It is well known that the presentation order of choice options often affects decision outcomes to a significant degree. However, despite the significance and wide occurrence of the effects, they are ignored in most preference models. Furthermore, psychophysical findings of stimulusmagnitude dependent presentation-order effects have not been acknowledged previously in the cognitive literature on preference judgments. Thus, the potential moderating effect of the level of stimulus magnitude (here, valence) on the direction and size of order effects in preference judgment has not been investigated previously. In two experiments, participants (117 and 204, respectively) rated their preference for pairs of everyday-type objects and phenomena (e.g., apple-pear, headache-stomachache). Stimuli were spaced horizontally, and each participant received them in one of two opposite within-pair presentation orders. Participants also rated the stimuli's valence on a scale from very bad to very good. The results showed a positive correlation between the rated valence and the tendency to prefer the first-mentioned (left) stimulus; that is, the effect was greatest, and opposite, for choices between the most attractive and the most unattractive options, respectively. In terms of Hellström's (1979) sensation-weighting model, the positive correlation is caused by a higher weight (i.e., impact on the preference judgment) for the left stimulus than for the right, which is possibly due to the left stimulus being compared to the right. The results suggest that researchers may have failed previously to find important moderators of presentation-order effects in preference judgment due to the failure to use sufficiently attractive or unattractive stimuli.

Despite the importance of both response probability and response time for testing models of choice, there is a dearth of chronometric studies examining systematic asymmetries that occur over time- and space-orders in the method of paired comparisons. In this study, systematic asymmetries in discriminating the magnitude of paired visual stimuli are examined by way of log odds ratios of binary responses as well as by signed response speed. Hierarchical Bayesian modeling is used to map response probabilities and response speed onto constituent psychological process, and processing capacity is also assessed using response time distribution hazard functions. The findings include characteristic order effects that change systematically in magnitude and direction with changes in the magnitude and separation of the stimuli. After Hellström (1979, 2000), sensation weighting (SW) model analyses show that such order effects are reflected in the weighted accumulation of noisy information about the difference between stimulus values over time, and interindividual differences in weightings asymmetries are related to the relative processing capacity of participants. An account of SW based on the use of reference level information and maximization of signal-to-noise ratios is posited, which finds support from theoretically driven analyses of behavioral data.

Englund and Hellström (Journal of Behavioral Decision Making 25:82-94, 2012a) found a tendency to prefer the left (first-read) of two attractive alternatives but the right (second-read) of two unattractive alternatives-a valence-dependent word-order effect (WOE). They used stimulus pairs spaced horizontally, and preference was indicated by choosing one of several written statements (e.g., "apple I like more than pear"). The results were interpreted as being due to stimulus position, with the magnitude of the left stimulus having a greater impact on the comparison outcome than the magnitude of the right. Here we investigated the effects of the positioning of the stimuli versus the semantics of the response alternatives (i.e., comparison direction) on the relative impacts of the stimuli. Participants rated preferences for stimuli spaced horizontally with the response alternatives not dictating a comparison direction (Exp. 1), and stimuli spaced vertically using Englund and Hellström's (Journal of Behavioral Decision Making 25:82-94, 2012a) response alternatives, which dictate a comparison direction semantically (Exp. 2). The results showed that the valence-dependent WOE found by Englund and Hellström (Journal of Behavioral Decision Making 25:82-94, 2012a) was not due to the horizontal stimulus positioning per se, but to the induced comparison direction, with the effect probably being mediated by attention directed at the subject of the comparison. We concluded that a set comparison direction is required for the valence-dependent WOE to appear, and that using Hellström's sensation-weighting model to determine stimulus weights is a way to verify the comparison direction. (Dean, 1980), and professional judges' ratings in figure-skating contests (Bruine de Bruin, 2005, 2006. Analogous effects have been found by psychophysicists for one and a half centuries (see, e.g., Guilford, 1954, andHellström, 1985, for reviews), and the psychophysical tradition to use many stimulus pairs of varying magnitudes has made it possible to discover that the size and direction of presentation-order effects vary with, among several factors, the stimuli's magnitude level. For example, Hellström (2003) found that, in length comparisons of lines of relatively long durations, subjects overestimated the left out of two short lines but the right out of two long lines. Similarly, in comparisons of musical excerpts, Koh (1967) found a tendency to prefer the first of two unpleasant excerpts but the second of two pleasant excerpts; the size of this effect varied linearly with the rated pleasantness of the stimulus pairs. Analogous results were found by Englund and Hellström (2012b) for pairs of successive jingles as well as for color patterns. These are but a few examples of what Fechner (1860) called space-order error (SOE) and time-order error (TOE). As is hinted at by the two terms, a SOE appears when stimuli are separated spatially, and a TOE when stimuli are separated temporally.M. P. Englund cut-e Sweden,

For preference comparisons of paired successive musical excerpts, Koh (American Journal of Psychology, 80, 171-185, 1967) found time-order effects (TOEs) that correlated negatively with stimulus valence-the first (vs. the second) of two unpleasant (vs. two pleasant) excerpts tended to be preferred. We present three experiments designed to investigate whether valence-level-dependent order effects for aesthetic preference (a) can be accounted for using Hellström's (e.g., Journal of Experimental Psychology: Human Perception and Performance, 5, 460-477, 1979) sensation-weighting (SW) model, (b) can be generalized to successive and to simultaneous visual stimuli, and (c) vary, in accordance with the stimulus weighting, with interstimulus interval (ISI; for successive stimuli) or stimulus duration (for simultaneous stimuli). Participants compared paired successive jingles (Exp. 1), successive color patterns (Exp. 2), and simultaneous color patterns (Exp. 3), selecting the preferred stimulus. The results were well described by the SW model, which provided a better fit than did two extended versions of the Bradley-Terry-Luce model. Experiments 1 and 2 revealed higher weights for the second stimulus than for the first, and negatively valence-level-dependent TOEs. In Experiment 3, there was no laterality effect on the stimulus weighting and no valence-level-dependent space-order effects (SOEs). In terms of the SW model, the valence-leveldependent TOEs can be explained as a consequence of differential stimulus weighting in combination with stimulus valence varying from low to high, and the absence of valence-leveldependent SOEs as a consequence of the absence of differential weighting. For successive stimuli, there were no important effects of ISI on weightings and TOEs, and, for simultaneous stimuli, duration had only a small effect on the weighting.Keywords Aesthetic preference . Presentation order . Time-order errors . Space-order errors . Visual perception . Audition . Math modeling Fechner (1860) was the first to notice the ubiquitous and enigmatic systematic errors that occur in comparisons of successive and simultaneous stimuli, which make two physically equal stimuli subjectively different when compared: the Zeitfehler (time-order error) and the Raumfehler (spaceorder error). The time-order effect (TOE) and space-order effect (SOE) were defined as positive (vs. negative) for overestimation (vs. underestimation) of the first or left stimulus, respectively, relative to the second or right stimulus. Fechner (1876) also introduced experimental aesthetics, with scaling of aesthetic appreciation. However, he never combined those two subjects, which we attempt to do in the present article.Since Fechner's (1860) discovery, TOEs have been found for a wide range of modalities, including heaviness, tone loudness, line length, duration (see, e.g., Guilford, 1954;Hellström, 1985, for reviews), and brightness (Maeda, 1959).

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