the maximum stable set problem has a polynomial time solution. These families extend several previously studied classes

Social influence protects collective decision making from equality bias

A basic tenet of research on wisdom of the crowds – and key assumption of Condorcet’s Jury Theorem – is the independence of voters’ opinions before votes are aggregated. However, we often look for others’ opinions before casting our vote. Such social influence can push groups towards herding, leading to “madness of the crowds”. To investigate the role of social influence in joint decision making, we had dyads of participants perform a visual odd-ball search task together. In the Independent (IND) condition participants initially made a private decision. If disagreeing, discussion and collective decision ensued. In the Influence (INF) condition no private decisions were made and collective decision was immediately negotiated. Dyads that did not accrue collective benefit under IND condition improved with added social influence under INF condition. In Experiment 2, covertly, we added noise to one of the dyad members’ visual search display. The resulting increased heterogeneity in dyad members’ performances impaired the dyadic performance under IND condition (Bahrami et al., 2010). Importantly, dyadic performance improved with social influence under INF, replicating Experiment 1. Further analyses revealed that under IND condition, dyads exercised equality bias (Mahmoodi et al., 2015) by granting undue credit to the less reliable partner. Under INF condition, however, the more reliable partner (correctly) dominated the joint decisions. While social influence may impede collective success under ideal conditions, our results demonstrate how it can help the group members overcome factors such as equality bias, which could potentially lead to catastrophic failure

Anleitung zur Analyse der Aschen und Mineralwasser von Robert Bunsen. Mit einer lithographirten Tafel und sechs Tabellen. Heidelberg. Carl Winter's Universitätsbuchhandlung. 1874

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Dynamics of gene expression and the regulatory inference problem

From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription factor molecules to regulatory DNA. Here, we construct stochastic models of gene expression dynamics and test them on experimental time-series data of messenger-RNA concentrations. The models are used to infer biophysical parameters of gene transcription, including the statistics of transcription factor-DNA binding and the target genes controlled by a given transcription factor.Comment: revised version to appear in Europhys. Lett., new titl

Making the most of community energies:Three perspectives on grassroots innovation

Grassroots innovations for sustainability are attracting increasing policy attention. Drawing upon a wide range of empirical research into community energy in the UK, and taking recent support from national government as a case study, we apply three distinct analytical perspectives: strategic niche management; niche policy advocacy; and critical niches. Whilst the first and second perspectives appear to explain policy influence in grassroots innovation adequately, each also shuts out more transformational possibilities. We therefore argue that, if grassroots innovation is to realise its full potential, then we need to also pursue a third, critical niches perspective, and open up debate about more socially transformative pathways to sustainability

Relaxation, closing probabilities and transition from oscillatory to chaotic attractors in asymmetric neural networks

Attractors in asymmetric neural networks with deterministic parallel dynamics were shown to present a "chaotic" regime at symmetry eta < 0.5, where the average length of the cycles increases exponentially with system size, and an oscillatory regime at high symmetry, where the typical length of the cycles is 2. We show, both with analytic arguments and numerically, that there is a sharp transition, at a critical symmetry \e_c=0.33, between a phase where the typical cycles have length 2 and basins of attraction of vanishing weight and a phase where the typical cycles are exponentially long with system size, and the weights of their attraction basins are distributed as in a Random Map with reversal symmetry. The time-scale after which cycles are reached grows exponentially with system size $N$, and the exponent vanishes in the symmetric limit, where $T\propto N^{2/3}$. The transition can be related to the dynamics of the infinite system (where cycles are never reached), using the closing probabilities as a tool. We also study the relaxation of the function $E(t)=-1/N\sum_i |h_i(t)|$, where $h_i$ is the local field experienced by the neuron $i$. In the symmetric system, it plays the role of a Ljapunov function which drives the system towards its minima through steepest descent. This interpretation survives, even if only on the average, also for small asymmetry. This acts like an effective temperature: the larger is the asymmetry, the faster is the relaxation of $E$, and the higher is the asymptotic value reached. $E$ reachs very deep minima in the fixed points of the dynamics, which are reached with vanishing probability, and attains a larger value on the typical attractors, which are cycles of length 2.Comment: 24 pages, 9 figures, accepted on Journal of Physics A: Math. Ge

Phase Diagram and Storage Capacity of Sequence Processing Neural Networks

We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium statistical mechanical analysis. Using generating functional methods we derive exact closed equations for dynamical order parameters, viz. the sequence overlap and correlation- and response functions, in the thermodynamic limit. We calculate the time translation invariant solutions of these equations, describing stationary limit-cycles, which leads to a phase diagram. The effective retarded self-interaction usually appearing in symmetric models is here found to vanish, which causes a significantly enlarged storage capacity of $\alpha_c\sim 0.269$, compared to \alpha_\c\sim 0.139 for Hopfield networks storing static patterns. Our results are tested against extensive computer simulations and excellent agreement is found.Comment: 17 pages Latex2e, 2 postscript figure