`@decidables/prospectable-elements`
Web Components for Visualizing Cumulative Prospect Theory in prospectαbλe

The web components used to visualize Cumulative Prospect Theory in prospectαbλe. There is an emphasis on direct manipulation and consistent use of color. SVG is used extensively to provide clean scalable diagrams.

Usage

Install

yarn add @decidables/prospectable-elements

Use

import '@decidables/prospectable-elements';

A bare import is used to register the elements in the custom registry, so they are then available for use in HTML.

Components

Building blocks for interactive visualizations of CPT

`CPTCalculation` / `<cpt-calculation>`

Calculation and comparison of subjective utility for gamble and sure options

Displays a live comparison of the subjective utilities for gamble and sure options, indicating which one is better, or if they are equal. Breaks the calculation down into multiple steps. Leverages the concepts from live equations to explicitly link objective value/probability to subjective value/decision weight to subjective utility.

Attributes

numeric: boolean = false
- Show values instead of just the names of variables
interactive: boolean = false
- Allow editing of numeric values
win: number = 100
- Winning value in gamble
loss: number = 0
- Losing value in gamble
probability: number = 0.75
- Probability of winning
sure: number = 50
- Sure value
alpha: number = 0.8
- Parameter α (diminishing marginal utility)
lambda: number = 1.2
- Parameter λ (loss aversion)
gamma: number = 0.8
- Parameter γ (probability distortion)

Custom Events

cpt-calculation-change
- Indicates that the values in the calculation have changed
- detail
  - xl: number
    - New losing value for gamble
  - xw: number
    - New winning value for gamble
  - pw: number
    - New probability of winning gamble
  - xs: number
    - New sure value
  - a: number
    - New value for parameter α (diminishing marginal utility)
  - l: number
    - New value for parameter λ (loss aversion)
  - g: number
    - New value for parameter γ (probability distortion)

Example

<cpt-calculation numeric interactive win="100" loss="0" probability="0.75" sure="50" alpha="0.8" lambda="1.2" gamma="0.8"></cpt-calculation>

`CPTFit` / `<cpt-fit>`

Fits CPT parameters to empirical data using a Bayesian model running in a WebWorker

The component displays trace plots of the sampling and histograms of the posterior distributions for the alpha, lambda, gamma, and luce parameters. The model consists of the following:

Parameters
- alpha: beta prior with mean of 0.5 and sample size of 2.5
- lambda: gamma prior with mean of 2.0 and shape of 3.0
- gamma: beta prior with mean of 0.5 and sample size of 2.5
- luce: gamma prior with mean of 2 and shape of 3
Data (for ith trial)
- xw_i: gamble winning value
- xl_i: gamble losing value
- pw_i: gamble winning probability
- xs_i: sure value
- response_i: 'gamble' or 'sure'
Functions
- v(): subjective value
  - v = if (x >= 0) x^a; if (x < 0) -l * (-x)^a
- w(): decision weight
  - w = p^g / (p^g + (1 - p)^g)^(1 / g)
- u(): utility
  - u = Sum_n(v_n * w_n)
- choice(): Luce choice probability
  - cg = 1 / (1 + e^(luce * (us - ug)))
Model
- ug_i: subjective utility of the ith gamble
  - ug_i = u([v(xw_i, alpha, lambda), v(xl_i, alpha, lambda)], [w(pw_i, gamma), 1 - w(pw_i, gamma)])
- us_i: subjective utility of the ith sure thing
  - us_i = v(xs_i, alpha, lambda)
- cg_i: probability of choosing the ith gamble
  - cg_i = choice(us_i, ug_i, luce)
- choice_i: Bernoulli distribution given response_i and cg_i

Methods

fit()
- Initiates a new fit, or queues one if the model is already fitting
clear()
- Removes all choice data, and initiates a data-free initial fit
get(name = 'default')
- Gets the specified choice data
- Parameters
  - name: string = 'default'
    - Identifier for the choice data
- Return value
  - choice: object or null
    - xl: number
      - Gamble losing value
    - xw: number
      - Gamble winning value
    - pw: number
      - Gamble winning probability
    - xs: number
      - Sure value
    - response: string
      - Chosen option, either 'gamble' or 'sure'
    - name: string
      - Identifier for choice
    - label: string
      - Label for choice
set(xl, xw, pw, xs, response, name = '', label = '')
- Creates or changes the specified choice data
- Parameters
  - xl: number
    - Gamble losing value
  - xw: number
    - Gamble winning value
  - pw: number
    - Gamble winning probability
  - xs: number
    - Sure value
  - response: string
    - Chosen option, either 'gamble' or 'sure'
  - name: string
    - Identifier for choice
  - label: string
    - Label for choice

Custom Events

cpt-fit-update
- Indicates that the fit has completed
- detail
  - a: number
    - New value for parameter α (diminishing marginal utility)
  - l: number
    - New value for parameter λ (loss aversion)
  - g: number
    - New value for parameter γ (probability distortion)

Example

<cpt-fit></cpt-fit>

`CPTProbability` / `<cpt-probability>`

Decision weight function for CPT

Maps from objective probability to subjective decision weight. Functions themselves and data points on the functions can be directly manipulated.

Attributes

interactive: boolean = false
- Allow direct manipulation of functions or data points
probability: number = null
- Probability
gamma: number = 0.5
- Parameter γ (probability distortion)
label: string = ''
- Label for data point

Methods

trial(xl, xw, pw, xs, trial, response)
- Creates or changes the specified trial data
- Parameters
  - xl: number
    - Gamble losing value
  - xw: number
    - Gamble winning value
  - pw: number
    - Gamble winning probability
  - xs: number
    - Sure value
  - trial: number
    - Trial count
  - response: string
    - Chosen option, either 'gamble' or 'sure'
pauseTrial()
- Pause trial animations
resumeTrial()
- Resume trial animations
clearFunctions()
- Remove all functions except the default
clearProbabilities()
- Remove all probabilities except the default
clear()
- Remove all functions and probabilities except the defaults
removeFunction(name)
- Remove the identified function
- Parameters
  - name: string
    - Identifier for function
removeProbability(name)
- Remove the identified probability
- Parameters
  - name: string
    - Identifier for probability
getFunction(name = 'default')
- Retrieve the identified function
- Parameters
  - name: string = 'default'
    - Identifier for function
- Return value
  - function: object
    - name: string
      - Identifier for function
    - g: number
      - Parameter γ (probability distortion)
getProbability(name = 'default')
- Retrieve the identified probability
- Parameters
  - name: string = 'default'
    - Identifier for probability
- Return value
  - probability: object
    - name: string
      - Identifier for probability
    - p: number
      - Probability
    - w: number
      - Decision weight
    - label: string
      - Label
    - function: string
      - Name of function
get(name = 'default')
- Retrieve the identified probability and function
- Parameters
  - name: string = 'default'
    - Identifier for probability and function
- Return value
  - probability & function: object
    - name: string
      - Identifier for probability and function
    - p: number
      - Probability
    - g: number
      - Parameter γ (probability distortion)
    - w: number
      - Decision weight
    - label: string
      - Label
    - function: string
      - Name of function
setFunction(g, name = 'default')
- Create or change the identified function
- Parameters
  - g: number
    - Parameter γ (probability distortion)
  - name: string = 'default'
    - Identifier for function
setProbability(p, name = 'default', label = '', func = name, trial = false)
- Create or change the identified probability
- Parameters
  - p: number
    - Probability
  - name: string = 'default'
    - Identifier for probability
  - label: string = ''
    - Label
  - func: string = name
    - Name of function
  - trial: boolean = false
    - Is this for an animated trial?
set(p, g, name = 'default', label = '', func = name)
- Create or change the identified probability and function
- Parameters
  - p: number
    - Probability
  - g: number
    - Parameter γ (probability distortion)
  - name: string = 'default'
    - Identifier for probability
  - label: string = ''
    - Label
  - func: string = name
    - Name of function

Custom Events

cpt-probability-change
- Indicates that a function and/or probability has changed
- detail
  - name: string
    - Identifier for probability
  - p: number
    - Probability
  - g: number
    - Parameter γ (probability distortion)
  - w: number
    - Decision weight
  - label: string
    - Label
  - function: string
    - Name of function

Example

<cpt-probability interactive probability="0.75" gamma="0.8"></cpt-probability>

`CPTSpace` / `<cpt-space>`

3D representation of CPT parameter space for a given decision

A 3D plot, with alpha, lambda, and gamma as the three dimensions. The current model parameters can be represented as a point in the space. A surface can be displayed representing the border between combinations of parameter values that will lead to a 'gamble' choice versus a 'sure' choice for the current decision.

Note: This component relies on Plotly's 3d Isosurface and Scatter Plots, which seem to require a few megabytes of code, and are laggy to update, though direct interaction with the plot is snappy.

Attributes

surface: boolean = true
- Should the surface separating 'gamble' choices versus 'sure' choices be displayed
point: boolean = true
- Should the point representing the current parameter values be displayed
updateable: boolean = false
- Can the color-coded response for the decision change based on current values
alpha: number = 0.8
- Parameter α (diminishing marginal utility)
lambda: number = 1.2
- Parameter λ (loss aversion)
gamma: number = 0.8
- Parameter γ (probability distortion)
win: number = 20
- Winning value in gamble
loss: number = 0
- Losing value in gamble
probability: number = 0.5
- Probability of winning
sure: number = 10
- Sure value

Example

<cpt-space updateable surface="true" point="true" alpha="0.75" lambda="1.2" gamma="0.8" win="20" loss="0" probability="0.5" sure="10"></cpt-space>

`CPTValue` / `<cpt-value>`

Value function for CPT

Maps from objective value to subjective value. Functions themselves and data points on the functions can be directly manipulated.

Attributes

interactive: boolean = false
- Allow direct manipulation of functions or data points
value: number = null
- Objective value
alpha: number = 0.5
- Parameter α (diminishing marginal utility)
lambda: number = 2
- Parameter λ (loss aversion)
label: string = ''
- Label for data point

Methods

trial(xl, xw, pw, xs, trial, response)
- Creates or changes the specified trial data
- Parameters
  - xl: number
    - Gamble losing value
  - xw: number
    - Gamble winning value
  - pw: number
    - Gamble winning probability
  - xs: number
    - Sure value
  - trial: number
    - Trial count
  - response: string
    - Chosen option, either 'gamble' or 'sure'
pauseTrial()
- Pause trial animations
resumeTrial()
- Resume trial animations
clearFunctions()
- Remove all functions except the default
clearValues()
- Remove all values except the default
clear()
- Remove all functions and values except the defaults
removeFunction(name)
- Remove the identified function
- Parameters
  - name: string
    - Identifier for function
removeValue(name)
- Remove the identified value
- Parameters
  - name: string
    - Identifier for value
getFunction(name = 'default')
- Retrieve the identified function
- Parameters
  - name: string = 'default'
    - Identifier for function
- Return value
  - function: object
    - name: string
      - Identifier for function
    - a: number
      - Parameter α (diminishing marginal utility)
    - l: number
      - Parameter λ (loss aversion)
getValue(name = 'default')
- Retrieve the identified value
- Parameters
  - name: string = 'default'
    - Identifier for value
- Return value
  - value: object
    - name: string
      - Identifier for value
    - x: number
      - Objective value
    - v: number
      - Subjective value
    - label: string
      - Label
    - function: string
      - Name of function
get(name = 'default')
- Retrieve the identified value and function
- Parameters
  - name: string = 'default'
    - Identifier for value and function
- Return value
  - value & function: object
    - name: string
      - Identifier for value and function
    - x: number
      - Objective value
    - a: number
      - Parameter α (diminishing marginal utility)
    - l: number
      - Parameter λ (loss aversion)
    - v: number
      - Subjective value
    - label: string
      - Label
    - function: string
      - Name of function
setFunction(a, l, name = 'default')
- Create or change the identified function
- Parameters
  - a: number
    - Parameter α (diminishing marginal utility)
  - l: number
    - Parameter λ (loss aversion)
  - name: string = 'default'
    - Identifier for function
setValue(x, name = 'default', label = '', func = name, trial = false)
- Create or change the identified probability
- Parameters
  - x: number
    - Objective value
  - name: string = 'default'
    - Identifier for value
  - label: string = ''
    - Label
  - func: string = name
    - Name of function
  - trial: boolean = false
    - Is this for an animated trial?
set(x, a, l, name = 'default', label = '', func = name)
- Create or change the identified value and function
- Parameters
  - x: number
    - Objective value
  - a: number
    - Parameter α (diminishing marginal utility)
  - l: number
    - Parameter λ (loss aversion)
  - name: string = 'default'
    - Identifier for value
  - label: string = ''
    - Label
  - func: string = name
    - Name of function

Custom Events

cpt-value-change
- Indicates that a function and/or value has changed
- detail
  - name: string
    - Identifier for value
  - x: number
    - Objective value
  - a: number
    - Parameter α (diminishing marginal utility)
  - l: number
    - Parameter λ (loss aversion)
  - v: number
    - Subjective value
  - label: string
    - Label
  - function: string
    - Name of function

Example

<cpt-value interactive value="20" alpha="0.8" lambda="1.2"></cpt-value>

`RiskyChoice` / `<risky-choice>`

A choice between two options, one a gamble, and one a sure thing

Presents a choice between two options, a gamble and a sure thing. The display can either show the choice, a fixation, or a blank display. It is optionally interactive, in which case the values of the gamble win and the sure thing and the probability of the gamble win can be edited.

Attributes

interactive: boolean = false
- Allow direct manipulation of probabilities and values
win: number = 20
- Winning value in gamble
loss: number = 0
- Losing value in gamble
probability: number = 0.5
- Probability of winning
sure: number = 10
- Sure value
state: string = 'choice'
- Current state of the display
- Options
  - 'choice'
    - Show the options with a question mark in between
  - 'fixation'
    - Show blank pies with a fixation in between
  - 'blank'
    - Show blank pies with a dot in between

Custom Events

risky-choice-change
- Indicates that one or more numbers in the choice have been changed
- detail
  - xl: number
    - Objective value of gamble loss
  - xw: number
    - Objective value of gamble win
  - pw: number
    - Probability of gamble win
  - xs: number
    - Objective value of sure thing

Example

<risky-choice interactive probability="0.75" win="20" loss="0" sure="10" state="choice"></risky-choice>

`ProspectableControl` / `<prospectable-control>`

Control panel for CPT demos

A configurable set of controls for user manipulation of examples of cumulative prospect theory. Controls can be provided for the number of trials, the timing of trials, and for running, pausing, or resetting a block of trials.

Attributes

trials: number = undefined
- Show a slider for setting the number of trials, initialized to the value provided
- Options
  - 1 to 100 in steps of 1
duration: number = undefined
- Show a slider for setting the duration of the stimulus, wait, and inter-trial interval on each trial, initialized to the value provided in milliseconds
- Options
  - 10 to 4000 in steps of 10
run: boolean = false
- Show a button to run the task
pause: boolean = false
- Show a button to pause the task
reset: boolean = false
- Show a button to reset the task

Methods

complete()
- Indicates that a trial block is done, so it can no longer be paused

Custom Events

prospectable-control-trials
- Indicates the number of trials slider has been adjusted
- detail
  - trials: number
    - The new number of trials
prospectable-control-duration
- Indicates the duration of trials slider has been adjusted
- detail
  - duration: number
    - The new duration
prospectable-control-run
- Indicates the run button has been pushed
prospectable-control-pause
- Indicates the pause button has been pushed
prospectable-control-reset
- Indicates the reset button has been pushed

Example

<prospectable-control trials="15" duration="1500" run pause reset></prospectable-control>

`RiskyOption` / `<risky-option>`

A single decision option consisting of one or more decision outcomes

Displays its possible outcomes as a pie chart, with the size representing the probability. Optionally, the size of the pie pieces can be directly manipulated and the values associated with them can be edited.

Attributes

interactive: boolean = false
- Allow direct manipulation of probabilities and values

Slots

unnamed
- Place the constituent decision outcomes here
- <risky-outcome>
  - This is the only meaningful tag for this slot - the total probabilities should sum to 1

Custom Events

risky-outcome-change
- Indicates that an outcome has been changed
- detail
  - x: number
    - Objective value
  - p: number
    - Probability
  - name: string
    - Name of outcome

Example

<risky-option interactive>
  <risky-outcome interactive probability="0.25" value="0" name="loss"></risky-outcome>
  <risky-outcome interactive probability="0.75" value="20" name="win"></risky-outcome>`
</risky-option>

`RiskyOutcome` / `<risky-outcome>`

A single outcome for a decision option (no display on its own)

A place-holder to specify an outcome with a particular value and probability. Only useable inside of a <risky-option>.

Attributes

interactive: boolean = false
- Allow direct manipulation of probabilities and values
value: number = 0
- Objective value
probability: number = 0
- Probability
name: string = ''
- Name for this outcome

Example

<risky-outcome interactive value="20" probability="0.8" name="win"></risky-outcome>

`ProspectableResponse` / `<prospectable-response>`

Response buttons, feedback, and payoffs for gambling decision tasks

This element provides 'gamble' and 'sure' response buttons. It can also display a running count of the trials, display feedback in comparative terms, and payoff outcome.

Attributes

interactive: boolean = false
- Allow user to respond, instead of just displaying simulated model responses
feedback: string = 'outcome'
- What type of feedback to display
- Options
  - 'none'
    - No feedback
  - 'outcome'
    - Feedback in terms of comparative selection, i.e. 'better', 'worse', 'even', or 'no response'
trial: boolean = false
- Display the running count of trials, i.e. 'Trial: 2 of 10'
payoff: string = 'none'
- What payoff information to display
- Options
  - 'none'
    - No payoff information displayed
  - 'selection'
    - Only display payoff for the selected option
  - 'both'
    - Display payoffs for both options

Methods

start(xl, xw, pw, xs, gamblePayoff, surePayoff, better, trial)
- Indicates that a trial has started, and its time to wait for a response
- Parameters
  - xl: number
    - Objective value of gamble loss
  - xw: number
    - Objective value of gamble win
  - pw: number
    - Probability of gamble win
  - xs: number
    - Objective value of sure thing
  - gamblePayoff: number
    - Actual outcome if gamble is selected
  - surePayoff: number
    - Actual outcome if sure thing is selected
  - better: string
    - Which option is better, either 'gamble', 'sure', or 'equal'
  - trial: number
    - The count of the trial within the block
stop()
- Indicates that the trial is over and it is time to display any requested feedback
- Note: If no response has been made yet, the trial is recorded as having no response
gamble()
- Emulate a 'gamble' response
sure()
- Emulate an 'sure' response
responded(response)
- Emulate a response
- Parameters
  - response: string
    - Whether to emulate a 'gamble' or 'sure' response
reset()
- Reset to the state at the start of a block of trials

Custom Events

prospectable-response
- Indicates that a response has been made on this trial
- detail
  - trial: number
    - The count of this trial in the block
  - better: string
    - Which option is better, either 'gamble', 'sure', or 'equal'
  - gamblePayoff: number
    - Actual outcome if gamble was selected
  - surePayoff: number
    - Actual outcome if sure thing was selected
  - xl: number
    - Objective value of gamble loss
  - xw: number
    - Objective value of gamble win
  - pw: number
    - Probability of gamble win
  - xs: number
    - Objective value of sure thing
  - response: string
    - Whether the response was 'gamble' or 'sure'
  - outcome: string
    - The outcome of the trial as 'better', 'worse' or 'even'
  - payoff: number
    - The payoff for this trial

Example

<prospectable-response interactive feedback="outcome" trial payoff="selection"></prospectable-response>

`DecisionSpace` / `<decision-space>`

3D representation of decision space for given parameter values

A 3D plot, with gamble win value, gamble win probability, and sure value as the three dimensions. The decisions are between a gamble with a win value with a win probability and a lose value of zero, and a sure thing with a sure value. Decisions can be represented as points in the space. A surface can be displayed representing the border between combinations of values and probabilities that will lead to a 'gamble' choice versus a 'sure' choice.

Note: This component relies on Plotly's 3d Isosurface and Scatter Plots, which seem to require a few megabytes of code, and are laggy to update, though direct interaction with the plot is snappy.

Attributes

surface: boolean = true
- Should the surface separating 'gamble' choices versus 'sure' choices be displayed
point: string = 'first'
- Should the points representing choices be displayed
- Options
  - 'all'
    - Show all choices as points
  - 'first'
    - Only show the first choice as a point
  - 'rest'
    - Show all but the first choice as points
  - 'none'
    - Don't show any choices as points
updateable: boolean = false
- Can the color-coded responses for decisions change based on current parameters
alpha: number = 0.8
- Parameter α (diminishing marginal utility)
lambda: number = 1.2
- Parameter λ (loss aversion)
gamma: number = 0.8
- Parameter γ (probability distortion)
win: number = 20
- Winning value in gamble
loss: number = 0
- Losing value in gamble
probability: number = 0.5
- Probability of winning
sure: number = 10
- Sure value

Methods

get(name = 'default')
- Retrieve the identified choice
- Parameters
  - name: string = 'default'
    - Identifier for choice
- Return value
  - choice: object or null
    - name: string
      - Identifier for choice
    - xw: number
      - Value of gamble win
    - pw: number
      - Probability of gamble win
    - xs: number
      - Value of sure thing
    - response: string
      - Chosen response
      - Options
        
        'gamble'
        
        'sure'
    - label: string
      - Label
set(xw, pw, xs, response, name = 'default', label = '')
- Create or change the value of the identified choice
- Parameters
  - xw: number
    - Value of gamble win
  - pw: number
    - Probability of gamble win
  - xs: number
    - Value of sure thing
  - response: string
    - Chosen response
    - Options
      - 'gamble'
      - 'sure'
  - name: string = 'default'
    - Identifier for choice
  - label: string = ''
    - Label for choice

Example

<decision-space updateable surface="true" point="all" alpha="0.75" lambda="1.2" gamma="0.8" win="20" loss="0" probability="0.5" sure="10"></cpt-space>

`RiskyTask` / `<risky-task>`

Displays stimuli for gambling decision task

When run, a block of trials is presented. Before each trial is an inter-trial interval (ITI). Each trial then consists of a stimulus during which a participant can respond. The stimulus consists of two options, each of which is represented as a pie chart. The proportion of the pie represents the probability, and a number in the pie piece represents the value. The choice is always between a gamble with a winning value and a losing value, and a sure thing. The task can be paused and then resumed, and it can also be reset and run again.

Attributes

duration: number = 2000
- Duration of stimulus in milliseconds
iti: number = 2000
- Duration of inter-trial interval in milliseconds
trials: number = 5
- Number of trials per block
running: boolean = false
- Currently executing block of trials

Methods

reset()
- Stops a currently running or ended block of trials and resets everything to be ready to run again

Custom Events

risky-block-start
- Indicates the beginning of a block of trials
risky-block-end
- Indicates the completion of a block of trials
- detail for risky-block-start and risky-block-end
  - trials: number
    - Number of trials in the block
risky-trial-start
- Indicates the beginning of a trial (iti is over and stimulus is about to start)
risky-trial-end
- Indicates the end of a trial (stimulus is over and iti is about to start)
- detail for risky-trial-start and risky-trial-end
  - trials: number
    - Number of trials in the block
  - duration: number
    - Duration of stimulus in milliseconds
  - iti: number
    - Duration of inter-trial interval in milliseconds
  - trial: number
    - Count of trial in block (one-based)
  - xl: number
    - Losing value in gamble
  - xw: number
    - Winning value in gamble
  - pw: number
    - Probability of winning gamble
  - xs: number
    - Value of sure thing
  - better: string
    - Which option is better according to expected value
    - Options
      - 'gamble'
      - 'sure'
      - 'equal'
  - gamblePayoff: number
    - Payoff for choosing the gamble (based on random outcome)
  - surePayoff: number
    - Payoff for choosing the sure thing

Example

<risky-task duration="3000" iti="500" trials="10" running></risky-task>

Equations

Interactive equations for CPT

The equations can either be static and display the variable names, be static and display names and values or be interactive with names and editable values, in which case only the values on the right side of the equals sign are editable.

Note: The layout for these equations leaves something to be desired, especially on smaller screens. Ideally a proper math renderer would be used, but I haven't found one that takes kindly to insertion of the custom elements needed for live editing.

`CPTEquationPG2W` / `<cpt-equation-pg2w>`

Subjective decision weight from objective probability and sensitivity

Attributes

numeric: boolean = false
- Show values instead of just the names of variables
interactive: boolean = false
- Allow editing of numeric values in the equation
p: number = 0.75
- Probability
g: number = 0.5
- Parameter γ (probability distortion)

Properties

w: number
- Decision weight

Custom Events

cpt-equation-pg2w-change
- Indicates that the values in the equation have changed
- detail
  - p: number
    - New value of probability
  - g: number
    - New value of parameter γ (probability distortion)
  - w: number
    - New value of decision weight

Example

<cpt-equation-pg2w numeric interactive p="0.75" g="0.8"></cpt-equation-pg2w>

`CPTEquationXAL2V` / `<cpt-equation-xal2v>`

Subjective value from objective value, marginal utility, and loss aversion

Attributes

numeric: boolean = false
- Show values instead of just the names of variables
interactive: boolean = false
- Allow editing of numeric values in the equation
x: number = 10
- Objective value
a: number = 0.5
- Parameter α (diminishing marginal utility)
l: number = 2
- Parameter λ (loss aversion)

Properties

v: number
- Subjective value

Custom Events

cpt-equation-xal2v-change
- Indicates that the values in the equation have changed
- detail
  - x: number
    - New value of objective value
  - a: number
    - New value of parameter α (diminishing marginal utility)
  - l: number
    - New value of parameter λ (loss aversion)
  - v: number
    - New value of subjective value

Example

<cpt-equation-xal2v numeric interactive x="20" a="0.75" l="2.5"></cpt-equation-xal2v>

`CPTEquationVW2U` / `<cpt-equation-vw2u>`

Subjective utility from subjective value and subjective decision weight

Attributes

numeric: boolean = false
- Show values instead of just the names of variables
interactive: boolean = false
- Allow editing of numeric values in the equation
v: Array = [10, 0]
- Subjective values
- Expressed in HTML as a space-separated list
w: Array = [0.75, 0.25]
- Decision weights
- Expressed in HTML as a space-separated list
n: number = 2
- Number of subjective value/decision weight pairs

Properties

u: number
- Subjective utility

Custom Events

cpt-equation-vw2u-change
- Indicates that the values in the equation have changed
- detail
  - v: Array
    - New values of subjective values
  - w: Array
    - New values of decision weights
  - n: number
    - Number of subjective value/decision weight pairs
  - u: number
    - New value of subjective utility

Example

<cpt-equation-vw2u numeric interactive v="20 0" w="0.25 0.75" n="2"></cpt-equation-vw2u>

`CPTEquation`

Base class for all interactive CPT equations

To define a new equation:

export default class CPTEquationSomething extends CPTEquation {
  ...
}

CPTEquation extends ProspectableElement extends DecidablesElement extends LitElement

Examples

Full examples built from multiple components

`CPTExampleHuman` / `<prospectable-example-human>`

User runs task, and results are fit and displayed in real-time using CPT

Used to build examples where the user is performing the gambling decision task. Can include controls, the task itself, response buttons with feedback and payoffs, the value function, the probability function, a 3D visualization of the decisions in the block with the decision surface, and trace plots and histograms for the parameters in the model fit. The value function and probability function should not be interactive, because their rendering is determined by the user's task performance.

Slots

unnamed
- Place relevant prospectable-elements components here
- Wired elements
  - <cpt-fit>
    - Fits the user's responses to CPT using a Bayesian model running in a Web Worker
  - <cpt-probability>
    - Displays the probability function based on the current model parameters
  - <cpt-value>
    - Displays the value function based on the current model parameters
  - <prospectable-control>
    - Allows user to adjust parameters and control the task
  - <prospectable-response>
    - Allows user to make responses and see feedback and payoffs
  - <decision-space>
    - Displays all completed trials in block in decision space with the model's decision surface
  - <risky-task>
    - Displays the task

Example

<cpt-example-human>
  <cpt-fit></cpt-fit>
  <cpt-probability></cpt-probability>
  <cpt-value></cpt-value>
  <prospectable-control trials="10" run pause reset></prospectable-control>
  <prospectable-response interactive trial feedback="outcome" payoff="both"></prospectable-response>
  <decision-space point="rest" alpha="1" lambda="1" gamma="1"></decision-space>
  <risky-task trials="10"></risky-task>
</cpt-example-human>

`CPTExampleInteractive`

Explore how decision and CPT model parameters relate

Used to build examples where the user can explore the relationship between a choice and model parameters. Can include the choice, a visual rendering of the comparative utility calculation, the value function with the current choice, the probability function with the current choice, a 3D visualization of the choice in decision space with the decision surface, and a 3D visualization of the choice in CPT model space with the decision surface. All components can be interactive (except the 3D visualizations which don't support it).

Attributes

Note: Since many attributes are set on the example, they don't need to be set on the individual components, as they will be propagated and kept in sync.

alpha: number = 0.8
- Parameter α (diminishing marginal utility)
lambda: number = 1.2
- Parameter λ (loss aversion)
gamma: number = 0.8
- Parameter γ (probability distortion)
loss: number = 0
- Losing value in gamble
win: number = 20
- Winning value in gamble
probability: number = 0.5
- Probability of winning
sure: number = 10
- Sure value

Slots

unnamed
- Place relevant prospectable-elements components here
- Wired elements
  - <cpt-calculation>
    - Display and change the utility calculations
  - <cpt-probability>
    - Display and change the probability function and gamble decision weight
  - <cpt-space>
    - Display the space of possible parameter values with the current values and decision surface current decision
  - <cpt-value>
    - Display and change the value function and subjective values of gamble win and sure thing
  - <risky-choice>
    - Display and change the choice between a gamble and a sure thing
  - <decision-space>
    - Display the space of possible decisions with the current decision and the decision surface

Example

<cpt-example-interactive probability="0.75" win="20" loss="0" sure="10" alpha="0.9" lambda="2" gamma="0.75">
  <risky-choice interactive></risky-choice>
  <cpt-probability interactive></cpt-probability>
  <cpt-value interactive></cpt-value>
  <cpt-calculation numeric interactive></cpt-calculation>
  <cpt-space updateable></cpt-space>
  <decision-space updateable></decision-space>
</cpt-example-interactive>

`CPTExampleModel` / `<cpt-example-model>`

Model simulates task based on CPT parameter values

Used to build examples where the model is simulated to perform the gambling decision task. Can include controls, the task itself, response buttons with feedback and payoffs, a visual rendering of the comparative utility calculation, the value function with the current choice, the probability function with the current choice, and a 3D visualization of the decisions in the block with the decision surface. The value and probability functions should be interactive, so the user can modify the model. The responses and the 3D visualization should not be interactive, because their values are received from the model's task performance.

Attributes

Note: Since model parameter attributes are set on the example, they don't need to be set on the individual components, as they will be propagated and kept in sync.

alpha: number = 0.8
- Parameter α (diminishing marginal utility)
lambda: number = 1.2
- Parameter λ (loss aversion)
gamma: number = 0.8
- Parameter γ (probability distortion)

Slots

unnamed
- Place relevant prospectable-elements components here
- Wired elements
  - <cpt-calculation>
    - Display the utility calculations
  - <cpt-probability>
    - Display and change the probability function
  - <cpt-value>
    - Display and change the value function
  - <prospectable-control>
    - Allows user to adjust parameters and control the task
  - <prospectable-response>
    - Allows user to view model responses, feedback, and payoffs
  - <decision-space>
    - Displays all completed trials in block in decision space with the model's decision surface
  - <risky-task>
    - Displays the task

Example

<cpt-example-model alpha="0.9" lambda="2" gamma="0.75">
  <prospectable-control trials="10" run pause reset></prospectable-control>
  <risky-task trials="10"></risky-task>
  <cpt-probability interactive></cpt-probability>
  <cpt-value interactive></cpt-value>
  <prospectable-response trial feedback="outcome" payoff="both"></prospectable-response>
  <decision-space updateable point="rest" alpha="1" lambda="1" gamma="1"></decision-space>
</cpt-example-model>

`CPTExample`

Base class for all CPT examples

To define a new example:

export default class CPTExampleSomething extends CPTExample {
  ...
}

CPTExample extends ProspectableElement extends DecidablesElement extends LitElement

Base class

`ProspectableElement`

Base class for all prospectable web components

To define a new element:

export default class ProspectableElementSomething extends ProspectableElement {
  ...
}

ProspectableElement extends DecidablesElement extends LitElement

Development

Features/Bugs/Notes

Add to CPTMath
- Luce choice rule
- utility from x, p, and parameters
Make sure to use corrected formula! v(xw) * w(xp) + v(xl) * w(1 - xp) ?> v(xs) (Nilsson, Rieskamp, & Wagenmakers, 2011) VERSUS v(xw) * w(xp) + v(xl) * 1 - w(xp) ?><? v(xs) (Nilsson, Rieskamp, & Wagenmakers, 2020) This follows (Tversky & Kahneman, 1992)!

Package Scripts

yarn gulp preparePlotly
- Injects Plotly styles into src/components/plotly-style.auto.js for inclusion in components
yarn lint
- Lints scripts in src/
yarn test
- Runs all tests and reports coverage in test/coverage/
yarn test:watch
- Runs all tests in watch mode and reports coverage in test/coverage/
yarn test:file <filename>
- Runs tests for a single file and reports coverage in test/coverage/
yarn build
- Builds browser-compatible optimized bundle from src/ to lib/

File Organization

prospectable-elements/
- lib/ (Bundles created from src/ by build) [autogenerated]
- src/ (Source files)
  - components/ (Source for visualizations)
  - equations/ (Source for equations)
  - examples/ (Source for examples combining visualizations)
- test/ (Testing files)
  - coverage/ (Code coverage results) [autogenerated]
- CHANGELOG.md (Based on conventional commits) [autogenerated]
- gulpfile.js (Tasks for gulp)
- package.json (Package config for yarn and npm)
- README.md (This file)
- rollup-stats.html (Report on js bundle composition and size) [autogenerated]

License

The content of this project is licensed under Creative Commons Attribution-ShareAlike 4.0 International License (CC-BY-SA-4.0) and the source code of this project is licensed under GNU General Public License v3.0 or any later version (GPL-3.0-or-later).

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