Update

Letters

Awareness, loss aversion, and post-decision wagering

Aaron Schurger1,2 and Shlomi Sher1

1 Department of Psychology, Princeton University, Princeton, NJ 08540, USA2 Center for the Study of Brain, Mind, and Behavior, Princeton University, Princeton, NJ 08540, USA

Box 1. Trial selection and awareness

In studying perceptual processing without awareness, conscious-

ness researchers design conditions in which they expect that

In their recent opinion article, Clifford et al. [1] present aninsightful critique of post-decision wagering (Persaudet al. [2]) as a means of objectively measuring awareness.As Clifford et al. point out, under the pay-off matrix ofPersaud et al., always betting high, independent ofawareness, is indeed an optimal strategy. There remains,however, the important question of why subjects wagersuboptimally in the presence of uncertainty in the firstplace. One likely reason (also independent of awareness)is loss aversion. According to prospect theory [3], humansin general have an asymmetric utility function – theprospect of losing, for example, $10 looms larger thanthe prospect of winning the same amount. We have beenusing post-decision wagering over the past severalmonths in experiments on sensory awareness. In anattempt to counter loss aversion, we tell our subjects that‘it is OK to bet high all of the time, but please avoidbetting low all of the time – try to ‘‘go for it’’ (i.e. bet high),even if you have only a vague hunch. It might help youwin more money’. In spite of this, only two out of morethan 100 subjects (to date) adopted the optimal strategy,and only after repeated testing sessions.

Because of loss aversion, subjective optima deviatesystematically from expected-value optima; the pay-offmatrix in a post-decision wagering paradigm should takethis into account. The pay-off matrix proposed by Cliffordet al. [1] encourages low bets when certainty is low. Aspointed out above, however, subjects seem to need pre-cisely the opposite sort of encouragement. Intuitively,the well-reasoned data analysis strategy proposed byClifford et al. [1] (their Figure 2) asks, ‘How well didsubjects do with the high wagers that they made?’This requires a precise estimate of the wagering hit rateand false-alarm rate, which in turn requires at least amoderate number of high wagers. With the pay-off

Table 1. Example of a pay-off matrix designed to counter loss-aversion

Although it is never advantageous to wager low, a loss-averse subject will do so

when uncertain.

Corresponding author: Schurger, A. (schurger@princeton.edu).

matrix of Clifford et al., subjects are likely to bet lowmost, if not all, of the time when certainty is low,knowing that with this strategy, although they mightnot stand to win as much, they are guaranteed a smallnet gain. We propose a pay-off matrix under which lowwagers serve mainly as a means of avoiding large losses(Table 1), so that subjects will sometimes bet high evenat low levels of signal strength, where measures ofawareness matter most.

The criterion of Clifford et al. constitutes a verificationcriterion of awareness (Box 1) because it is designed toassess the presence of awareness in the aggregate through-out a dataset. Although verificationmeasures are valuable,filtering measures are more versatile. Any filteringmeasure must satisfy the ‘coin toss’ condition (Box 1).The most promising avenue for devising such an indexusing post-decision wagering would vary probabilitiesrather than pay-offs. If subjects are given a default optionof winning a fixed sum with a probability (P) of 0.5 but canoverride the default to choose an alternative gamble inwhich the same sum is won with a P � 0.5, we expect thefollowing: because of well-documented default biases [4],subjects might tend to choose the default when P for thealternative gamble is also 0.5 – but they are likely alwaysto override the default when P is even slightly above 0.5.Building on this idea, one could simply replace the alterna-tive (nondefault) gamble with an opportunity to bet onone’s own judgment. If subjects sometimes choose thedefault, such trials might plausibly be regarded as sub-jective equivalents of a coin toss. Although the psychologi-

subjects will often or always be unaware of the stimuli. Absence

of awareness can be assessed in one of two ways. (i) The

researchers can confirm this on the ensuing dataset with a

‘verification criterion’ – a condition for a preselected dataset that,

if satisfied, enables us to infer that awareness was absent in the

aggregate throughout the dataset. (ii) Researchers can devise a

‘consciousness sieve’, some criterion that only lets trials without

awareness pass through. Such a ‘filtering criterion’ enables the

researcher to post-select a special subset of trials on which further

analysis of possible perception-without-awareness can be con-

ducted. Any adequate filtering criterion of awareness using post-

response wagering should satisfy the following ‘coin toss’ condi-

tion: when the subject regards her judgment as the subjective

equivalent of a coin toss, she will sometimes choose wager A; but

when she regards her judgment as anything better than the

subjective equivalent of a coin toss, she will always choose wager

B. The selection of wager A then becomes a plausible sufficient

condition for the absence of any awareness on a trial.

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Update Trends in Cognitive Sciences Vol.12 No.6

cal validity of this method would need to be tested exper-imentally, it skirts the problem of loss aversion and has thepotential to meet the coin toss condition for an adequatefiltering criterion.

References1 Clifford, C.W.G. et al. (2008) Getting technical about awareness. Trends

Cogn. Sci. 12, 54–58

Corresponding author: Clifford, C.W.G. (colinc@psych.usyd.edu.au).

210

2 Persaud, N. et al. (2007) Post-decision wagering objectively measuresawareness. Nat. Neurosci. 10, 257–261

3 Kahneman, D. and Tversky, A. (1979) Prospect theory - analysis ofdecision under risk. Econometrica 47, 263–291

4 Johnson, E.J. and Goldstein, D. (2003) Do defaults save lives? Science302, 1338–1339

1364-6613/$ – see front matter � 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tics.2008.02.012 Available online 14 May 2008

Letters Response

A good bet to measure awareness?

Colin W.G. Clifford, Ehsan Arabzadeh and Justin A. Harris

School of Psychology, The University of Sydney, Sydney, NSW 2006, Australia

Persaud et al. [1] proposed that post-decision wagering canbe used to measure awareness objectively. However, therelationship between wagering and awareness is far fromdirect because post-decision wagering reflects not onlyawareness of the sensory evidence, but also the wageringstrategy of the subject. In an effort to disambiguate theeffects of strategy and awareness, we showed how the pay-off matrix for post-decision wagering could be designed toreward a particular strategy [2]. In their response, Schur-ger and Sher [3] pointed out that the subjective pay-off of awager can differ markedly from its objective value. Theyrefer in particular to the well-known phenomenon of lossaversion, whereby people typically exhibit greater sensi-tivity to losses than to equivalent gains when makingdecisions. Given that subjects differ in the degree to whichthey demonstrate loss aversion [4], a possible method forachieving the desired ratio of high to low wagers would beto determine the pay-off matrix adaptively for each subject.Consider, for example, the pay-off matrix designed bySchurger and Sher [3] to counter loss aversion. If a subjectwas making predominantly low wagers with this pay-offmatrix (i.e. still showing loss aversion), then the penalty fora low wager following an incorrect decision could beincreased. If, instead, a subject made exclusively highwagers (i.e. showed no loss aversion), then they could beencouraged to bet low by decreasing the penalty for a lowwager below the size of the corresponding reward (as inClifford et al. [2], Table 3). In this way, individual subjectscould be encouraged to make approximately equal num-bers of high and low wagers.

Schurger and Sher [3] also propose an alternative meansto counter loss aversion by fixing the amount to be wageredand thus the magnitude of any potential loss. Instead ofwagering low or high on the correctness of the precedingperceptual decision, the subject wagers a fixed amounteither on a 50–50 default option or on the correctness oftheir decision. Assuming that the perceptual decision is

never worse than a guess, the best strategy of theobserver for maximizing their expected gain is to wageralways on the correctness of their decision, regardless of theweight of the sensory evidence. Schurger and Sher [3]suggest that subjects might exhibit a default bias to wageron the 50–50 option when they feel that their perceptualdecision was no more than a guess, such that the choice towager on the 50–50 default option potentially constitutes asufficient condition for the absence of any awareness on atrial.Nonetheless, given that there is no gain inwagering onthe 50–50 default option rather than wagering on thedecision, oneneeds to be cautious in interpreting the reason-ing behind the choice of a subject. For example, they mightbe less averse to losing money on the ‘unlucky’ outcome of acoin toss than on the basis of their own wrong decision. Inthis case, the choice to wager on the 50–50 default optionwould not be sufficient grounds for inferring absence ofawareness. Thus, it remains an empirical question whetherthere is any advantage to trading loss aversion for defaultbias. To establish the answer requires that the data areanalyzed in away that distinguishes a suboptimalwageringstrategy from a genuine lack of awareness, such as theapplication of signal detection theory that we describedpreviously [2].

References1 Persaud, N. et al. (2007) Post-decision wagering objectively measures

awareness. Nat. Neurosci. 10, 257–2612 Clifford, C.W.G. et al. (2008) Getting technical about awareness. Trends

Cogn. Sci. 12, 54–583 Schurger, A. and Sher, S. (2008) Awareness, loss aversion, and post-

decision wagering. Trends Cogn. Sci. 12, 209–2104 Tom, S.M. et al. (2007) The neural basis of loss aversion in decision-

making under risk. Science 315, 515–518

1364-6613/$ – see front matter � 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tics.2008.02.011 Available online 24 April 2008