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A temporal basis for Weber's law in value perception.

Namboodiri VM, Mihalas S, Hussain Shuler MG - Front Integr Neurosci (2014)

Bottom Line: We show that the precision of reward magnitude perception is correlated with the precision of time perception and that Weber's law in time estimation can lead to Weber's law in value perception.The strength of this correlation is predicted to depend on the reward history of the animal.Subsequently, we show that sensory integration noise (either alone or in combination with time estimation noise) also leads to Weber's law in reward magnitude perception in an accumulator model, if it has balanced Poisson feedback.

View Article: PubMed Central - PubMed

Affiliation: Department of Neuroscience, Johns Hopkins University Baltimore, MD, USA.

ABSTRACT
Weber's law-the observation that the ability to perceive changes in magnitudes of stimuli is proportional to the magnitude-is a widely observed psychophysical phenomenon. It is also believed to underlie the perception of reward magnitudes and the passage of time. Since many ecological theories state that animals attempt to maximize reward rates, errors in the perception of reward magnitudes and delays must affect decision-making. Using an ecological theory of decision-making (TIMERR), we analyze the effect of multiple sources of noise (sensory noise, time estimation noise, and integration noise) on reward magnitude and subjective value perception. We show that the precision of reward magnitude perception is correlated with the precision of time perception and that Weber's law in time estimation can lead to Weber's law in value perception. The strength of this correlation is predicted to depend on the reward history of the animal. Subsequently, we show that sensory integration noise (either alone or in combination with time estimation noise) also leads to Weber's law in reward magnitude perception in an accumulator model, if it has balanced Poisson feedback. We then demonstrate that the noise in subjective value of a delayed reward, due to the combined effect of noise in both the perception of reward magnitude and delay, also abides by Weber's law. Thus, in our theory we prove analytically that the perception of reward magnitude, time, and subjective value change all approximately obey Weber's law.

No MeSH data available.


Related in: MedlinePlus

Errors in measurement of the delay to a future reward results in a corresponding error in subjective value. If the delay to the reward is perceived as earlier by the just-noticeable difference (JND), the subjective value is perceived as being larger. This error in subjective value is shown in the red bar and is calculated analytically in Section Contribution of time measurement error to the error in subjective value.
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Figure 2: Errors in measurement of the delay to a future reward results in a corresponding error in subjective value. If the delay to the reward is perceived as earlier by the just-noticeable difference (JND), the subjective value is perceived as being larger. This error in subjective value is shown in the red bar and is calculated analytically in Section Contribution of time measurement error to the error in subjective value.

Mentions: From this relation, we can now calculate the error in subjective value of a delayed reward resulting from an error in the representation of subjective time (Figure 2). To this end, let us denote that the just-noticeable-difference (JND) in the subjective representation ST(t) of the delay t by δST(t), and that the error in the corresponding subjective value is denoted by δSV(r, t). For the purpose of this section, we assume that the measurement of the reward magnitude is noiseless. Then, as the subjective representation of the delay t increases by its JND, the subjective value will increase by the corresponding error. This can be expressed mathematically as:


A temporal basis for Weber's law in value perception.

Namboodiri VM, Mihalas S, Hussain Shuler MG - Front Integr Neurosci (2014)

Errors in measurement of the delay to a future reward results in a corresponding error in subjective value. If the delay to the reward is perceived as earlier by the just-noticeable difference (JND), the subjective value is perceived as being larger. This error in subjective value is shown in the red bar and is calculated analytically in Section Contribution of time measurement error to the error in subjective value.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4196632&req=5

Figure 2: Errors in measurement of the delay to a future reward results in a corresponding error in subjective value. If the delay to the reward is perceived as earlier by the just-noticeable difference (JND), the subjective value is perceived as being larger. This error in subjective value is shown in the red bar and is calculated analytically in Section Contribution of time measurement error to the error in subjective value.
Mentions: From this relation, we can now calculate the error in subjective value of a delayed reward resulting from an error in the representation of subjective time (Figure 2). To this end, let us denote that the just-noticeable-difference (JND) in the subjective representation ST(t) of the delay t by δST(t), and that the error in the corresponding subjective value is denoted by δSV(r, t). For the purpose of this section, we assume that the measurement of the reward magnitude is noiseless. Then, as the subjective representation of the delay t increases by its JND, the subjective value will increase by the corresponding error. This can be expressed mathematically as:

Bottom Line: We show that the precision of reward magnitude perception is correlated with the precision of time perception and that Weber's law in time estimation can lead to Weber's law in value perception.The strength of this correlation is predicted to depend on the reward history of the animal.Subsequently, we show that sensory integration noise (either alone or in combination with time estimation noise) also leads to Weber's law in reward magnitude perception in an accumulator model, if it has balanced Poisson feedback.

View Article: PubMed Central - PubMed

Affiliation: Department of Neuroscience, Johns Hopkins University Baltimore, MD, USA.

ABSTRACT
Weber's law-the observation that the ability to perceive changes in magnitudes of stimuli is proportional to the magnitude-is a widely observed psychophysical phenomenon. It is also believed to underlie the perception of reward magnitudes and the passage of time. Since many ecological theories state that animals attempt to maximize reward rates, errors in the perception of reward magnitudes and delays must affect decision-making. Using an ecological theory of decision-making (TIMERR), we analyze the effect of multiple sources of noise (sensory noise, time estimation noise, and integration noise) on reward magnitude and subjective value perception. We show that the precision of reward magnitude perception is correlated with the precision of time perception and that Weber's law in time estimation can lead to Weber's law in value perception. The strength of this correlation is predicted to depend on the reward history of the animal. Subsequently, we show that sensory integration noise (either alone or in combination with time estimation noise) also leads to Weber's law in reward magnitude perception in an accumulator model, if it has balanced Poisson feedback. We then demonstrate that the noise in subjective value of a delayed reward, due to the combined effect of noise in both the perception of reward magnitude and delay, also abides by Weber's law. Thus, in our theory we prove analytically that the perception of reward magnitude, time, and subjective value change all approximately obey Weber's law.

No MeSH data available.


Related in: MedlinePlus