Out of Sight, Out of Mind:Visual Attention and Loss Aversion

Alejandro Hirmas & Jan EngelmannUniversity of Amsterdama.hirmas@uva.nl

Objectives

• Can attentional biases for gains versus losses describe choicesof subjects?

• Does relative fixation duration correlate with Loss-Aversion(λ)?

• Is it possible to obtain additional information from the Confi-dence Levels and Reaction Times?

Introduction

• Expected Utility Theory (EU) has been the predominantmodel to describe risk-taking behavior.

• It does not describe the psychological process, but the predic-tions are good for the average behavior [2].

• Cumulative Prospect Theory [CPT; 6] advanced in describingbetter the psychological process.

• EU and CPT allow for individual differences between sub-jects, not within.

• There is strong evidence that attention might affect the de-cision process and potentially explain individual differences[3, 4, 1, 5]

Experimental Task

Initially, a white cross is shown for fixation for a random duration, jittered between 300msand 1100ms. The prospect is then presented. The decision had to be made by pressing theup or down keys of the keyboard to accept or reject respectively. A feedback of the decisioncame after one second. In experiment 2, the trial continued with a question of how confidentthe subject is with their decision.

Data

• 160 Trials with randomly ordered Gambles, varying in Lossesand Gains

• Fixation times on each attribute collected by EyeLink 1000 at500Hz.

• Data calibrated every 80 trials. Individuals deviations cor-rected by k-mean clustering.

• Attention in an attribute is defined as the proportion of timelooking at that object.

• We measure attention to Losses (AL) and Gains (AG) as theproportion of time spent on that attribute.

Figure 1: Example of fixation centering

050

010

00Ve

rtica

l Pos

ition

0 470 900 1400 1980Horizontal Position

050

010

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rtica

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0 470 900 1400 1980cx

The fixations of each subject where clustered into three groups by k-means. The means ofeach group were centered to the original positions.

Table 1: Summary description of relevant Variables

Variable Mean St. Dev. Min Max Accept RT Conf. Gain Loss At. Loss At. Gain L. LeftAccept 0.410 0.49 0 1 1Reaction Time 1.379 0.72 0.03 5.0 0.009 1Confidence 5.010 1.37 1 7 -0.106 -0.367 1Gain 29 5.74 20 38 0.394 0.047 -0.090 1Loss 20 4.58 13 27 -0.388 -0.012 0.076 0.000 1Attention Loss 0.301 0.15 0 1 -0.090 0.048 0.051 -0.010 0.070 1Attention Gain 0.320 0.16 0 0.9 0.117 0.132 -0.065 0.035 -0.053 -0.300 1Loss Left 0.475 0.50 0 1 -0.027 0.012 -0.013 0.000 0.005 -0.208 0.214 1

Figure 2: Pr(Accept) by Attribute and Attention

20 22 24 26 28 30 32 34 36 38

Gain

1

2

3

4

AttG

Mean of Dec

0.5538

0.559

0.5358

0.5487

0.617

0.5091

0.5508

0.5628

0.6971

0.5566

0.626

0.6293

0.7101

0.5894

0.6517

0.728

0.7752

0.1104

0.1123

0.1373

0.1327

0.1313

0.1556

0.1468

0.1718

0.1754

0.1924

0.2235

0.2536

0.2951

0.2176

0.3173

0.3483

0.3377

0.3398

0.4144

0.4397

0.4146

0.4519

0.4524

0.2

0.3

0.4

0.5

0.6

0.7

Theoretical Model• We exploit one specification for the three behavioral vari-

ables.• We use a Logit model for the choice.• RT is estimated with a Weibull duration model.• We use a linear regression approach for the Confidence• The three models use fixed effects.• The models for RT and confidence depend on the choice• We assume the weights of gains and losses depend on the time

spend at each region of interest (Center, Gains and Losses).

Pr(Accept) = (1 + exp(−SV (βD)))−1

S(RT ) = exp[− exp(−SV (βRT ))RT p

]E(Confidence) = SV (βC)

ResultsTable 2: Estimations of the Subjective Valuation for the different variables

Choice RT (Accept) RT (Reject) Conf. (Accept) Conf. (Accept)wC(Losses) -0.288∗∗∗ -0.030 0.009 -0.074∗∗∗ 0.077∗∗∗

(0.056) (0.019) (0.017) (0.024) (0.019)wL(Losses) -0.556∗∗∗ -0.073∗∗ 0.058∗∗∗ -0.224∗∗∗ 0.102∗∗∗

(0.056) (0.030) (0.021) (0.044) (0.021)wG(Losses) -0.517∗∗∗ -0.068∗∗∗ 0.068∗∗∗ -0.157∗∗∗ 0.142∗∗∗

(0.070) (0.023) (0.021) (0.029) (0.023)wC(Gains) 0.263∗∗∗ 0.065∗∗∗ -0.016 0.089∗∗∗ -0.032∗

(0.053) (0.014) (0.014) (0.015) (0.018)wL(Gains) 0.385∗∗∗ 0.062∗∗ -0.039∗∗ 0.132∗∗∗ -0.111∗∗∗

(0.044) (0.024) (0.017) (0.029) (0.020)wG(Gains) 0.452∗∗∗ 0.019 -0.083∗∗∗ 0.082∗∗∗ -0.115∗∗∗

(0.050) (0.022) (0.016) (0.021) (0.023)AL 1.058 -0.291 -2.182∗∗ 0.756 1.458∗

(1.914) (1.042) (0.858) (1.363) (0.794)AG 0.222 0.386 -1.494∗∗ 1.381 0.158

(1.641) (0.942) (0.639) (0.954) (0.783)Observations 14158 5765 8553 3195 4965AIC 8189.078 4524.521 8093.838 9077.896 14428.904BIC 8272.216 4604.436 8178.487 9144.658 14500.516Standard errors in parentheses∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Figure 3: Weights of Gains and Losses

(a) Gains (b) Losses

.26

.39

.45

.065

.062 .019

.089

.13 .082

-.032 -.11

-.12

-.016

-.039 -.083

-.20

.2.4

.6W

eigh

t of G

ains

Center Losses Gains

Decision RT(Accept)Conf.(Accept) Conf.(Reject)RT(Reject)

-.29

-.56

-.52

-.03 -.073

-.068

-.074

-.22

-.16

.077

.1

.14

.0089

.058

.068

-.6-.4

-.20

.2W

eigh

t of L

osse

s

Center Losses Gains

Decision RT(Accept)Conf.(Accept) Conf.(Reject)RT(Reject)

The Figure presents the weights assigned to the Gains (a) and Losses (b) when attending tothe three regions of interest. The parameters presented correspond to the five estimations ofTable 2 . Note: The subjective value has an opposite effect on the models when the gamblewas rejected, thus those parameters have opposite signs.

Figure 4: Loss Aversion

11.

21.

41.

6Lo

ss A

vers

ion

( λ )

0 0.1 0.2 0.3 0.4 0.5 0.6Relative Attention to Losses

Figure 4 shows the estimations for the Loss-Aversion parameter in the decisionmodel. The Loss-Aversion is defined as the weight of Losses relative to Gains, λ =−w(Losses)/w(Gains). The Figure shows the Loss aversion, when the dwelling time onthe center is the average (0.38 of RT) and there is a complete replacement between the fixa-tion on Losses to Gains (i.e. if the subject fixates one porcent less on gains and one more onlosses, what is the effect on the Loss Aversion).

Figure 5: Effect of AttentionChoice

0.2

.4.6

.8Pr

(Acc

ept)

0 .1 .2 .3 .4 .5 .6Relative Attention (Gains)

Gains = 20 Gains = 38

0.2

.4.6

.8Pr

(Acc

ept)

0 .1 .2 .3 .4 .5 .6Relative Attention (Losses)

Losses = 13 Losses = 27

RT (Accept)

11.

52

Rea

ctio

n Ti

me

0 .1 .2 .3 .4 .5 .6Relative Attention (Gains)

Gains = 20 Gains = 38

11.

52

2.5

Rea

ctio

n Ti

me

0 .1 .2 .3 .4 .5 .6Relative Attention (Losses)

Losses = 13 Losses = 27

RT (Reject)

11.

52

2.5

Rea

ctio

n Ti

me

0 .1 .2 .3 .4 .5 .6Relative Attention (Gains)

Gains = 20 Gains = 38

11.

52

2.5

Rea

ctio

n Ti

me

0 .1 .2 .3 .4 .5 .6Relative Attention (Losses)

Losses = 13 Losses = 27

Confidence (Accept)

34

56

Pr(A

ccep

t)

0 .1 .2 .3 .4 .5 .6Relative Attention (Gains)

Gains = 20 Gains = 38

23

45

6Pr

(Acc

ept)

0 .1 .2 .3 .4 .5 .6Relative Attention (Losses)

Losses = 13 Losses = 27

Confidence (Reject)

3.5

44.

55

5.5

6Pr

(Acc

ept)

0 .1 .2 .3 .4 .5 .6Relative Attention (Gains)

Gains = 20 Gains = 38

44.

55

5.5

6Pr

(Acc

ept)

0 .1 .2 .3 .4 .5 .6Relative Attention (Losses)

Losses = 13 Losses = 27

Figure 5 shows the effect of Attention of both Gains and Losses when the outcome is at the max-imum and minimum. Each figure shows the conditional expectation of the behavioral variable onthe vertical axis, while the horizontal axis shows the respective attention measure.

Conclusions

• Attention is strongly correlated with the decision process.

• RT and Confidence are correlated with the decision process.

• When the attention is too focalized (much attention to one at-tribute), the reaction times are longer. This effect is strongerif the fixated attribute is larger.

• Attention seems to be correlated with the weight of the nega-tive outcome when assessing confidence levels.

References

[1] Kelvin Balcombe, Iain Fraser, and Eugene McSorley. Visualattention and attribute attendance in multi-attribute choiceexperiments. Journal of Applied Econometrics, 30(3):447–467, 2015.

[2] Milton Friedman and Leonard J Savage. The utility analy-sis of choices involving risk. Journal of Political Economy,56(4):279–304, 1948.

[3] Ian Krajbich, Carrie Armel, and Antonio Rangel. Visual fixa-tions and the computation and comparison of value in simplechoice. Nature Neuroscience, 13(10):1292, 2010.

[4] Ian Krajbich, Dingchao Lu, Colin Camerer, and AntonioRangel. The attentional drift-diffusion model extends to sim-ple purchasing decisions. Frontiers in Psychology, 3:193,2012.

[5] Thorsten Pachur, Michael Schulte-Mecklenbeck, Ryan OMurphy, and Ralph Hertwig. Prospect theory reflects selec-tive allocation of attention. Journal of Experimental Psychol-ogy: General, 147(2):147, 2018.

[6] Amos Tversky and Daniel Kahneman. Advances in prospecttheory: Cumulative representation of uncertainty. Journal ofRisk and uncertainty, 5(4):297–323, 1992.