Why we should quit while we’re ahead: When do averages matter more than sums?

Abstract

An enduring debate in decision-making and social cognition concerns the algorithm governing the formation of intuitive preferences and attitudes. Here we contrast 2 principles that are considered central to such judgments: averaging versus summation. Participants in 4 experiments were prompted to rely on their intuition when rating the Hall of Fame eligibility of basketball players, or their liking of athletes, lecturers or slot-machines, on the basis of rapid numerical sequences that represent performances, class feedback, or rewards. Experiment 1 showed that participants are sensitive to the sequences’ averages, and prefer alternatives with high averages over those with high sums. Experiment 2 replicated these findings, and further showed that in a comparison between several models such as averaging, summation and the Peak-End heuristic, averaging type models account best for participants’ preferences. Experiment 3 indicated that these evaluations are mediated by automatic/intuitive processes. Based on computational considerations we propose that the critical variable, determining whether preferences are more sensitive to sums or to averages, is the presentation and evaluation format: one by one versus grouped. This prediction is confirmed in Experiment 4.

The averaging of numerosities: A psychometric investigation of the mental line

“…In three experiments we examined the ability of human participants in a task of averaging of numerosity stimuli (sets of dots). This extends the range of operations on which numerosity representations were used from comparisons, addition or subtractions on pairs of stimuli, to the averaging of multiple stimulian operation that is of key importance to decision-making (Brusovansky et al, 2017;Vanunu et al, 2018;Weber, 2010). This task also extends the domain of stimuli on which the extraction of summary statistics was established, from domains such as size, orientation, emotional expression or object category (Ariely, 2001;Chong & Treisman, 2005;Dakin, 2001;Habrman et al, 2009;Haberman & Whitney, 2011;Khayat & Hochstein, 2018Parkes et al, 2001;Robitaille & Harris, 2011) to the domain of nonsymbolic numerosities across temporal sequences.…”

“…This is important for several reasons. First the estimation of the average is critical for common life activities, like decision-making, in which one has to estimate the utility of alternatives that vary across time or attributes (Betsch, Kaufmann, Lindow, Plessner, & Hoffmann, 2006;Brusovansky, Glickman, & Usher, 2018;Brusovansky, Vanunu, & Usher, 2017;Pleskac, Yu, Hopwood, & Liu, 2019;Roe, Busemeyer, & Townsend, 2001;Spitzer, Waschke, & Summerfield, 2017;Tsetsos, Chater, & Usher, 2012;Usher & McClelland, 2004;Vanunu, Pachur, & Usher, 2018;Zeigenfuse, Pleskac, & Liu, 2014). Second, recent research has indicated an impressive ability of human subjects in estimating summary statistics (in particular the average) of perceptual properties of sets of elements, such as size, orientation, and even emotional expression (Ariely, 2001;Chong & Treisman, 2005;Dakin, 2001;Haberman, Harp & Whitney, 2009;Haberman & Whitney, 2011;Khayat & Hochstein, 2018;Parkes, Lund, Angelucci, Solomon, & Morgan, 2001;Robitaille & Harris, 2011).…”

Goal-dependent flexibility in preferences formation from rapid payoff sequences

“…For example, Betsch and colleagues (2001) have demonstrated that human observers formed accurate attitudes towards alternatives (stocks—characterised as sequences of returns), which were presented as distractors and which the observers had no explicit goal to evaluate (see also Betsch, Kaufmann, Lindow, Plessner, & Hoffmann, 2006). More recently, Brusovansky, Vanunu, and Usher (2017) have shown that participants evaluated the subjective-value (attractiveness) of rapid sequences of numbers (of variable length, presented at two items per second, exceeding the capacity for symbolic computations 1 ), which represented athletes competing in an athletics contest, in a way that reflected the mean of the numbers in the sequence. Critically, participants were not able to discount deviant numbers that were enclosed in a salient red frame and that were said to represent “computer-errors,” although they expressed confidence that they did.…”

“…A central question that was subject to some debate is the principle that drives such intuitive preferences. While some studies (Betsch et al, 2006; Betsch et al, 2001) suggested that value integration follows a summative principle, others showed results consistent with an averaging principle (Anderson, 1981; Brusovansky et al, 2017; Kahneman, 2011). 2 For example, Brusovansky and colleagues (2017) demonstrated a so-called “Jordan-effect” whereby participants gave higher ratings (to indicate “Hall of Fame” potential) to sequences (corresponding to careers of basketball players) with a high mean, compared with the same sequences to which few extra numbers were added (i.e., few extra seasons, increasing the sum but reducing the mean).…”

“…3 These results suggest that people might favour averaging even when summation is more appropriate. Furthermore, Brusovansky et al (2017) examined the discrepancy between studies that supported summation and those that supported averaging, and proposed a critical factor that could explain the different results: the presentation and evaluation format. Accordingly, averaging dominates preferences in a one-by-one format, in which the values corresponding to each alternative appear sequentially and each alternative is evaluated before the next one is presented.…”