The notion of “mixtures” has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied–for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes.

Classical value-based decision theories state that economic choices are solely based on the value of available options. Experimental evidence suggests, however, that individuals' choices are biased towards default options, prompted by the framing of decisions. Although the effects of default options created by exogenous framing-such as how choice options are displayed-are well-documented, little is known about the potential effects and properties of endogenous framing, that is, originating from an individual's internal state. In this study, we investigated the existence and properties of endogenous default options in a task involving choices between risky lotteries. By manipulating and examining the effects of three experimental features-time pressure, time spent on task and relative choice proportion towards a specific option-, we reveal and dissociate two features of endogenous default options which bias individuals' choices: a natural tendency to prefer certain types of options (natural default), and the tendency to implicitly learn a default option from past choices (learned default). Additional analyses suggest that while the natural default may bias the standard choice process towards an option category, the learned default effects may be attributable to a second independent choice process. Overall, these investigations provide a first experimental evidence of how individuals build and apply diverse endogenous default options in economic decision-making and how this biases their choices.

In a wide variety of cognitive domains, participants have access to several alternative strategies to perform a particular task and, on each trial, one specific strategy is selected and executed. Determining how many strategies are used by a participant as well as their identification at a trial level is a challenging problem for researchers. In the current paper, we propose a new method – the non-parametric mixture model – to efficiently disentangle hidden strategies in cognitive psychological data, based on observed response times. The developed method derived from standard hidden Markov modeling. Importantly, we used a model-free approach where a particular shape of a response time distribution does not need to be assumed. This has the considerable advantage of avoiding potentially unreliable results when an inappropriate response time distribution is assumed. Through three simulation studies and two applications to real data, we repeatedly demonstrated that the non-parametric mixture model is able to reliably recover hidden strategies present in the data as well as to accurately estimate the number of concurrent strategies. The results also showed that this new method is more efficient than a standard parametric approach. The non-parametric mixture model is therefore a useful statistical tool for strategy identification that can be applied in many areas of cognitive psychology. To this end, practical guidelines are provided for researchers wishing to apply the non-parametric mixture models on their own data set.

32Classical value-based decision theories state that economic choices are solely based on the value of available 33 options. Experimental evidence suggests, however, that individuals' choices are biased towards default 34 options, prompted by the framing of decisions. Although the effects of default options created by 35 exogenous framing -such as how choice options are displayed -are well-documented, little is known about 36 the potential effects and properties of endogenous framing, that is, originating from an individual's internal 37 state. In this study, we investigated the existence and properties of endogenous default options in a task 38 involving choices between risky lotteries. By manipulating and examining the effects of three experimental 39 features -time pressure, time spent on task and relative choice proportion towards a specific option -, we 40 reveal and dissociate two features of endogenous default options which bias individuals' choices: a natural 41 tendency to prefer certain types of options (natural default), and the tendency to implicitly learn a default 42 option from past choices (learned default). Additional analyses suggest that while the natural default may bias 43 the standard choice process towards an option category, the learned default effects may be attributable to a 44 second independent choice process. Overall, these investigations provide a first experimental evidence of 45 how individuals build and apply diverse endogenous default options in economic decision-making and how 46 this biases their choices. 47 48 Keywords: value-based decision-making, default options, natural default, learned default, fixed-point 49 property 3 50 Introduction 51 Consider the choice between an investment involving a low amount of money but a high chance of getting 52 that amount versus an investment involving a high amount but a low chance of getting that amount. Classical 53 decision theories state that, when making such a choice, individuals aggregate attributes of available options 54 (i.e., probabilities and amounts) into a decision variable ("value") and select the highest valued option [1,2]. 55 Under this value-based decision-making framework, choices were initially assumed to be based solely on 56 the value of the options [3,4]. This assumption has, however, been challenged by robust evidence suggesting 57 that choices often depend on apparently irrelevant factors. For instance, individuals' choices have been 58 shown to be biased towards default options, induced by the way the options and decision problems are 59 framed [5,6]. Extensive research has evidenced the strength and pervasiveness of such biases, created by 60 exogenous -external -framing effects in our daily life: dramatic behavioral differences in the choice to save 61 money towards retirement [7] or to be an organ donor [8] have been reported, depending on the decision 62 being presented as "opting-out" or "opting-in". A recent meta-analysis of 58 studies further reveals that the 63 effects of exogenous default-options are hig...