Assessing behavioural profiles following neutral, positive and negative feedback.

Previous data suggest zero-value, neutral outcomes (draw) are subjectively assigned negative rather than positive valence. The combined observations of faster rather than slower reaction times, subsequent actions defined by shift rather than stay behaviour, reduced flexibility, and, larger rather than smaller deviations from optimal performance following draws all align with the consequences of explicitly negative outcomes such as losses. We further tested the relationships between neutral, positive and negative outcomes by manipulating value salience and observing their behavioural profiles. Despite speeded reaction times and a non-significant bias towards shift behaviour similar to losses when draws were assigned the value of 0 (Experiment 1), the degree of shift behaviour approached an approximation of optimal performance when the draw value was explicitly positive (+1). This was in contrast to when the draw value was explicitly negative (-1), which led to a significant increase in the degree of shift behaviour (Experiment 2). Similar modifications were absent when the same value manipulations were applied to win or lose trials (Experiment 3). Rather than viewing draws as neutral and valence-free outcomes, the processing cascade generated by draws produces a complex behavioural profile containing elements found in response to both explicitly positive and explicitly negative results.

1. Introduction

Responsiveness to feedback is a fundamental aspect of learning (e.g., [1]). Principles of operant conditioning clearly express the common ways in which the outcome of current behaviour influences future action [2]. While changing action as a consequence of negative outcome (ie, lose-shift) and repeating action as a consequence of positive outcome (ie, win-stay) seem to be two sides of the same coin, punishment and reinforcement remain anatomically [3], evolutionarily [4, 5] and mechanistically [6, 7] distinct. In addition to operating in environments such as gambling and education- where feedback is both salient and explicitly negative or positive- there are other cases where information regarding our performance is often ambiguous or incomplete [8]. The interpretation of outcomes that do not have a clear valence, either as a result of the absence of feedback (ambiguous; [9]) or the explicit delivery of neutral feedback, such as the zero value assigned to drawing against an opponent [10], is a neglected feature of the decision-making literature.

The behavioural and neural responses following supposedly ‘neutral’ outcomes have provided a number of unique insights into the subjective aspects of decision-making. Within a simple case where three possible outcomes of a competitive interaction are assigned different values (win = +1, draw = 0, lose = -1), a draw may co-opt aspects of positive or negative outcomes as a result of the transient state of the organism (see [11]). [5] (2001, p. 225) express this interpretive tension generated by draws as “to tie is to fail to win, but on the other hand to tie is to avoid a loss.” Thus, a draw may be perceived as worse-than-expected in the context of not winning, or better-than-expected in the context of not losing. This need for personal interpretation means that individuals- in otherwise identical environments in which they encounter the same types and frequencies of outcomes- can form different subjective states where they experience more successes than failures (i.e., [win = draw] > lose), or, more failures than successes (i.e., win < [draw = lose]). This is important for at least two reasons. First, given the inherent ambiguity of draws, these responses can speak to the degree of optimistic bias or depressive realism held as a trait [12, 13]. Second, draws play a critical component in determining gambling behaviour, since a draw could be equally perceived as either a near-win or a near-loss thereby perpetuating erroneous beliefs in performance success [14, 15]. Given the ubiquity of traditional operant conditioning responses to clear gains and losses (win-stay, lose-shift), it seems probable that the behavioural profile for draw outcomes has its hallmark in these more hard-wired reactions. We can start to understand the subjective interpretation of draws by comparing performance with explicitly positive and negative outcomes, in addition to reviewing the previous literature in terms of a number of metrics including decision times, neural flexibility, and, the quality and optimality of action following outcome.

With respect to decision time, we can draw from the literature on post-loss slowing / speeding (c.f., impulsivity; [16-18]). Here, differences in future decision time are determined by the type of outcome caused by the current action: post-loss slowing is defined as increased decision time following losses relative to wins, and, post-loss speeding is defined as decreased decision time following losses relative to wins. A contributing factor in the observation of slowing or speeding is the degree to which failure is rare [19]. For example, if an individual interacts with an opponent who cannot be beaten (unexploitable), or interacts with an opponent who can be beaten (exploitable) but who the participant fails to beat, then performance is characterized by post-loss speeding. In contrast, the degree to which individuals successfully exploit an opponent increases the magnitude of post-loss slowing (see [20]; Fig 1). However, outcome frequency does not provide a complete account of post-loss slowing since post-loss slowing is intact when positive and negative outcomes are experienced to the same degree (eg., [21]). Previous data utilizing draw outcomes further show that when participants engage with unexploitable opponents where long-run outcome frequencies were equivalent, decision times following wins were slower than decision times following both losses and draws (i.e., post-draw speeding; [21, 22]). Therefore, decision time speeding data establish a connection between neutral (draw) outcomes and explicitly negative (lose) outcomes.

Fig 1

Left column depicts proportion of shift behaviour following wins, losses and draws as a function of cumulative score presentation (score, no score) and the value of draws (0, +1, -1; Experiment 1), (+1, -1; Experiment 2), or, the value of losses (-2) and wins (+2; Experiment 3).

Horizontal grey dotted line represents optimal performance (66.6%). Right column depicts subsequent reaction time following wins, losses and draws. Error bars represent standard errors.

A second metric to ascertain the subjective interpretation of draws is the response of the brain following outcomes. Feedback-related negativity (FRN; [23]) is a scalp-recorded electrical potential related to dopaminergic influences on anterior cingulate cortex (ACC; [24]) and is a reliable index of the positive or negative nature of trial outcome [25]. Paradigms directly using neutral outcomes have shown that FRN amplitudes generated following draws are often statistically indistinguishable from unambiguously negative (i.e., lose) outcomes (e.g., [10, 25, 26]). In contrast, both lose and draw trials generate larger FRN amplitude than unambiguously positive trials (i.e., win; e.g., [27, 28]). Therefore, event-related potential data also align draws with a negative rather positive interpretation.

Of final interest is the flexibility of behaviour exhibited following outcome. Operant conditioning dictates the tendency to repeat action following success (win-stay) and the tendency to switch action following failure (lose-shift). Under baseline conditions (win = +1, draw = 0, loss = -1), the degree of win-stay behaviour approximates the optimal proportion (33.3%) as predicted by a mixed-strategy-style approach guaranteeing the absence of exploitation (see [10, 21; Experiment 1]). In contrast, the degree of lose-shift behaviour exceeds the optimal proportion (66.6%), making participants more predictable following loss. In follow-up studies [22], the objective values of losses and wins was manipulated relative to baseline (see also [6, 29]). Data produced by these schemes showed that value manipulations changed behaviour for wins but not for losses [6, 22]. Specifically, even when the objective cost of losing was reduced to half the gain of winning (-1, +2), participants still exhibited robust lose-shift behaviour to the same degree observed in a baseline condition (-1, +1) or a condition in which the objective cost of losing was doubled relative to the gain of winning (-2, +1). In contrast, win-stay behaviour was more flexible and significantly increased when wins and losses had different objective values. Therefore, negative outcomes are characterized by subsequently less flexible shift behaviour, whereas positive outcomes are characterized by subsequently more flexible stay behaviour. One of the basic principles of loss aversion is that losses have roughly twice the subjective magnitude of their objective value [22, 30, 31]. Therefore, the inflexibility of shift behaviour following loss might be associated with the greater subjective value of negative relative to positive outcomes.

From our previous data however, we note a seemingly reliable observation that prohibits the wholesale acceptance of draws as functionally equivalent to losses. For example, in [18] (Experiment 1, no credit condition), the degree of shift behaviour is smaller following draws relative to losses (76.63% vs. 70.62%; t[39] = -2.267, p = .029; n = 40). Similar reductions in shift behaviour following draws relative to losses were also extracted from [10) (Experiment 1: 72.53% vs. 78.51%; t[35] = -2.530, p = .016; n = 36), [22] (baseline condition; 71.97% vs. 77.68%; t[35] = -2.120, p = .041; n = 36), and, [21] (70.63% vs. 75.89%; t[30] = -2.307, p = .028; n = 31). Given the attenuation of shift bias following draws relative to losses, then there is clearly some sense in which these are not identical examples of negative outcomes. Draws generate a less negative state, which enables the individual to approach optimized performance in the long run (ie 66.6% shift behaviour).

2. Experiment 1

In Experiment 1, participants engaged in the three-response game Rock, Paper, Scissors using a novel objective value manipulation for draws (+1, 0, -1). Critically, performance was evaluated against a computerized opponent playing according to a mixed-strategy variant, where each of the three responses appeared 33.3% of the time, in a random order. (MS; [32-34]).

In principle, playing against an opponent operating according to MS should guarantee- in the long run- an equivalent number of wins, losses and draws. Thus, when the opponent is unexploitable, there is no reliable model of successful performance for participants to acquire. Once again, this type of performance is critical for the current debate as it allows the same exposure to positive (win), neutral (draw) and negative (lose) outcomes. Starting at the position that draws are objectively neutral (0), we consider the consequences of making the value outcome of draws equivalent to wins (+1) and losses (-1). If objective value is the only factor contributing to performance, then the behavioural changes we see when draws are assigned +1 and -1 should be of the same magnitude. If value and valence interact, then the behaviour following +1 and -1 draws should be different. Since draws are observed to have both behavioural [21, 22] and neural [25, 27] hallmarks similar to objectively negative outcomes (losses), moving the value to +1 should be a more salient manipulation than moving the value to -1.

Changing draw value from 0 to +1 or -1, and evaluating performance against an unexploitable opponent in Experiment 1, we make the following predictions. This is guided by data from 12 previously published experiments that use a similar win (+1), draw (0), lose (-1) outcome value assignment against an opponent who cannot be beaten [10, 18, 20–22, 35]. First, reaction times following draws should be faster than reaction times following wins (post-draw speeding). Second, actions following draws should be more likely to elicit shift than stay behaviour, once again aligning with the consequences of losing rather than winning. Third, the degree to which participants stray from optimal performance should be greater for draw-shift than win-shift, consistent with the behavioural sub-optimality often associated with negative relative to positive outcomes. The expected value for all shift behaviour is 66.6%. Fourth, if draws are interpreted as negative when assigned the value of 0, changing the value of the draw to +1 (i.e., moving from subjectively negative to objectively positive) should alter behaviour more than changing the value of the draw to -1 (i.e., moving from subjectively negative to objectively negative).

2.1 Method

40 participants provided informed consent for Experiment 1 (37 provided demographic information: 28 women, 32 right-handed; mean age = 19.03, sd = 1.11). Participants received course credit and were only eligible to take part in one experiment in the following series. The protocol was approved at the University of Alberta under Research Ethics Board 2 (Pro00083768). Sample sizes were estimated with 80% power [36] using G*Power [37] from two recent studies described above, in which reduction in shift behaviour following draw (0) relative to loss (-1) trials were observed: [18]: dz = 0.6894, one-tailed, yielding n = 15, and, [10]: dz = 0.4217, one-tailed, yielding n = 37.

Static pictures of blue-gloved (left; opponent) and white-gloved (right; participant) hands signalling Rock, Paper and Scissors poses (from [22]) were displayed center screen at approximately 12° x 6°, with participants sat approximately 57 cm away from a 22" ViewSonic VX2757 Monitor. Stimulus presentation was controlled by Presentation 20.2 (build 07.25.18) and responses were recorded using a keyboard.

Participants completed 3 counterbalanced blocks of 120 trials. Within each block, the computerized opponent played Rock, Paper, Scissors 40 times each in a random order. With wins consistently assigned the value of +1 and losses consistently assigned the value of -1, the only difference between the conditions was the value assigned to draw trials (+1, 0, -1). At the beginning of each block, participants were informed how much game outcomes were worth. At the start of each trial, the participant was presented with a fixation cross and cumulative score for the opponent (bottom left) and player (bottom right). After pressing 4, 5 or 6 on the number pad (representing Rock, Paper, Scissors), the choices made by the opponent and the participant were displayed for 1000 ms. Choices were cleared over a 500 ms period, after which the outcome of the trial was displayed for 1000 ms. Scoring was updated during 500 ms and the next trial began.

2.2 Results

Statistica 13.3 (TIBCO Software) was used to analyze the data. The comparison of wins (32.92%), loses (33.97%) and draws (33.12%) collapsed across condition was not significant according to a one-way repeated-measures ANOVA [F(2,78) = 1.274, MSE < .001, p = .286, ƞp2 = .031], suggestive of long-run equivalence of outcomes in Experiment 1. Median RTs on trial n following wins, loses and draws at trial n-1 were compared across the three conditions (draw value: +1, 0, -1) in a two-way repeated-measures ANOVA (see right-hand panel of Fig 1). Only a significant main effect of outcome was revealed [F(2,78) = 6.334, MSE = 107065, p = .003, ƞp2 = .140], with significant speeding for draws (502 ms) relative to wins (hence, post-draw speeding; 650 ms; Tukey’s HSD, p = .002) but not between losses (553 ms) and wins (p = .062). The main effect of draw value [F(2,78) = 0.327, MSE = 207042, p = .722, ƞp2 = .008], and, the interaction between draw value x outcome [F(4,156) = 2.136, MSE = 43307, p = .003, ƞp2 = .052] were not significant.

The proportion of shift behaviour following wins, losses and draws was calculated from the last 119 trials in each block (the first trial has no history; see Table 1). In this way, an observed value less than the expected value of 66.6% represents a bias towards stay behaviour, where an observed value more than the expected value of 66.6% represents a bias towards shift behaviour. Shift proportions were compared across outcome (win, lose, draw) and draw value (+1, 0,-1) in a two-way repeated-measures ANOVA (see left-hand panel of Fig 1; the horizontal grey line represents the expected value of 66.6%). The main effect of draw value was not significant [F(2,78) = 0.215, MSE = .029, p = .807, ƞp2 = .005], nor was the interaction between draw value x outcome [F(4,156) = 2.420, MSE = .010, p = .051, ƞp2 = .058]. A significant main effect of outcome [F(2,78) = 16.874, MSE = .025, p < .001, ƞp2 = .302] demonstrated that the degree of shift behaviour for wins (64.35%) was smaller than that for both losses (76.17%) and draws (70.70%). The degree of draw-shift behaviour was also significantly smaller than the degree of lose-shift behaviour (all Tukey’s HSD, p < .05).

Table 1

Distribution of item, outcome, outcome-response contingency and reaction time, and randomness deviation as a function of the value of draw trials (+1, 0, -1) in Experiment 1.

Standard error in parenthesis.

	Item			Outcome
	Rock	Paper	Scissors	Win	Lose	Draw
D+1	.370 (.020)	.323 (.013)	.307 (.011)	.327 (.006)	.336 (.008)	.337 (.007)
D0	.356 (.013)	.327 (.011)	.316 (.011)	.322 (.006)	.347 (.007)	.331 (.007)
D-1	.348 (.012)	.335 (.010)	.318 (.015)	.339 (.007)	.336 (.006)	.325 (.007)
	Outcome-Response Contingency			Reaction Time (ms)
	Win-Stay	Lose-Shift	Draw-Shift	Win	Lose	Draw
D+1	.348 (.033)	.748 (.028)	.690 (.033)	619 (121)	588 (115)	524 (67)
D0	.345 (.033)	.784 (.023)	.695 (.026)	729 (150)	527 (82)	501 (66)
D-1	.377 (.029)	.753 (.022)	.736 (.021)	600 (78)	542 (62)	480 (53)

Observed shift proportions following wins, losses and draws were also compared to the expected value predicted by the participant playing according to MS (66.6%) via one-sampled t-tests. Neither win-shift (t[39] = 0.875, p = .387) nor draw-shift (t[39] = 1.885, p = .067) was significantly different from expected value, but lose-shift (t[39] = 5.163, p < .001) proportions did supporting a significant bias towards shift behaviour following losses.

2.3 Discussion

Experiment 1 establishes a number of key observations with respect to the subjective interpretation of draw outcomes. First, there was a clear indication of post-draw speeding, in alignment with negative rather than positive valence interpretation. Second, behaviour following draws was characterized by shift (70.70%) rather than stay (29.30%) behaviour, again consistent with reactions to negative (i.e., lose-shift) rather than positive (i.e., win-stay) outcomes. Third, in terms of the quality of behaviour as a consequence of outcome, shift proportions following draws were closer to optimized MS performance compared to losses. This leads us away from the wholesale adoption of the view that draws are functionally equivalent to losses.

Finally, we note changing the value of a draw to -1 did not significantly impact behaviour less than changing the value of a draw to +1. Instead, an examination of Table 1 shows a non-significant increase of shift behaviour when draws were assigned -1 (73.6%), relative to when draws were assigned both 0 (69.5%) and +1 (69.0%).

3. Experiment 2

The data from Experiment 1 identified distinct behavioural effects that underline the ambiguities associated with draws. Draws were aligned with negative outcome in that future actions were characterized by speeding rather than slowing, and, shift rather than stay behaviour, similar to losses. However, draws did not generate identical states as losses, since the degree of shift behaviour was equivalent to MS performance in the former case. Draws were also weakly aligned with positive outcomes in that the degree of shift behaviour was constant when the value of the draw was made explicitly positive but rose (non-significantly) when the value of the draw was made explicitly negative. In Experiment 2, we focused more specifically on the hypothesis that shift behaviour should increase- away from MS performance- via the explicit assignment of draw value equivalent to losses (-1) compared to wins (+1; c.f., [38]).

We also considered the contribution of a potentially hidden variable in Experiment 1- namely, the presence of a cumulative score. In addition to the immediate effect of adding or subtracting individual points on a trial-by-trial basis, cumulative scores provide a longer-range index of success or failure. This subjective, longer-range evaluation of outcome has support at a neural level, given the observation that the anterior cingulate cortex (ACC) represents current outcomes against the broader context of average task value [39]. In particular, the presence of such cumulative scores may have been particularly important in Experiment 1 exactly due to the manipulation of draw value. Since MS opponents were used in all three conditions, participants experienced a broadly equivalent number of wins, draws and losses. Therefore, the degree of success / failure was equivalent across conditions. However, when draw outcomes were assigned to non-zero values, the use of +1 guaranteed an increasingly positive score as the block progressed, in contrast to the use of -1 guaranteeing an increasingly negative score. This is clearly borne out in the data from Experiment 1: the final average score when draw = 0 was -3.00 (SE = 1.30), when draw = +1 was +39.25 (SE = 1.85), and, when draw = -1 was -38.65 (SE = 1.72; F[2,78] = 628.15, MSE = 96.84, p < .001, ƞp2 = .942; one-way repeated measures ANOVA, all comparisons, Tukey’s HSD p < .05).

Therefore, it is possible that experiencing an increasingly positive or negative score impacts upon any immediate effects generated by individual trial-by-trial outcome values [39]: positive scoring (+1) become less salient against a backdrop of a reliably increasing total, just as negative scoring (-1) becomes less salient against a backdrop of a reliably decreasing total. Consequently, in Experiment 2, the central manipulation of draw value in accordance with explicitly positive (+1) or explicitly negative (-1) outcomes was combined with the manipulation of the presence or absence of a cumulative score.

3.1 Method

36 participants were analyzed for Experiment 2 (for the 35 individuals who provided demographic information: 26 women, 32 right-handed; mean age = 19.40, sd = 0.32). One individual was replaced due to experimenter error. Four conditions were completed in a counterbalanced order, in which the value of draw (+1, -1) and cumulative score (present, absent) varied. Blocks were now 90 trials (4 conditions) rather than 120 trials (3 conditions) used in Experiment 1. Participants also reported their subjective impression of each condition along a visual analog scale from total luck to total skill, as part of a larger empirical exercise to be reported elsewhere. All other parameters in Experiment 2 were identical to Experiment 1.

3.2 Results

As in Experiment 1, the comparison of wins (33.39%), losses (33.75%) and draws (32.85%) was not significant [F(2,708) = 0.757, MSE < .001, p = .473, ƞp2 = .021; see Table 2]. Median trial n RTs were submitted to a three-way repeated-measures ANOVA featuring draw value (+1, -1), cumulative score (present, absent) and outcome on trial n-1 (win, lose, draw). Only the two-way interaction between cumulative score x outcome was significant: [F(2,70) = 5.42, MSE = 18945, p = .006, ƞp2 = .134]. The interaction showed both post-loss speeding (384 ms) and post-draw speeding (434 ms) relative to RTs following wins (510 ms) but only in cases where the cumulative score was present (Tukey’s HSD, ps < .05).

Table 2

Distribution of item, outcome, outcome-response contingency and reaction time as a function of the value of draw trials (+1, -1) and presence (S) or absence (NS) of cumulative score in Experiment 2.

Standard error in parenthesis.

		Item			Outcome
		Rock	Paper	Scissors	Win	Lose	Draw
D+1	S	.333 (.015)	.327 (.015)	.340 (.014)	.353 (.007)	.329 (.008)	.318 (.007)
D+1	NS	.345 (.016)	.339 (.013)	.316 (.016)	.325 (.009)	.342 (.008)	.333 (.007)
D-1	S	.333 (.013)	.324 (.011)	.343 (.011)	.331 (.008)	.345 (.008)	.324 (.007)
D-1	NS	.338 (.013)	.342 (.012)	.319 (.011)	.326 (.008)	.335 (.009)	.339 (.009)
		Outcome-Response Contingency			Reaction Time (ms)
		Win-Stay	Lose-Shift	Draw-Shift	Win	Lose	Draw
D+1	S	.415 (.039)	.734 (.035)	.644 (.033)	474 (49)	397 (55)	412 (37)
D+1	NS	.417 (.040)	.717 (.013)	.636 (.039)	389 (50)	367 (41)	363 (34)
D-1	S	.376 (.030)	.723 (.026)	.728 (.031)	546 (72)	371 (40)	455 (43)
D-1	NS	.385 (.036)	.722 (.027)	.746 (.024)	417 (44)	401 (51)	381 (32)

Reaction times when the cumulative score was present following wins were also slower than all outcomes when the cumulative score was absent (384, 372, 403 ms for losses, draws and wins, respectively). All other comparisons were non-significant, with the interaction arising from the magnitude of post-loss and post-draw speeding decreasing without cumulative score. In these respects, the presentation of an increasingly positive-going / negative-going score would appear to be a prerequisite for the reliable observation of speeding following ‘negative’ outcomes.

All other main effects and interactions were not significant: cumulative score main effect [F(1,35) = 3.029, MSE = 112624, p = .091, ƞp2 = .079], draw value main effect [F(1,35) = 1.347, MSE = 63459, p = .254, ƞp2 = .037], outcome main effect [F(2,70) = 2.789, MSE = 71944, p = .068, ƞp2 = .074], cumulative score x draw value interaction [F(1,35) = 0.004, MSE = 65721, p = .950, ƞp2 < .001], draw value x outcome interaction [F(2,70) = 1.105, MSE = 17437, p = .337, ƞp2 = .031], and, the three-way interaction [F(2,70) = 1.052, MSE = 25991, p = .355, ƞp2 = .022].

Shift proportions were compared across draw value, cumulative score and outcomes in a three-way repeated-measures ANOVA (see Fig 1). Shift proportions were significantly modulated by a main effect of draw value [F(1,35) = 5.165, MSE = 0.042, p = .029, ƞp2 = .129], a main effect of outcome [F(1,35) = 8.500, MSE = 0.069, p < .001, ƞp2 = .195], and, an interaction between draw value x outcome [F(2,70) = 5.080, MSE = 0.017, p = .009, ƞp2 = .126]. Here, win-shift did not differ as a function of draw value (-1 = 61.99%; +1 = 58.38%), nor did lose-shift (-1 = 72.74%; +1 = 72.58%). However, draw-shift behaviour was significantly larger when draws were assigned the value of -1 relative to +1 (73.73% and 63.98%, respectively; Tukey’s HSD, p < .05). According to one-sampled t-tests, draw-shift behaviour when draws were assigned the value of +1 did not significantly differ from the expected value of 66.6% (63.98%; t[35] = -0.892, p = .378) but did show a significant bias in favour of shift behaviour when draws were assigned the value of -1 (73.73%; t[35] = 3.105, p = .003). Behaviour following wins showed a significant bias in favour of stay (60.18% shift; t[35] = -2.214, p = .033), whereas behaviour following losses showed a significant bias in favour of shift (72.66% shift; t[35] = 2.269, p = .030).

All other main effects and interactions of the ANOVA were non-significant: cumulative score main effect [F(1,35) = 0.052, MSE = 0.048, p = .821, ƞp2 = .001], draw value x cumulative score interaction [F(1,35) = 0.097, MSE = 0.021, p = .758, ƞp2 = .003], draw value x outcome interaction [F(2,70) = 0.201, MSE = 0.017, p = .819, ƞp2 = .005], and, the three-way interaction [F(2,70) = 0.333, MSE = 0.008, p = .718, ƞp2 = .009].

Experiment 2 produced a significant effect of draw value, wherein the degree of shift behaviour was increased when draw trials were assigned the same valence and value as lose trials. This was confirmed by further analysis of the degree of draw-shift as a function of draw value (+1, -1) and Experiment (1, 2 [score present conditions only]) via a mixed, two-way ANOVA. The main effect of draw value [F(1,74) = 9.353, MSE = .018, p = .003, ƞp2 = .112] in the absence of a main effect of Experiment [F(1,74) = 0.558, MSE = .049, p = .457, ƞp2 = .007], or interaction with Experiment [F(1,74) = 0.778, MSE = .017, p = .381, ƞp2 = .010] confirms that the proportion of draw-shift behaviour increased when draws were assigned the value of -1 relative to +1 (73.25% vs. 66.69%, respectively). Once again, draw-shift behaviour exceeded that predicted by MS when draws were assigned a negative value (t[75] = 3.630, p < .001) but was equivalent to MS behaviour when draws were assigned a positive value (t[75] = 0.067, p = .947), on the basis of one-sampled t-tests.

3.3 Discussion

Across Experiments 1 and 2 we conclude that there is a minor impact of adding 1 to a neutral draw value of 0, relative to a major impact of subtracting 1. This observation is consistent with the view that losses carry twice the subjective magnitude of their objective value [6, 30, 31]. However, if we carry the principle that the negative-going modulation of value should have a greater impact than the positive-going modulation of value irrespective of the outcome in question, then increasing the cost of loss from -1 to -2 should produce a stronger effect on shift behaviour than increasing the benefit of win from +1 to +2 produces on stay behaviour. Therefore, Experiment 3 applied the same value manipulations to win and loss value, once again combined with the presence or absence of cumulative score. In these regards, this final experiment serves as a test that ambiguous outcomes (draws) are more sensitive to value manipulations than explicit outcomes (wins, losses).

4. Experiment 3

4.1 Method

36 participants were analyzed for Experiment 3. For the 35 individuals who provided demographic information, 24 were women, 30 were right-handed, and the mean age was 19.83 (sd = 2.85). All parameters in Experiment 3 were identical to Experiment 2, apart from the value assignments of outcomes. In one condition, wins, draws and losses were assigned +2, 0, -1, respectively, while in a second condition, they were assigned +1, 0, -2, respectively (win-heavy, and, loss-heavy; after Forder & Dyson, 2016).

4.2 Results

As in all previous experiments, the occurrence of wins (33.16%), losses (33.46%) and draws (33.38%) was equivalent [F(2,70) = 0.099, MSE < .001, p = .906, ƞp2 = .002; see Table 3]. Median RTs from trial n were submitted to a three-way repeated-measures ANOVA featuring value (win-heavy, lose-heavy) and cumulative score (present, absent) and outcome at trial n-1 (win, lose, draw). The two-way interaction between cumulative score x outcome found in Experiment 2 replicated in Experiment 3: [F(2,70) = 3.340, MSE = 48207, p = .041, ƞp2 = .087] in addition to a main effect of outcome: [F(1,35) = 7.321, MSE = 85044, p = .001, ƞp2 = .173].

Table 3

Distribution of item, outcome, outcome-response contingency and reaction time as a function of the value of win (+2) and lose (-2) trials and presence (S) or absence (NS) of cumulative score in Experiment 3.

Standard error in parenthesis.

		Item			Outcome
		Rock	Paper	Scissors	Win	Lose	Draw
W+2	S	.378 (.023)	.318 (.016)	.303 (.015)	.335 (.009)	.335 (.010)	.330 (.007)
W+2	NS	.356 (.015)	.353 (.013)	.292 (.015)	.332 (.006)	.324 (.008)	.344 (.007)
L-2	S	.370 (.022)	.334 (.014)	.296 (.014)	.332 (.010)	.342 (.008)	.325 (.008)
L-2	NS	.347 (.014)	.352 (.011)	.301 (.013)	.327 (.008)	.337 (.007)	.335 (.008)
		Outcome-Response Contingency			Reaction Time (ms)
		Win-Stay	Lose-Shift	Draw-Shift	Win	Lose	Draw
W+2	S	.412 (.048)	.763 (.040)	.676 (.036)	651 (115)	567 (129)	491 (73)
W+2	NS	.363 (.040)	.753 (.031)	.694 (.033)	489 (74)	399 (45)	499 (88)
L-2	S	.427 (.045)	.783 (.031)	.667 (.033)	665 (98)	472 (66)	470 (52)
L-2	NS	.418 (.043)	.786 (.025)	.668 (.036)	508 (78)	410 (46)	406 (48)

As in Experiment 2, post-loss speeding (519 ms) and post-draw speeding (481 ms) relative to RTs following wins (658 ms) were only observed in the condition where the cumulative score was present (Tukey’s HSD, ps < .004). Reaction times when the cumulative score was present following wins were also slower than all outcomes when the cumulative score was absent (498, 405, 453 ms for wins, losses and draws, respectively). Post-loss speeding was also significant in the cumulative score absent condition (Tukey’s HSD, p = .030) and all other comparisons were non-significant.

All other ANOVA main effects and interactions were not significant: cumulative score main effect [F(1,35) = 3.361, MSE = 325091, p = .075, ƞp2 = .088], value main effect [F(1,35) = 0.553, MSE = 149089, p = .462, ƞp2 = .016], cumulative score x value interaction [F(1,35) = 0.010, MSE = 434503, p = .919, ƞp2 < .001], value x outcome interaction [F(2,70) = 1.357, MSE = 39730, p = .264, ƞp2 = .037], and, the three-way interaction [F(2,70) = 2.298, MSE = 31233, p = .108, ƞp2 = .062].

Shift proportions were analysed across value (win-heavy, lose-heavy),cumulative score (present, absent) and outcome (win, lose, draw) in a three-way repeated-measures ANOVA (see Fig 1). A main effect of outcome was noted [F(2,70) = 14.632, MSE = 0.077, p < .001, ƞp2 = .295], along with an interaction between value x outcome [F(2,70) = 3.597, MSE = 0.010, p = .033, ƞp2 = .093]. None of the pairwise comparisons between value were significant (win: win-heavy = 57.76% vs lose-heavy = 61.27%; lose: win-heavy 78.44% vs. lose-heavy = 75.80%; draw: win-heavy = 66.73% vs. lose-heavy = 68.52%; all Tukey’s HSD, p > .05). Aggregate behaviour following win was not significantly different from the expected value of 66.6% (59.51%; t[35] = -1.909, p = .065), aggregated behaviour following lose was significantly biased towards shift (77.12%; t[35] = 4.174, p < .001), and aggregated behaviour following draw was not significantly different from the expected value of 66.6% (67.62%; t[35] = 0.363, p = .719).

4.3 Discussion

The data from Experiment 3 show that wins and losses do not respond to value manipulations in the same way as draws (Experiments 1 and 2). Contrary to expectations, increasing the cost of loss from -1 to -2 did not produce a stronger effect on shift behaviour than increasing the benefit of win from +1 to +2 in order to change stay behaviour (contra [22]). As such, ambiguous outcomes (draws) appear more amenable to value manipulations than explicit outcomes (wins, losses). Moreover, this cannot be due to the average absolute score achieved in the different value conditions. The assignment of values as win +1, draw +1, lose -1 in Experiment 2 (mean final score = 29.67, standard error = 1.03) was functionally equivalent to the assignment of values as win +2, draw 0, lose -1 in the win-heavy condition of Experiment 3 (mean final score = 30.35, standard error = 1.37), just as the assignment of values as win +1, draw -1, lose -1 in Experiment 2 (mean final score = -30.86, standard error = 1.00) was functionally equivalent to the assignment of values as win +1, draw 0, lose -2 in the lose-heavy condition of Experiment 3 (mean final score = -31.44, standard error = 1.37). This was supported by the results of a two-way, repeated measures ANOVA with final score as the dependent variable. This yielded a main effect of value [F(1,70) = 2163.64, MSE = 62.2, p < .001, ƞp2 = .969] in the absence of main effect of experiment [F(1,70) = 0.002, MSE = 47.4, p = .966, ƞp2 < .001], and in the absence of an interaction [F(1,70) = 0.231, MSE = 62.2, p = .632, ƞp2 = .003].

Although the presence / absence of a cumulative score does not play a role in the quality of decision-making, a consistent picture emerges from Experiments 2–3 in that the presentation of an increasingly positive-going / negative-going score plays a role in the speed of decision-making- namely, accentuating speeding following ‘negative’ outcomes. This reinforces the idea that individual moments of feedback are compared against a backdrop of historic performance (c.f., [39]), reminding us that reactions to outcome are idiosyncratic, and influenced by the salience of both internal and external signals.

It remains possible that the comparison between Experiments 2 and 3 is not exact, as the subjective change from 0 to +1 (or -1) in the case of draws is not as dramatic as the subjective change from -1 to -2 in the case of losses, or, from +1 to +2 in the case of wins (cf, Prospect Theory; [30]). Indeed, more radical pay-off matrices regarding the value of wins and losses can be proposed (eg [40]). However, such refinements will reintroduce the confound of different average absolute scores across different conditions. Thus, the aim to equate the subjective rather than objective value of outcomes also has a number of hidden assumptions that will require consideration.

5. General discussion

In the absence of explicit reinforcement or punishment, we must still evaluate the relative success or failure of our actions and prepare for future behaviour accordingly. The current data speak clearly to outcome instances which are- on the surface- neither gains nor losses.

Previous data have strongly argued for the draw experience to elicit negative rather than positive responses. For example, models of human performance are better when draws are directly punished in the same way as losses (that is, assigned the value of -1), rather than being neither punished nor rewarded (assigned the value of 0; [38]). Similar profiles for draws and losses are shown in terms of a speeded bias towards shift behaviour, further implying their subjective interpretation as negative rather than positive (e.g., [22, 41]). While our data also support the contention that responses following draws will be initiated faster than those following explicit wins, and, that draws produce a future response switch (rather than stay) bias, the experience of draws is not wholly negative. This is borne out in the logic that fast rather than slow reaction times following loss represent a self-imposed limitation on future decision-making time that makes automatic, sub-optimal performance more likely ([10, 18, 31]). However, the post-draw speeding observed in the current experimental series did not produce the same sub-optimal performance as that observed for post-loss speeding. The average proportion of draw-shift behaviour was equivalent to that predicted by mixed-strategy performance wherein all three possible response associations between consecutive trials were equal (draw-stay ≈ 33.3%; draw-shift ≈ 66.6%). Such performance guarantees loss minimization and matches the approximation of mixed-strategy performance often observed following wins.

Moreover, draws allowed for a greater degree of behavioural flexibility relative to outcomes that were clearly marked as negative. Our data show that changing the value of draws also leads to changes in behaviour- specifically, assigning draws the value of explicit wins (+1) enabled an approximation of optimal behaviour (see above). In contrast, assigning draws the value of explicit losses (-1) lead to an increase in shift bias thereby placing the participant in a potentially precarious and exploitable competitive position (see Fig 1). These comparisons strongly suggest another way in which draws can behave like wins rather than losses. The suggestion that the draw outcome as chameleon-like in nature, however, must be tempered by additional observations. Based on a reviewer’s suggestion, we examined the degree of shift behaviour following wins (+1; 61.99%) in Experiments 1 and 2 against the concomitant behaviour generated by draws (+1; 66.62%) within those same conditions. We noted a significant reduction in win-shift behavior relative to draw-shift behaviour, when both categories were assigned a constant value of +1 t[75] = -3.051, p = .003. Similarly, we examined the degree of shift behaviour following losses (-1; 74.10%) in Experiments 1 and 2 against the concomitant behaviour generated by draws (-1; 73.69%), we noted a non-significant difference in lose-shift behavior relative to draw-shift behaviour, when both categories were assigned a constant value of -1: t[76] = 0.292, p = .771. Our reading of these results are that draw outcomes may more readily co-opt the behavioural signatures of explicitly negative, relative to explicitly positive, outcomes when the same values are assigned. If a +1 draw does not have the exact same properties as a +1 win, then value in and of itself cannot completely predict the behavioural consequences of outcomes.

Thus, the study of neutral outcomes will continue to represent an important addition to decision-making for two reasons. First, our current data imply a cognitive flexibility following draw trials that is not triggered by more clearly valenced wins and losses. This provides a clear route to studying the subjective aspects of outcome response, and how reaction to neutral trials may be shaped by preceding trial history. For example, we have recently shown that relative to draw-draw trials, the trial outcome sequence of win-draw causes an increase in shift behaviour whereas the sequences of lose-draw causes a decrease in shift behaviour- at least at a group level [11]. The concomitant increase and decrease in shift behaviour appears to us as an objective manifestation of the subjective nature of signed prediction error theory (eg, [42, 43]). In other words, draw trials preceded by a win are interpreted as worse-than-expected (making the draw appear more negative) whereas draw trials preceded by a loss are interpreted as better-than-expected (making the draw appear more positive). Second, introducing a third outcome (draw) requires a concomitant increase in the number of responses within the decision-making space. This is important as there are growing concerns as to the degree to which the modal use of binary decision-making paradigms severely limits our understanding of more naturalistic, non-binary decision spaces [44, 45].

In sum, mitigating the adverse emotional and cognitive consequences of negative outcomes remains an important goal in the context of education, gambling and economics. However, our data show that moving away from binary conceptualizations of outcome is critical to understanding the full palette of subjective responses elicited by decision-making. Specifically, our consideration of draws highlights the subjective aspects of decision-making, and the ways in which supposedly neutral outcomes take on the hues of more clearly valenced results. The processing cascade generated by neither being explicitly reinforced or punished produces a complex behavioural profile containing elements found in both explicitly positive and explicitly negative results. The reaction to draws appears more flexible than those produced by wins and losses, and generates a response signature that is simultaneously positive and negative, but apparently never ‘neutral’.

(XLSX)

Click here for additional data file.

26 Apr 2022

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Reviewer #1: The current paper presents a neat set of experiments that adds nicely to the literature on post-error/post-loss responses by adding a third possible outcome such as a draw. This draw somewhat resembles near-misses in the gambling literature, however not entirely and therefore is a good addition in order to investigate decision making in response to different outcomes.

I just have a couple of points that the authors might want to take into consideration:

On the theoretical level, I am not entirely sure whether the frequency argument made by the orienting account is the only explanation for speeding vs. slowing. In addition to the fact, that Eben et al. (2020) observed speeding after losses with an equal amount of wins and losses (which seems so do you), recent research (e.g. Damaso et al. 2020) suggests that speeding vs. slowing might be determined by the controllability of the outcome (which in turn allows the idea that speeding is not necessarily maladaptive ...).

Personally, I would find a sample size rationale helpful.

I am curious why the authors chose to determine whether rock, paper or scissors were chosen instead of predetermining the outcome to be win, draw or loss? We usually followed the latter approach to be sure we indeed have an equal amount of outcomes, so I am happy to hear other options.

In the spirit of openness I always encourage authors not only to share their data but also the analyses scripts and the material which increases the reproducibility of your experiments and analyses.

Reviewer #2: The current paper reports three experiments that examined the behavioral profiles following wins, losses and draws. The effects of draws on subsequent responses are interesting, and as noted by the authors, certainly largely neglected in the literature so far. From this perspective, the current paper makes a useful contribution. However, the way the data is analyzed and the results are presented seem to hinder the understanding of the findings. Furthermore, I am not totally convinced that based on the results, the authors can claim that draws differ from both wins and losses because they show different sensitivity to value manipulation (see major comment 8). Hope my comments will be helpful to the authors in preparing the manuscript for publication.

Major comments:

1. First of all, I would like to commend the authors for making the aggregate data publicly available on the Open Science Framework. Aggregate data will allow other researchers to check the accuracy of the reported results, and is thus probably one of the most important products of a research project. That being said, other products generated during the process of research are also important, and I would encourage the authors to publicly share these products as much as possible. For instance, these may include the experimental materials, the Presentation code for the experiment, raw data files, analysis code used to analyze data etc. By making these materials open, other researchers will be able to repeat the analysis, re-analyze the raw data in new ways, or run replications and extensions in the future. I think this will be essential for a cumulative and robust science.

2. The introduction set the stage up very well to highlight the importance of examining 'draw' outcomes, a type of outcome that has largely been neglected so far in the literature. The following paragraphs on reaction times, FRN and shift/stay behavior also did an excellent job of reviewing relevant previous work. However, what seem to be missing are clear statements of the research questions that the current paper aims to address. After learning that both RT and FRN show similar patterns after a draw and a loss, it seems clear that draws are more like unambiguously negative loss outcomes. If that is the case, what are the remaining questions or gaps that the current paper aims to address? A paragraph at the end of the introduction on what remains unknown, and what this paper will examine, would be helpful.

3. The sample sizes of the experiments seem relatively low (N = 40, 36 and 36), especially given that the designs involve multiple factors and interaction effects are of interest (see e.g., Brysbaert, M. (2019). How Many Participants Do We Have to Include in Properly Powered Experiments? A Tutorial of Power Analysis with Reference Tables. Journal of Cognition, 2(1), 1–38. https://doi.org/10.5334/joc.72). Of course, whether a certain sample size provides sufficient statistical power or not depends on the expected effect size. I would therefore like the authors to provide more information on how the sample sizes were determined, and the achieved statistical power.

4. Figure 1 (and the corresponding analyses on stay/shift behavior) is difficult to follow, partly because it shows the proportion of stay for the win condition, and the proportion of shift for the lose and draw conditions. While stay and shift are complementary (they add up to 100%), they are not directly comparable. That the values in the win-stay condition are lower than the values in the lose-shift and draw-shift conditions in Figure 1 is thus not very informative. I would suggest showing the proportion of shift (or the proportion of stay) for all three outcomes. The authors may then add a horizontal line at 66.6%, showing the expected shift proportion of a player who chooses randomly. Values higher than 66.6% indicate a tendency to shift, while values lower than 66.6% indicate a tendency to stay.

5. The analyses on stay/shift behavior can be organized accordingly. For Experiment 1 for example, this would mean to start with a 3 (previous outcome, win, loss vs. draw) by 3 (draw value, 0, 1 vs. -1) ANOVA on the proportion of shift, followed up by separate ANOVAs or t tests if necessary. The proportions of shift can then be compared against the baseline of 66.6%, to establish (1) whether they differ from the baseline, and if yes, (2) in which direction (stay vs. shift). Note that in the approach adopted by the authors, they needed to look at the shift behavior after wins (in the very last analysis) anyways. I think consistently using the proportion of shift as the dependent variable may provide a better structure for the analyses and the results.

6. Statistical results are selectively reported, in the sense that for ANOVAs, only the details for significant effects but not non-significant effects are presented. This is OK for the sake of brevity and simplicity, but I think it is still important to show the detailed results for all effects from all analyses, regardless of statistical significance. For instance, the authors may report the full results in the Supplemental Materials and refer readers to it in the main text should they be interested. Related, some of the conclusions are based on non-significant results. However, absence of evidence is not evidence of absence. Non-significant results can also mean that the evidence is inconclusive (given the relatively small sample sizes), rather than supporting the null hypothesis. To obtain evidence for the absence of an effect, the authors will need to adopt other statistical approaches, such as Bayesian analysis.

7. In the discussion of Experiment 2, the authors noted that "losses carry twice the subjective magnitude of their objective value". My understanding of this statement is that in the value function in the Prospect theory, the decrease in subjective value from 0 to -1 is about twice as large as the increase in subjective value from 0 to 1. Thus, losses carry twice the subjective magnitude, in comparison to wins. I'm not sure if this would necessarily imply that the difference between -2 and -1 in the loss domain would still be twice as large as the difference between 2 and 1 in the win domain. After all, the value function has an S shape, and as the magnitude of wins and losses increases, any additional win or loss will have an increasingly smaller influence on the subjective value.

8. Related, one of the conclusions of the paper is that "wins and losses do not respond to value manipulations in the same way as draws". However, changing the value from 1 to 2 or from -1 to -2 is probably different from changing the value from -1 to 1. So I am not sure if the authors can ascribe the difference to wins and losses being different from draws. To make such a claim, a better test may be to give a value of -1 or -2 to a draw , and compare it to e.g. loss when the value for a loss is also varied from -1 to -2. Some of the data may already provide some initial insights into this issue. For instance, what results would the authors get from Experiments 1 and 2 if they would compare shift/stay between (a) draw (-1) and loss (-1) and (b) draw (+1) and win (+1)? When the values are matched, are there still any differences between the different types of outcomes?

Minor comments:

1. Page 4: While the rest of the paper mainly used the term "post-loss speeding" (which is also the term used in Verbruggen et al. and Eben et al.,), the term "post-error slowing/speeding" was used here. Losses and errors may both be seen as failures or sub-optimal outcomes, but they are often used in different contexts: losses often denote losing a reward, while errors indicate incorrect responses in mostly cognitive psychology tasks (and may not be explicitly rewarded or punished). I think a short discussion/clarification on how the two may be related would be useful, instead of directly treating them as the same.

2. Page 5: Related, while Notebaert et al. indeed showed that the frequency of errors influences post-error slowing or speeding, Eben et al. (Experiment 3) has observed post-loss speeding while losses, wins and non-gamble outcomes occur equally often. Outcome frequency alone thus does not seem sufficient to explain post-loss speeding.

3. Page 5: "A second metric to ascertain the subjective interpretation of draws is the flexibility of responding following outcomes.". The paragraph then went on to discuss previous findings on feedback-related negativity, rather than response flexibility.

4. Page 6: I feel the paragraph on behavior flexibility would be easier to follow if the authors would first start with the phenomenon (loss-shift is not sensitive to objective values while win-shift appears to be sensitive) and then explain the underlying mechanism (that loss subjectively looms larger than win).

5. Page 6: "a mixed-strategy-style approach guaranteeing the absence of exploitation". Please explain what this strategy is when it first occurs. Does it mean choosing randomly?

6. Page 7: The introduction of Experiment 1 may be substantially shortened, by saying that since outcome frequencies influence reaction times (Notebaert et al.) and potentially the subjective interpretation of draws (e.g., when wins are frequent, draws may be more likely to be interpreted as failing to win), the authors used an opponent that chose randomly to ensure equal probabilities of win, loss and draw.

7. Page 9: One of the predictions for Experiment 1 is that "the degree to which participants stray from optimal performance should be greater for draw-shift than win-stay". My interpretation of this prediction is that the deviation from 66.6% for draw-shift would be larger than the deviation from 33.3% for win-stay. Or, if the authors adopt the suggestion of consistently using the proportion of shift (see above), this would mean the absolute difference between draw-shift and 66.6% would be larger than the absolute difference between win-shift and 66.6%. This does not seem to be tested. Or did I misunderstand this prediction?

8. An inconsistency in the description of the method. Page 9: "white-gloved (left; opponent) and blue-gloved (right; participant)". Page 10: "the opponent (blue glove on the left) and the participant (white glove on the right)".

9. Did participants get a reward based on their performance in the task? In other words, was the task incentivized?

10. In the instructions given to the participants, were there any indications as to whether the opponent could potentially be exploited? For instance, were participants explicitly told that they were playing against the computer, which would select the options randomly?

11. Which statistical software (and version) was used to analyze the data?

12. Page 14: "we note changing the value of a draw to -1 did not significant impact". Significant should be significantly?

13. Figure 1 currently only plots the shift/stay proportions. Since reaction times are of interest as well, plotting RT would be useful. So Figure 1 would contain 6 subplots, with one column for RTs and one column for shift/stay.

14. Page 19: The first paragraph of the Discussion seems better suited for the Results section.

15. Page 23: What is 'sterr'?

16. Page 23: What is the dependent variable in the two-way, repeated-measures ANOVA?

17. When participants shift, there are two different options that they can shift to. I wonder if the authors also looked at different types of shift to see if draw and loss differ.

18. Page 25: "a win followed by a draw causes an increase in shift behaviour whereas a loss followed by a draw causes shift behaviour to decrease". This sounds like a win leads to an increase in shift behavior and a loss leads to a decrease, but I think the authors meant that the draws have such an effect.

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Reviewer #1: Yes: Charlotte Eben

Reviewer #2: Yes: Zhang Chen

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17 May 2022

16 / 05 / 2022

Thank you for allowing us to revise and resubmit our manuscript “Assessing the behavioural profiles following neutral, positive and negative feedback” (PONE-D-22-06419). In accordance with your guidance, we have revised the manuscript, and, provided detailed point-by-point coverage, of both Reviewers’ comments.

If you require anything further, please do not hesitate to contact me directly.

With best wishes,

Dr Ben Dyson.

Reviewer #1: The current paper presents a neat set of experiments that adds nicely to the literature on post-error/post-loss responses by adding a third possible outcome such as a draw. This draw somewhat resembles near-misses in the gambling literature, however not entirely and therefore is a good addition in order to investigate decision making in response to different outcomes.

I just have a couple of points that the authors might want to take into consideration:

On the theoretical level, I am not entirely sure whether the frequency argument made by the orienting account is the only explanation for speeding vs. slowing. In addition to the fact, that Eben et al. (2020) observed speeding after losses with an equal amount of wins and losses (which seems so do you), recent research (e.g. Damaso et al. 2020) suggests that speeding vs. slowing might be determined by the controllability of the outcome (which in turn allows the idea that speeding is not necessarily maladaptive ...).

We agree that the frequency argument is not the only way to frame the speeding / slowing account. Damaso et al (2020) cites our previous work (Dyson, Sundvall, Forder & Douglas, 2018), where we also claim that impulsive behavior following failure is more likely when an individual cannot control the outcome of their environment either as a result of interacting with an unexploitable opponent, or, interacting with an exploitable opponent whom they fail to exploit. Furthermore, we are starting to see some links at the individual level where the degree of post-error slowing relates to the degree to which the participant can successfully exploit their opponent (Dyson, 2021).

Similar to the comments made by Reviewer #2 we now make a statement that frequency of outcome cannot provide a complete account of post-loss slowing since post-loss slowing is intact when positive and negative outcomes have equal frequency.

Personally, I would find a sample size rationale helpful.

Similar to the suggestion of Reviewer 2, we now provide a sample size rationale in the manuscript.

I am curious why the authors chose to determine whether rock, paper or scissors were chosen instead of predetermining the outcome to be win, draw or loss? We usually followed the latter approach to be sure we indeed have an equal amount of outcomes, so I am happy to hear other options.

We have previously used both variable win-rate controlling for the distribution of items (current experiments) and fixed win-rate paradigms controlling for the distribution of outcomes (eg, Dyson, Musgrave, Rowe & Sandhur, 2020). We see two potential disadvantages with fixed win-rate paradigms. First, if participants are completing a series of conditions (in our manuscript, either 3 or 4), there may be symmetries in the final score (eg., always 0, -30 or +30) that might change the way participants approach the study. In other words, fixed win rates can increase the belief that their computerized opponent is somehow ‘cheating’. Second, in cases where the experience of dominance is simulated by increasing win rates to the same degree, the mental model participants develop for their ‘successful strategy’ is idiosyncratic, or, nonexistent. The separation between success and the mechanism(s) for success might lead participants towards a belief that the task was one of luck rather than skill.

However, there are also disadvantages with the variable win-rate approach. For example, distributing items equally and randomly across a series of trials raises the possibility of accidental exploitation if a high degree of item bias is exhibited in the earlier stages of the block. For example, opponent overplay of rock in the first half of the block requires the underplay of rock in the second half of the block. However, empirical analyses do not support the idea that participants used the degree of preliminary item bias to increase their win rate in ‘unexploitable’ conditions (see Dyson et al., 2018, footnote 1).

In the long-run, both variable and fixed win rates have their uses as long as we remain aware of the potential pitfalls of both.

In the spirit of openness I always encourage authors not only to share their data but also the analyses scripts and the material which increases the reproducibility of your experiments and analyses.

Echoing the comments of Reviewer 2, we have now added experimental scripts and raw data to our pre-print and summary data on https://psyarxiv.com/cqeg7/

Reviewer #2: The current paper reports three experiments that examined the behavioral profiles following wins, losses and draws. The effects of draws on subsequent responses are interesting, and as noted by the authors, certainly largely neglected in the literature so far. From this perspective, the current paper makes a useful contribution. However, the way the data is analyzed and the results are presented seem to hinder the understanding of the findings. Furthermore, I am not totally convinced that based on the results, the authors can claim that draws differ from both wins and losses because they show different sensitivity to value manipulation (see major comment 8). Hope my comments will be helpful to the authors in preparing the manuscript for publication.

Major comments:

1. First of all, I would like to commend the authors for making the aggregate data publicly available on the Open Science Framework. Aggregate data will allow other researchers to check the accuracy of the reported results, and is thus probably one of the most important products of a research project. That being said, other products generated during the process of research are also important, and I would encourage the authors to publicly share these products as much as possible. For instance, these may include the experimental materials, the Presentation code for the experiment, raw data files, analysis code used to analyze data etc. By making these materials open, other researchers will be able to repeat the analysis, re-analyze the raw data in new ways, or run replications and extensions in the future. I think this will be essential for a cumulative and robust science.

We thank the Reviewer for the reminder to improve our commitment to Open Science. Similar to the comments of Reviewer #1, we have now added experimental scripts and raw data to our pre-print and summary data on https://psyarxiv.com/cqeg7/

2. The introduction set the stage up very well to highlight the importance of examining 'draw' outcomes, a type of outcome that has largely been neglected so far in the literature. The following paragraphs on reaction times, FRN and shift/stay behavior also did an excellent job of reviewing relevant previous work. However, what seem to be missing are clear statements of the research questions that the current paper aims to address. After learning that both RT and FRN show similar patterns after a draw and a loss, it seems clear that draws are more like unambiguously negative loss outcomes. If that is the case, what are the remaining questions or gaps that the current paper aims to address? A paragraph at the end of the introduction on what remains unknown, and what this paper will examine, would be helpful.

In terms of providing evidence that draws may generate a unique behavioural fingerprint relative to losses, we now identify a seemingly reliable observation from our previous work in the Introduction. Specifically, the degree of shift behaviour is reliably and significantly smaller following draws relative to losses (cf, Dyson, 2021, Experiment 1, no credit condition; Dyson, Stewart, Meneghetti & Forder, 2020, Experiment 1; Forder & Dyson, 2016, baseline condition; Dyson, Wilbiks, Sandhu, Papanicolaou & Lintag, 2016). These previous observations prohibit the wholesale acceptance of draws as functionally equivalent to losses, justify the further study of draw trials, and provide a rationale for our sample sizes (see below).

3. The sample sizes of the experiments seem relatively low (N = 40, 36 and 36), especially given that the designs involve multiple factors and interaction effects are of interest (see e.g., Brysbaert, M. (2019). How Many Participants Do We Have to Include in Properly Powered Experiments? A Tutorial of Power Analysis with Reference Tables. Journal of Cognition, 2(1), 1–38. https://doi.org/10.5334/joc.72). Of course, whether a certain sample size provides sufficient statistical power or not depends on the expected effect size. I would therefore like the authors to provide more information on how the sample sizes were determined, and the achieved statistical power.

Sample sizes were derived with 80% estimates of power (cf, Brysbaert, 2019) using G*Power (Faul, Erdfelder, Lang & Buchner, 2007) from two recent studies described above, in which reduction in shift behaviour following draw (0) relative to loss (-1) trials were observed: Dyson (2021): dz = 0.6894, one-tailed, yielding n = 15, and, Dyson, Stewart, Meneghetti & Forder (2020): dz = 0.4217, one-tailed, yielding n = 37.

4. Figure 1 (and the corresponding analyses on stay/shift behavior) is difficult to follow, partly because it shows the proportion of stay for the win condition, and the proportion of shift for the lose and draw conditions. While stay and shift are complementary (they add up to 100%), they are not directly comparable. That the values in the win-stay condition are lower than the values in the lose-shift and draw-shift conditions in Figure 1 is thus not very informative. I would suggest showing the proportion of shift (or the proportion of stay) for all three outcomes. The authors may then add a horizontal line at 66.6%, showing the expected shift proportion of a player who chooses randomly. Values higher than 66.6% indicate a tendency to shift, while values lower than 66.6% indicate a tendency to stay.

In accordance with the Reviewer’s suggestions, Figure 1 has been redrawn for shift proportion throughout, in addition to the plotting of a baseline of 66.6%.

5. The analyses on stay/shift behavior can be organized accordingly. For Experiment 1 for example, this would mean to start with a 3 (previous outcome, win, loss vs. draw) by 3 (draw value, 0, 1 vs. -1) ANOVA on the proportion of shift, followed up by separate ANOVAs or t tests if necessary. The proportions of shift can then be compared against the baseline of 66.6%, to establish (1) whether they differ from the baseline, and if yes, (2) in which direction (stay vs. shift). Note that in the approach adopted by the authors, they needed to look at the shift behavior after wins (in the very last analysis) anyways. I think consistently using the proportion of shift as the dependent variable may provide a better structure for the analyses and the results.

Full factorial ANOVAs are applied to Experiments 1-3. One-sampled t-tests comparing observed values to the baseline of 66.6% are also applied to assess any direction of bias.

6. Statistical results are selectively reported, in the sense that for ANOVAs, only the details for significant effects but not non-significant effects are presented. This is OK for the sake of brevity and simplicity, but I think it is still important to show the detailed results for all effects from all analyses, regardless of statistical significance. For instance, the authors may report the full results in the Supplemental Materials and refer readers to it in the main text should they be interested. Related, some of the conclusions are based on non-significant results. However, absence of evidence is not evidence of absence. Non-significant results can also mean that the evidence is inconclusive (given the relatively small sample sizes), rather than supporting the null hypothesis. To obtain evidence for the absence of an effect, the authors will need to adopt other statistical approaches, such as Bayesian analysis.

All statistical terms arising from the full factorial ANOVAs (see 5) are now included in the manuscript. In the context of cross-experimental comparisons (such as those suggested by the Reviewer; see below), we feel that a significant difference between Experiments removes some of the framing concerns related to ‘non-significant results.’ Moreover, it is not the case that specific experiments was so insensitive as to yield no significant results. For example, in Experiment 3, we replicated the relationship between post-loss speeding and the presence (rather than absence) of cumulative score. We also replicated the observations that behaviour following loss was significantly biased towards shift (see also Experiment 2). Rather, it seems to us more appropriate to discuss the manuscript in terms of the strength of specific manipulations that we deployed (also, see below).

7. In the discussion of Experiment 2, the authors noted that "losses carry twice the subjective magnitude of their objective value". My understanding of this statement is that in the value function in the Prospect theory, the decrease in subjective value from 0 to -1 is about twice as large as the increase in subjective value from 0 to 1. Thus, losses carry twice the subjective magnitude, in comparison to wins. I'm not sure if this would necessarily imply that the difference between -2 and -1 in the loss domain would still be twice as large as the difference between 2 and 1 in the win domain. After all, the value function has an S shape, and as the magnitude of wins and losses increases, any additional win or loss will have an increasingly smaller influence on the subjective value.

We thank the Reviewer for this comment, and have integrated a discussion of this into the revised manuscript. In particular, we discuss the tension between assigning outcome values that maintain long-run equivalent between cumulative scores across Experiments 2 and 3 (and potentially decreasing subjective value), and, assigning outcome values that confound long-run equivalent between cumulative scores across Experiments 2 and 3 (but potentially equate subjective value). We feel the former approach as a valid one as it ensures that the differences we observed cannot be due to the average absolute score achieved in the different value conditions. As we mention in our original version of our manuscript:

“The assignment of values as win +1, draw +1, lose -1 in Experiment 2 (mean final score = 29.67, standard error = 1.03) was functionally equivalent to the assignment of values as win +2, draw 0, lose -1 in the win-heavy condition of Experiment 3 (mean final score = 30.35, standard error = 1.37), just as the assignment of values as win +1, draw -1, lose -1 in Experiment 2 (mean final score = -30.86, standard error = 1.00) was functionally equivalent to the assignment of values as win +1, draw 0, lose -2 in the lose-heavy condition of Experiment 3 (mean final score = -31.44, standard error = 1.37). This was supported by the results of a two-way, repeated measures ANOVA with final score as the dependent variable. This yielded, observing a main effect of value [F(1,70) = 2163.64, MSE = 62.2, p < .001, ƞp2 = .969] in the absence of main effect of experiment [F(1,70) = 0.002, MSE = 47.4, p = .966, ƞp2 < .001], and in the absence of an interaction [F(1,70) = 0.231, MSE = 62.2, p = .632, ƞp2 = .003].”

8. Related, one of the conclusions of the paper is that "wins and losses do not respond to value manipulations in the same way as draws". However, changing the value from 1 to 2 or from -1 to -2 is probably different from changing the value from -1 to 1. So I am not sure if the authors can ascribe the difference to wins and losses being different from draws. To make such a claim, a better test may be to give a value of -1 or -2 to a draw, and compare it to e.g. loss when the value for a loss is also varied from -1 to -2. Some of the data may already provide some initial insights into this issue. For instance, what results would the authors get from Experiments 1 and 2 if they would compare shift/stay between (a) draw (-1) and loss (-1) and (b) draw (+1) and win (+1)? When the values are matched, are there still any differences between the different types of outcomes?

Once again, we thank the Reviewer for this suggestion. We examined the degree of shift behaviour following wins (+1; 61.99%) in Experiments 1 and 2 against the concomitant behaviour generated by draws (+1; 66.62%) within those same conditions. We noted a significant reduction in win-shift behavior relative to draw-shift behaviour, when both categories were assigned a constant value of +1 t[75] = -3.051, p =.003. Similarly, we examined the degree of shift behaviour following losses (-1; 74.10%) in Experiments 1 and 2 against the concomitant behaviour generated by draws (-1; 73.69%), we noted a non-significant difference in lose-shift behavior relative to draw-shift behaviour, when both categories were assigned a constant value of -1: t[76] = 0.292, p =.771. Our reading of these results are that a) draw outcomes may more readily co-opt the behavioural signatures of explicitly negative relative to explicitly positive outcomes, and, b) value in and of itself cannot completely predict the behavioural consequences of outcomes.

Minor comments:

1. Page 4: While the rest of the paper mainly used the term "post-loss speeding" (which is also the term used in Verbruggen et al. and Eben et al.,), the term "post-error slowing/speeding" was used here. Losses and errors may both be seen as failures or sub-optimal outcomes, but they are often used in different contexts: losses often denote losing a reward, while errors indicate incorrect responses in mostly cognitive psychology tasks (and may not be explicitly rewarded or punished). I think a short discussion/clarification on how the two may be related would be useful, instead of directly treating them as the same.

To avoid confusion, we have removed explicit references to ‘post-error’ and now focus on ‘post-loss’ speeding.

2. Page 5: Related, while Notebaert et al. indeed showed that the frequency of errors influences post-error slowing or speeding, Eben et al. (Experiment 3) has observed post-loss speeding while losses, wins and non-gamble outcomes occur equally often. Outcome frequency alone thus does not seem sufficient to explain post-loss speeding.

Similar to the comments made by Reviewer #1, we now make a statement that frequency of outcome cannot provide a complete account of post-loss slowing since post-loss slowing is intact when positive and negative outcomes have equal frequency.

3. Page 5: "A second metric to ascertain the subjective interpretation of draws is the flexibility of responding following outcomes.". The paragraph then went on to discuss previous findings on feedback-related negativity, rather than response flexibility.

We have now changed this to ‘neural responding’

4. Page 6: I feel the paragraph on behavior flexibility would be easier to follow if the authors would first start with the phenomenon (loss-shift is not sensitive to objective values while win-shift appears to be sensitive) and then explain the underlying mechanism (that loss subjectively looms larger than win).

The paragraph has been rewritten with this new structure.

5. Page 6: "a mixed-strategy-style approach guaranteeing the absence of exploitation". Please explain what this strategy is when it first occurs. Does it mean choosing randomly?

The programming of the computerized opponent is now described in that section.

6. Page 7: The introduction of Experiment 1 may be substantially shortened, by saying that since outcome frequencies influence reaction times (Notebaert et al.) and potentially the subjective interpretation of draws (e.g., when wins are frequent, draws may be more likely to be interpreted as failing to win), the authors used an opponent that chose randomly to ensure equal probabilities of win, loss and draw.

The Introduction to Experiment 1 has now been edited with the above revisions in mind.

7. Page 9: One of the predictions for Experiment 1 is that "the degree to which participants stray from optimal performance should be greater for draw-shift than win-stay". My interpretation of this prediction is that the deviation from 66.6% for draw-shift would be larger than the deviation from 33.3% for win-stay. Or, if the authors adopt the suggestion of consistently using the proportion of shift (see above), this would mean the absolute difference between draw-shift and 66.6% would be larger than the absolute difference between win-shift and 66.6%. This does not seem to be tested. Or did I misunderstand this prediction?

Now that the dependent variable of interest in shift behaviour following wins, losses and draws, the case (as in Experiment 1) where the average win-shift value of 64.35% does not significantly differ from the expected value of 66.6%, but the average lose-shift value of 76.17% was significantly larger than the expected value of 66.6%, is taken as greater deviation from optimal performance following losses.

8. An inconsistency in the description of the method. Page 9: "white-gloved (left; opponent) and blue-gloved (right; participant)". Page 10: "the opponent (blue glove on the left) and the participant (white glove on the right)".

This is now corrected “(blue-gloved (left; opponent) and white-gloved (right; participant)”

9. Did participants get a reward based on their performance in the task? In other words, was the task incentivized?

The task was not incentivized.

10. In the instructions given to the participants, were there any indications as to whether the opponent could potentially be exploited? For instance, were participants explicitly told that they were playing against the computer, which would select the options randomly?

For each condition, as part of the instructions participants were informed, “Your opponents may play in different ways and use different strategies to try and win.”

11. Which statistical software (and version) was used to analyze the data?

We now list Statistica 13.3 as the software used to analyze the data.

12. Page 14: "we note changing the value of a draw to -1 did not significant impact". Significant should be significantly?

Changed to ‘significantly’.

13. Figure 1 currently only plots the shift/stay proportions. Since reaction times are of interest as well, plotting RT would be useful. So Figure 1 would contain 6 subplots, with one column for RTs and one column for shift/stay.

Reaction Time data are now also provided as a separate column in Figure 1.

14. Page 19: The first paragraph of the Discussion seems better suited for the Results section.

The first paragraph of the Discussion (3.3) has now been included in the Results section (3.2).

15. Page 23: What is 'sterr'?

Standard error.

16. Page 23: What is the dependent variable in the two-way, repeated-measures ANOVA?

The manuscript has been updated to reflect that final score is the dependent variable.

17. When participants shift, there are two different options that they can shift to. I wonder if the authors also looked at different types of shift to see if draw and loss differ.

We have previously identified the selection of an item at trial n + 1 that would have beaten the previous item at trial n (e.g., rock followed by paper), or, the selection of an item in trial n + 1 that would have been beaten by the previous item at trial n (e.g., rock followed by scissors). In the first instance, such behavior is described as an ‘ascending’, ‘right-shift’, ‘one-ahead’ or ‘upgrade’ strategy, whereas in the second instance, behavior has been described as a ‘descending’, ‘left-shift’ or ‘downgrade’ strategy (Baek et al., 2013; Stöttinger, Filipowicz, Danckert & Anderson, 2014; Wang & Xu, 2014). In terms of behavioural data, there is weak evidence that losses initiate more downgrade responses and draws initiate more upgrade responses (Dyson, Wilbiks, Sandhu, Papanicolaou & Lintag, 2016). However, a close examination of the framing of such specific ‘strategies’ is problematic in terms of the isomorphism with other- perhaps simpler- responses. The framing problem of strategy is discussed in Dyson (2019).

18. Page 25: "a win followed by a draw causes an increase in shift behaviour whereas a loss followed by a draw causes shift behaviour to decrease". This sounds like a win leads to an increase in shift behavior and a loss leads to a decrease, but I think the authors meant that the draws have such an effect.

We have now re-written this section to be clearer that the trial outcome sequence of win-draw causes an increase in shift behaviour, whereas the sequence of lose-draw causes a decrease in shift behaviour.

References

Baek, K.; Kim, Y.-T.; Kim, M.; Choi, Y.; Lee, M.; Lee, K.; Hahn, S. & Jeong, J. (2013). Response randomization of one-and two-person Rock-Paper-Scissors games in individuals with schizophrenia. Psychiatry Research. 207, 158–163.

Brysbaert, M. (2019) How many participants do we have to include in properly powered experiments? A tutorial of power analysis with reference tables. Journal of Cognition, 16, 1-38.

Damaso, K., Williams, P. & Heathcote, A. (2020). Evidence for different types of errors being associated with different types of post-error changes. Psychonomic Bulletin and Review, 27, 435–440.

Dyson, B. J., Wilbiks, J. M. P., Sandhu, R., Papanicolaou, G. & Lintag, J. (2016). Negative outcomes evoke cyclic irrational decisions in Rock, Paper, Scissors. Scientific Reports, 6: 20479.

Dyson, B. J., Sundvall, J., Forder, L. & Douglas, S. (2018). Failure generates impulsivity only when outcomes cannot be controlled. Journal of Experimental Psychology: Human Perception and Performance, 44, 1483-1487.

Dyson, B. J. (2019). Behavioural isomorphism, cognitive economy and recursive thought in non-transitive game strategy. Games, 10: 32.

Dyson, B. J., Musgrave, C. Rowe, C. & Sandhur, R. (2020). Behavioural and neural interactions between objective and subjective performance in a Matching Pennies game. International Journal of Psychophysiology, 147, 128-136.

Dyson, B. J. (2021). Variability in competitive decision-making speed and quality against exploiting and exploitable opponents. Scientific Reports, 11: 2859.

Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39, 175-191.

Kahneman, D. & Tversky, A. (1979). Prospect Theory: An analysis of decision under risk. Econometrica, 47, 263–291.

Pulford, B. D., Colman, A. M. & Loomes, G. (2018). Incentive magnitude effects in experimental games: Bigger is not necessarily better. Games, 9: 4.

Stöttinger, E.; Filipowicz, A.; Danckert, J.; Anderson, B. (2014). The effects of prior learned strategies on updating an opponent’s strategy in the Rock, Paper, Scissors game. Cognitive Science, 38, 1482–1492.

Wang, Z.; Xu, B. (2014). Incentive and stability in the Rock-Paper-Scissors game: An experimental investigation. arXiv:1407.1170.

Submitted filename: PLoS One Review_RR_v3.4.doc

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13 Jun 2022

Assessing behavioural profiles following neutral, positive and negative feedback

PONE-D-22-06419R1

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Reviewer #1: Thank you very much for your responses. My questions have been answered adequately and I don't not have any further comments. Congratulations to this interesting paper.

Reviewer #2: Thank you for the opportunity to review the revised manuscript. I appreciate the authors’ detailed and thoughtful responses, and most of my comments have been addressed very satisfactorily. I have only a few relatively minor comments left for the revised manuscript.

1. P9. The power analysis is based on the difference between draw (0)-shift and loss (-1)-shift observed in two previous studies. However, this particular comparison does not seem to be the main focus of the paper. For instance, none of the four predictions listed for Experiment 1 (on p.8-9) is about this particular comparison. Given the large number of tests, I think it would be helpful if the authors could clearly state which analyses are theoretically most relevant, and base the power consideration on the theoretically informative effects. Since the sample sizes are known, sensitivity analysis rather than a priori power analysis may be more appropriate here.

2. P5. “However, outcome frequency does not provide a complete account of post-loss slowing since post-loss slowing is intact when positive and negative outcomes are experienced to the same degree (eg., Eben et al., 2020)”. Eben et al. found post-loss speeding, rather than slowing.

3. P5. “A second metric to ascertain the subjective interpretation of draws is the flexibility of responding following outcomes.” Perhaps the authors forgot to change this sentence in the manuscript?

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25 Jun 2022

PONE-D-22-06419R1

Assessing behavioural profiles following neutral, positive and negative feedback

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