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Choice mechanisms for past, temporally extended outcomes.

Vestergaard MD, Schultz W - Proc. Biol. Sci. (2015)

Bottom Line: A biologically plausible mechanism underlying evaluation of temporally extended outcomes is leaky integration of evidence.The disadvantageous inclination towards persistent growth was mitigated in some individuals in whom a longer time constant of the leaky integrator resulted in fewer violations of dominance.These results demonstrate how focusing on immediate gains is less beneficial than considering longer perspectives.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, Development and Neuroscience, University of Cambridge, Cambridge CB2 3DY, UK mdv23@cam.ac.uk.

ABSTRACT
Accurate retrospection is critical in many decision scenarios ranging from investment banking to hedonic psychology. A notoriously difficult case is to integrate previously perceived values over the duration of an experience. Failure in retrospective evaluation leads to suboptimal outcome when previous experiences are under consideration for revisit. A biologically plausible mechanism underlying evaluation of temporally extended outcomes is leaky integration of evidence. The leaky integrator favours positive temporal contrasts, in turn leading to undue emphasis on recency. To investigate choice mechanisms underlying suboptimal outcome based on retrospective evaluation, we used computational and behavioural techniques to model choice between perceived extended outcomes with different temporal profiles. Second-price auctions served to establish the perceived values of virtual coins offered sequentially to humans in a rapid monetary gambling task. Results show that lesser-valued options involving successive growth were systematically preferred to better options with declining temporal profiles. The disadvantageous inclination towards persistent growth was mitigated in some individuals in whom a longer time constant of the leaky integrator resulted in fewer violations of dominance. These results demonstrate how focusing on immediate gains is less beneficial than considering longer perspectives.

No MeSH data available.


Related in: MedlinePlus

Stochastic value coding by suboptimal integration predicts choice of dominated options. Simulations (n = 15 000) in (b,d,e). (a) The state (En) of each option is sequentially observed under sampling noise (ɛS). The value function encodes state estimate (En + ɛS) as perceived value (xn). Incentive value (yn) is accumulated by suboptimal integration of the perceived values with decay parameter τ =−1/log(1−a). Choice is mediated under noisy discrimination of the evidence εA = log (yA/yB). The decision noise components  and  predict decision bias (β) and sensitivity (B) of the agent, β = μA − μB and  where C is a scaling constant for aligning the logistic and normal distributions. Thus, there are two free parameters, β and B, derived from the decision noises. (b) Decreasing and increasing temporal profiles characterizing two options with identical contents (i) but with differential cumulative incentive for τ = 21s (ii), expected value of evidence, EV(εA) = 0.08. The grey areas show two-sigma bounds of the sampling noise for signal-to-noise ratios, SNR ∈ {0, 4, 8 dB}. (c) Difference in expected incentive relative to linear integration for a range of value function exponents (κ) and integration decays (τ). (d) Psychometric functions (grey) and simulations relating evidence for the increasing profile to choice probability for three parametric implementations (I, II, III). EV(εA) and indifference points for evidence are indicated by dashed and dotted vertical lines, respectively. Average preference (±s.e.m.) shown in five bins equally distributed around EV(εA). (e) The effect of SNR and integration decay for a fixed value function (κ = 0.67), predictions (grey lines, based on EV(εA) without decision noise) and simulated choice data (average ±s.e.m., incl. decision noise). The grey curves approach the asymptotes determined by the leaky integrator for low τ (i) and for high SNR (ii).
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RSPB20141766F2: Stochastic value coding by suboptimal integration predicts choice of dominated options. Simulations (n = 15 000) in (b,d,e). (a) The state (En) of each option is sequentially observed under sampling noise (ɛS). The value function encodes state estimate (En + ɛS) as perceived value (xn). Incentive value (yn) is accumulated by suboptimal integration of the perceived values with decay parameter τ =−1/log(1−a). Choice is mediated under noisy discrimination of the evidence εA = log (yA/yB). The decision noise components and predict decision bias (β) and sensitivity (B) of the agent, β = μA − μB and where C is a scaling constant for aligning the logistic and normal distributions. Thus, there are two free parameters, β and B, derived from the decision noises. (b) Decreasing and increasing temporal profiles characterizing two options with identical contents (i) but with differential cumulative incentive for τ = 21s (ii), expected value of evidence, EV(εA) = 0.08. The grey areas show two-sigma bounds of the sampling noise for signal-to-noise ratios, SNR ∈ {0, 4, 8 dB}. (c) Difference in expected incentive relative to linear integration for a range of value function exponents (κ) and integration decays (τ). (d) Psychometric functions (grey) and simulations relating evidence for the increasing profile to choice probability for three parametric implementations (I, II, III). EV(εA) and indifference points for evidence are indicated by dashed and dotted vertical lines, respectively. Average preference (±s.e.m.) shown in five bins equally distributed around EV(εA). (e) The effect of SNR and integration decay for a fixed value function (κ = 0.67), predictions (grey lines, based on EV(εA) without decision noise) and simulated choice data (average ±s.e.m., incl. decision noise). The grey curves approach the asymptotes determined by the leaky integrator for low τ (i) and for high SNR (ii).

Mentions: We consider the mechanism in the discrete domain (figure 2a). The contents of each option are sequentially observed under sampling noise, and a value function encodes the observed stimuli as perceived values (xn). Meanwhile, the incentive values (yn) are accumulated suboptimally by leaky integration of the perceived values, and subsequent choice is mediated under noisy discrimination of the final evidence εA = log (yA/yB).Figure 2.


Choice mechanisms for past, temporally extended outcomes.

Vestergaard MD, Schultz W - Proc. Biol. Sci. (2015)

Stochastic value coding by suboptimal integration predicts choice of dominated options. Simulations (n = 15 000) in (b,d,e). (a) The state (En) of each option is sequentially observed under sampling noise (ɛS). The value function encodes state estimate (En + ɛS) as perceived value (xn). Incentive value (yn) is accumulated by suboptimal integration of the perceived values with decay parameter τ =−1/log(1−a). Choice is mediated under noisy discrimination of the evidence εA = log (yA/yB). The decision noise components  and  predict decision bias (β) and sensitivity (B) of the agent, β = μA − μB and  where C is a scaling constant for aligning the logistic and normal distributions. Thus, there are two free parameters, β and B, derived from the decision noises. (b) Decreasing and increasing temporal profiles characterizing two options with identical contents (i) but with differential cumulative incentive for τ = 21s (ii), expected value of evidence, EV(εA) = 0.08. The grey areas show two-sigma bounds of the sampling noise for signal-to-noise ratios, SNR ∈ {0, 4, 8 dB}. (c) Difference in expected incentive relative to linear integration for a range of value function exponents (κ) and integration decays (τ). (d) Psychometric functions (grey) and simulations relating evidence for the increasing profile to choice probability for three parametric implementations (I, II, III). EV(εA) and indifference points for evidence are indicated by dashed and dotted vertical lines, respectively. Average preference (±s.e.m.) shown in five bins equally distributed around EV(εA). (e) The effect of SNR and integration decay for a fixed value function (κ = 0.67), predictions (grey lines, based on EV(εA) without decision noise) and simulated choice data (average ±s.e.m., incl. decision noise). The grey curves approach the asymptotes determined by the leaky integrator for low τ (i) and for high SNR (ii).
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RSPB20141766F2: Stochastic value coding by suboptimal integration predicts choice of dominated options. Simulations (n = 15 000) in (b,d,e). (a) The state (En) of each option is sequentially observed under sampling noise (ɛS). The value function encodes state estimate (En + ɛS) as perceived value (xn). Incentive value (yn) is accumulated by suboptimal integration of the perceived values with decay parameter τ =−1/log(1−a). Choice is mediated under noisy discrimination of the evidence εA = log (yA/yB). The decision noise components and predict decision bias (β) and sensitivity (B) of the agent, β = μA − μB and where C is a scaling constant for aligning the logistic and normal distributions. Thus, there are two free parameters, β and B, derived from the decision noises. (b) Decreasing and increasing temporal profiles characterizing two options with identical contents (i) but with differential cumulative incentive for τ = 21s (ii), expected value of evidence, EV(εA) = 0.08. The grey areas show two-sigma bounds of the sampling noise for signal-to-noise ratios, SNR ∈ {0, 4, 8 dB}. (c) Difference in expected incentive relative to linear integration for a range of value function exponents (κ) and integration decays (τ). (d) Psychometric functions (grey) and simulations relating evidence for the increasing profile to choice probability for three parametric implementations (I, II, III). EV(εA) and indifference points for evidence are indicated by dashed and dotted vertical lines, respectively. Average preference (±s.e.m.) shown in five bins equally distributed around EV(εA). (e) The effect of SNR and integration decay for a fixed value function (κ = 0.67), predictions (grey lines, based on EV(εA) without decision noise) and simulated choice data (average ±s.e.m., incl. decision noise). The grey curves approach the asymptotes determined by the leaky integrator for low τ (i) and for high SNR (ii).
Mentions: We consider the mechanism in the discrete domain (figure 2a). The contents of each option are sequentially observed under sampling noise, and a value function encodes the observed stimuli as perceived values (xn). Meanwhile, the incentive values (yn) are accumulated suboptimally by leaky integration of the perceived values, and subsequent choice is mediated under noisy discrimination of the final evidence εA = log (yA/yB).Figure 2.

Bottom Line: A biologically plausible mechanism underlying evaluation of temporally extended outcomes is leaky integration of evidence.The disadvantageous inclination towards persistent growth was mitigated in some individuals in whom a longer time constant of the leaky integrator resulted in fewer violations of dominance.These results demonstrate how focusing on immediate gains is less beneficial than considering longer perspectives.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, Development and Neuroscience, University of Cambridge, Cambridge CB2 3DY, UK mdv23@cam.ac.uk.

ABSTRACT
Accurate retrospection is critical in many decision scenarios ranging from investment banking to hedonic psychology. A notoriously difficult case is to integrate previously perceived values over the duration of an experience. Failure in retrospective evaluation leads to suboptimal outcome when previous experiences are under consideration for revisit. A biologically plausible mechanism underlying evaluation of temporally extended outcomes is leaky integration of evidence. The leaky integrator favours positive temporal contrasts, in turn leading to undue emphasis on recency. To investigate choice mechanisms underlying suboptimal outcome based on retrospective evaluation, we used computational and behavioural techniques to model choice between perceived extended outcomes with different temporal profiles. Second-price auctions served to establish the perceived values of virtual coins offered sequentially to humans in a rapid monetary gambling task. Results show that lesser-valued options involving successive growth were systematically preferred to better options with declining temporal profiles. The disadvantageous inclination towards persistent growth was mitigated in some individuals in whom a longer time constant of the leaky integrator resulted in fewer violations of dominance. These results demonstrate how focusing on immediate gains is less beneficial than considering longer perspectives.

No MeSH data available.


Related in: MedlinePlus