Michael Lamport Commons Harvard Medical School Commonstiacnet Presented to the Department of Psychology University of Minho Thursday July 4 th 2012 Braga Portugal 2012 Dare Association Inc ID: 490355
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Slide1
A Model of Stage and Value to Predict Behavior
Michael Lamport CommonsHarvard Medical SchoolCommons@tiac.net
Presented to the Department of Psychology, University of Minho
Thursday, July 4
th
, 2012,
Braga, Portugal
© 2012 Dare Association, Inc
., Cambridge, MASlide2
1. Measuring the A Priori Difficulty of a Task Contingency Using Order of Hierarchical Complexity
The Model of Hierarchical Complexity is a quantitative behavioral-developmental theory that suggests an objective way of determining the a priori difficulty of a task's contingencies. The model explains why stage-like performances are observed. The model proposes that stages result from the hierarchical structure of tasks. A task is defined as hierarchically more complex when it organizes, in a non-arbitrary fashion, two or more less complex tasks. Using this model, sixteen orders of hierarchical complexity have been generated. In this study, the model is used to generate stimuli in the form of either problems or stories. The stimuli within a domain consist of an ordered series of tasks, from order 1, reflexes and conditioned reflexes, up to order 12, the discrimination of efficient market. Tasks were generated in several domains, including reinforcement contingencies (economic), mathematical, scientific, moral, political, and social domains. 280 people were recruited through online groups. A Rasch analysis of the responses showed that, within each domain, items were well scaled on a single dimension reflecting the predicted difficulty of the item. Participants' performances were shown to conform to the predictions of the model, with very high amounts of variance accounted for (from .73% and up).
2Slide3
1. Measuring the A Priori Difficulty of a Task Contingency Using Order of Hierarchical Complexity
Michael Lamport Commons3Slide4
The Model of Hierarchical Complexity
The Model of Hierarchical Complexity is a quantitative behavioral-developmental theoryIt suggests an objective way of determining the a priori difficulty of a task's contingenciesThe model explains why stage-like performances are observedSlide5
The Model of Hierarchical Complexity
Behavior can be analyzed by the difficulty of tasks that an individual successfully addressWe divide the task properties that influence item difficulty into three parts: Order of hierarchical complexity of the items in a task Task content
Language
And the associated country of the participants
It is hypothesized that the most important predictor of difficulty is the order of hierarchical complexityCommons’ model identifies 16 orders of hierarchical complexity
It deconstructs tasks into the actions that must be done at each order to build the behavior needed to successfully complete the task
It classifies each task by its order of hierarchical complexitySlide6
A task is at a higher order if:It is defined in terms of two or more lower order task actions
It organizes lower order task actionsThis organization is non-arbitrarySlide7
16 Orders of Hierarchical Complexity
Order
Name Complexity
0
Calculatory
1
Sensory & Motor
2
Circular Sensory-motor
3
Sensory-motor
4
Nominal
5
Sentential
6Preoperational7Primary
8Concrete9Abstract10Formal11Systematic12Metasystematic13Paradigmatic14Crossparadigmatic15Meta Crossparadigmatic
7Slide8
The Model of Hierarchical Complexity
Task sequences form a hierarchy from simpler to more complexTask-Performance should always follow that certain (developmental) order
Under the above conditions, development occurs in stages reflecting the necessity to coordinate lower level actionSlide9
Empirical Studies
The Model of Hierarchical Complexity is used to generate stimuli in the form of either problems or storiesThe stimuli within a domain consist of an ordered series of tasks, from usually Preoperational order 6 up to Metasystematic order 12Tasks were generated in several domainsReinforcement contingencies (economic)
Mathematical, scientific
Moral, political, and social domainsSlide10
The Laundry Instrument
The Laundry Instrument consists of isolation of Variable problemsInhelder and Piaget (1958) developed the pendulum and chemicals tasksParticipants had to perform an experiment by manipulating a single variable while holding all other variables constant They had to figure out which variable controlled the rate that a pendulum weight would cross the low point
Participants were instructed to answer a series of multiple choice questions
The answers were coded right or wrong
The questions were constructed so that the higher order questions coordinated the lower order questionsSlide11
Laundry Instrument Example: Abstract Order 9
This
is the first order in which participants are required to see what the operative variable isSlide12
Laundry Instrument Example: Formal Order 10
Higher order problems added more ingredients to the mixtureAlso make deduction more difficult by including many more possible operative
variables
They also included multiple possible relationships among the variables such as
And/Or scenariosSlide13
The overall study is made up of data collected from 5 separate convenience samples
Each was tested on one of five similarly constructed isolation of variables problems There were a total of 1263 participants across all studiesHere, we will briefly describe
The
characteristics of each separate
sampleThe characteristics of the instrument used with each sample.There were two quasi-independent
variables that were not independent of one another
Content
Language
The Laundry Instrument
ParticipantsSlide14
The Laundry InstrumentSubsample Language, Version and Content
1) Iraqi, Arabic speaking, Laundry Instrument: 450 participants completed paper and pencil versions of the Arabic laundry instrument. 2) English, First Revised Laundry Instrument: 215 participants from various Listservs 3) English speaking, Short Laundry Instrument: 78 participants from various Listservs
4) German speaking, Combustion Instrument: 459 students completed paper and pencil versions
5) English speaking, Atheism and Belief Instrument: 61 participants from various Listservs Slide15
The Laundry InstrumentProcedure
Participants filled out the questionnaires either on paper or onlineThe subtasks were presented in a sequence from easy to hard
Low to high order of hierarchical complexity
Having successfully completed the easy
problems, which most of the participants did, served as support for the harder problems One gets better performance in going from easy to hard (e.g. Aamodt
& Mcshane, 1992; Hodson, 2006
)
Rasch
(1980/1980) Analysis was used to analyze the dataSlide16
Rasch Model
Under the Rasch model these linear measures areItem-free (item-distribution-free)Person-free (person-distribution-free) This means that the measures are statistically equivalent
For the items regardless of which persons (from the same population) are analyzed, and
For the people regardless of which items (from the same set) are analyzed
The person and item total raw scores were also used as dependent variablesSum the item raw scores separately for each order of complexity and then that could be used to correlate with hierarchical complexity
The Rasch
person reliability
of the combined data was .94
The Rasch
item reliability
was 1.0
In the context of a
Rasch
analysis, this means that there is a high probability that items estimated with higher measures do in fact have higher measures than those estimated with lower measures
There is no equivalent traditional measureSlide17
Rasch Analysis of Data from All Studies
How well did the order of hierarchical complexity predict performance stage on that item? The results are illustrated using a Rasch variable map
If
performance on the items were in perfect order, there would be no item
reversalsNo cases in which a higher order item appears below a lower order item The closer to the top the items are, the more difficult they were to answer
Participants had a 50% chance of correctly answering items that are located directly across from them Slide18
Person
Rasch
scores on the left hand side
Rasch
scaled items scores on the right hand side
The scaling showed
The primary items at the bottom
The
metasystematic
items at the top
All of the other stage are seen to be in the correct order
The exception is the abstract and concrete orders, which are intermixed
One can see gaps between the stages
The mixing of concrete and abstract was due to the concrete tasks having too many ingredients (variables)
These were removed in subsequent versions of the instrumentsSlide19
Item Stage Score Versus Item Order of Hierarchical Complexity
The item stage score plot shows how the items performedItems with a hierarchical complexity of 10 would be expected to have a stage score of 10
This plot shows that this trend is followed
r
2 = .804Slide20
A series of studies were conducted using content that is related to social and behavioral problem
Political development (Sonnert & Commons, 1994)Therapists’ decisions to report patient’s prior crimes (Commons, Lee, Gutheil, Goldman, Rubin, & Appelbaum, 1995) The relationships between more and less powerful persons such as doctors and patients (Commons & Rodriguez, 1990, 1993) & counselors and patients (Commons, et al, 2006
)
In each study, participants
received 5 vignettes about interactions between two personEach vignette represented each order of Hierarchical Complexity
Social and Behavioral Tasks
20Slide21
21
Helper-Person Problem
Figure 2a. Method
Figure 2b. Inform
Figure 2c. Guide
The vignettes were about the interaction between a helper and a person
Participants
were asked
three questions
Rate the method of offering guidance and assistance of each
Helper
Rate the degree to which each Helper informed their
Person
how likely you would be to accept the guidance and assistance offered by the
HelperSlide22
22
Politician-Voter Problem
Figure 3a. Method
Figure 3b. Inform
Figure 3c. Vote
*** Each data point represents an average of all 3 items at each stage***
They
rated three issues about the interaction between politician and voter
Rate
each of the politicians'
methods
Rate
the degree to which the Politicians informed their Voters
Rate
how likely you would be to vote for the
PoliticiansSlide23
Item Order of Hierarchical Complexity Predicted Item Rasch Scaled Scores
Helper-Person
r
(3) = .967,
r(3) = .978, r(3) = .973Politician-Voter
r
(3) = .920,
r
(3) = .895,
r
(3) = .900
Anti-Incest Reporting
r
(3) = .898,
r
(3) = .850, r(3) = .834Anti Death Penalty r(3) = .854, r(3) = .801Pro Death Penalty r(3) = .849, r(3) = .758, r(3) = .875Jesus Stoning Dilemma r(3) = .539, r(3) = .564The measured difficulty reflects the theoretical difficulty (Order of hierarchical complexity)23Slide24
24
**Overall Best Next Best
Figure 9a. Overall
Figure 9b. Helper-Person Inform
Figure 9c. Politician-Voter InformSlide25
Summary
The Model of Hierarchical Complexity measures the a priori difficulty of tasks, a new approach to Behavioral Developmental AnalysisEmpirical studies show that theOrder of Hierarchical Complexity of tasks predict the difficulty in performing such tasks, as measured by Rasch Analysis (r = 0.8 to .984)Tasks have been constructed in a variety of domains showing the generality of these results
The
MHC behaviorally explains
why there are stage like behaviors in developmentSlide26
2. Can Perceived Value Be Explained by Schedules of Reinforcement?
Can schedules perceived value be explained by the perceived value of just a few reinforcers? The additive noise model states that discounted reinforcer value simply adds together linearly but as time passes noise is added, VO = Overall value = Σ
v
i
where vi = effective or perceived value of a reinforcer at time i. Our unified theory integrates initial value of outcomes, delay and risk. Results from samples suffice to characterize entire schedules. Three difference equations of immediate reinforcer value with respect to time of a reinforcer summate many properties of discounting accounts of reinforcement schedules. A trial consisted of a two chain schedule. The first link consisted of the presentation of one of a large number of samples from a
t
schedule (Schoenfeld & Cole, 1972 Schoenfeld & Cole, 1972). The second link was a choice between a left key indicting the sample was lean or the right key indicating it rich. The overall value was Am = the total value of all the reinforcers delivered until total satiation has occurred, Am =
ΣΔA
m
. The value of an instantaneous reinforcer is Δ
A
m
. The perceived sample value was an hyperbolic function of how soon before choice a single reinforcer was (first difference equation) as the Commons et al.(1982)/Mazur’s (1987) equation for delay, s20
V
i
(delay) = ΔAi/(1+ k2di), d = Δt – 1 delay equals change in time minus 1; k2 = Sensitivity to delay. Risk is the second difference equation of Commons et al.(1982)/Mazur’s (1987) equation for delay: vi (risk) = Δ(ΔAi / Δd) Δd = Δ(ΔAi/(1 + kd3)/c, sensitivity to change in delay was well fit by a negative power function as proposed.26Slide27
2. Can Perceived Value Be Explained by Schedules of Reinforcement?
Nicholas Hewlett Keen Commons-Miller, Tufts UniversityMichael Lamport Commons, Harvard Medical SchoolRobin Francis Gane-McCalla, Dare Institute
Alex Pekker, University of Texas
Michael Woodford, Columbia University
The pigeons were run in the laboratories of
John Anthony Nevin at Columbia University
Michael Lamport Commons at the University of Manitoba and Northern Michigan University
Richard J. Herrnstein at Harvard University
Robert Cook at Tufts UniversitySlide28
Motivations For This Research
There have been a number of proposals for how value is determined with delay using schedules of reinforcement Bickel, Miller, et. al. 2010; Lawyer, William, et al. 2010; McKerchar, Green, (2008, 2010)There should be a unified explanation that relates responding to Immediate reinforcementDelayed reinforcement or
Time between possible reinforcements
Change in delays
An account should integrate over micro, molecular and molar levels A micro view looks at the contribution of each occurrence or non-occurrence of a reinforcer or other event A molecular view looks at a sample or local rates of reinforcement
A molar view looks at the overall rate of reinforcement
28Slide29
Issue This Research Resolves
This presentation addresses five unresolved issues that should allow for an integration these issues To relate the micro to the molecular what needs to be known is how well do samples from schedules approximate the overall schedulesThe integration should also to address what events from the micro analysis are accumulated, and how
Do reinforcers, after being discounted, simply add together?
Is a pigeon’s perception of the discounting of value based on relative rates of reinforcement and delay of reinforcement?
Also, can the equations explaining immediate value, and its difference equations, represent not only the simplest account of value, delay and risk, but fit the data well?
29Slide30
30
Evolutionary Explanations For Organisms’ Systems of Reward Processing
Organisms are always faced with the decision to stay or move on to a new source (patch) of reinforcement
Energy expenditure over long periods of time is regular
Obtaining energy is critical, and is dependent on time between reinforcers
To model this decision people have been interested in the reinforcement value of schedules and schedule samples Slide31
31
How Do We Model Organisms’ Discounting of Value Over Time?
There have been a number of simple models in which discounted reinforcing events are aggregated
There has been a great deal of interest in how reinforcing events are discounted in
Behavioral economics
Quantitative analysis of behavior
Comparative animal cognition
There has also been interest in how the discounted values combine
Do they add?
Do the values interact in some fashion?Slide32
32
The Additive Noise Model
Reinforcers add together linearly
But as time passes reinforcer noise added earlier interferes with control by reinforcers further from choice
The expected value of a reinforcer,
S
R+
, at instant
i
is the product of the probability the reinforcer occurs and the value of the reinforcer. (Economic Model)
Expected Value of a reinforcer (S
R+
) of a sample of equal probability possible reinforcer events at instances,
i
, is the product
EV = Σip(SR+) * Vi (SR+) (1)i = the instance being examined; Vi(SR+) = value of reinforcer, SR+ , i;p(SR+) = probability of obtaining a reinforcer immediately after time iSlide33
33
Quantitative Analysis of Behavioral View
The first equation simply states that the expected value,
EV
,
Is the sum of probability of an instance of reinforcement
p
, times
The effective or perceived value of that reinforcer,
V
i
, at instance
i
.
This has been a general tenet of both older and
even more modern learning theoriesOur model goes beyond this simple formulation to show that how an organism assigns value is also a function of other parameters Slide34
34
Advantages and Purpose
Most economic models of utility use value and probability
In contrast, this paper tests the idea that animals are sensitive to relative time, but not directly sensitive to probability
The rates of change of value with respect to time mimic the regularities in the evolutionary environment
Regularities involve
Immediate value of reinforcement
Temporal delay of reinforcement
Changes in temporal delay of reinforcement
Accordingly, we use rates of change of value to test whether animals are sensitive to relative timeSlide35
Commons-Miller et al. (2010) proposed a model for choice that includes three variables, and their associated parameters
The first variable is reinforcementIts associated parameter is sensitivity to reinforcement.The second variable is delayAlong with its associated parameter, sensitivity to delayThere is risk and sensitivity to risk
35Slide36
Total Reinforcement Value
Consider that reinforcement is a single accession from a long sequence of reinforcements. There is a possibility that all reinforcers satiate. Food, water, tastes do. Does money do so? Gates and Buffett and others seem to think so Am = the total value of all the reinforcers delivered until total satiation has occurred. Each instance of a reinforcer,
m
, occurs in what may be a very long sequence of events. For creative scientists, it may be an event every few years.
ΔAm = the change in overall value of reinforcers delivered with no delay when the position in a sequence of reinforcers is ignored until satiation occurs. In equation 1, this is the perceived reinforcing value of event
m.
A
m
=
ΣΔ
A
m
(1)
36Slide37
The term, “Diminishing Returns”, is the way economists talk about the fact that the value of reinforcement decreases as the number of delivered reinforcers increases.
Each time a reinforcer is delivered as m increases, it reduces the value of ΔAm by a discrete amount.Mathematically this is:
m
= the
mth delivered reinforcer in a sequence of reinforcing events Δ
A
1
, >
Δ
A
2
, >
Δ
A
3
.... > 037Slide38
Total Value
The total value, Am , is the total value of all the reinforcers delivered with no delayWhen total satiation has occurred and ΔA
i
decreases in value to 0.
The strength of ΔAm not only varies with where in a sequence of reinforcing events it occurs, but on a number of other factors: The animal under consideration
Its preferences for food, water, mates, prey, companions, tastes, etc.
In humans,
Δ
A
i
also varies with personal interests, culture and genes.
38Slide39
Sensitivity to Delay
The effect of delay on reinforcement value as reflected in performance was modeled early on by Chung and Herrnstein (1967), Anslie (1974) and Fantino, Abarca and Dunn (1987) The value of a reinforcement instance, ΔA
i
, is measured with respect to changes in the time
Change in time is measured from the instance of the reinforcer to the choice, is Δti.Now if the ratio of the differences, value, Δ
A
i
with respect to time, Δ
d
i
,
is taken
One gets the Commons/Mazur additive noise model (Commons, Woodford & Duchney, 1982; Mazur, 1987) shown immediately below.
This is a slightly revised version of Commons/Mazur,
V
is replaced by ΔV because Ai has been replaced by ΔAi in equation 2. 39Slide40
Sensitivity to Delay Equation 2
ΔV = ΔAi /(1+ k1d) = Discounted value of a reinforcer
i
(2)
d = Δt – 1 delay equals change in time minus 1.Δt
= Change in time.
Note that for
t
= 1, reinforcement is not delayed i.e.,
d
= 0.
j
= is an index of which difference equation it is.
j
=
1 value; j = 2 is delay, j = 3 is riskk2 = is for sensitivity to delay Consider the case of ΔAi /(1+ k2d) with d = 0, no delayThis makes 1+ k2d = 1, then ΔVi = ΔAi 40Slide41
In contrast, taking the long view, means being relatively insensitive to delay
It should be reflected in a small value for k2, the delay parameterTo successfully address high order of complexity scientific tasks, one has to have long term goals that allow for a large delay of reinforcementMost discoveries take multiple years to achieve.
41Slide42
Sensitivity to Change in Delay
Here risk is represented by how sensitive an individual is to a change in delay, usually increases in delay.This is the quantification of Vaughan’s (1976; 1981; Herrnstein & Vaughan 1980) melioration concept (also see Herrnstein, & Prelec, 1991). This is represented by taking the differences with respect to changes in time in the second
difference equation, Commons/Mazur equation 2:
This would be Δ(Δ
Ai/ Δd)Δd = Δ(Δ
A
i
/(1+
k
3
d
))/Δ
d
(3)
k
3 = is sensitivity to risk, the change in value with respect to change in delay42Slide43
43
There is no theory describing discounting of reinforcement that integrates
Different length samples from a schedule
Schedules themselves
First and second difference equations of value with respect to time
Our unified theory integrates
Initial value of outcomes
Delayed values
Risk
Results from samples may suffice to characterize entire schedules Slide44
44
Samples and Schedules
Schedules are a sequence of samples
When the number of instances per sample is low, the values of the instances in a sample simply add
But when the number of instances per sample gets large, then process of addition breaks down and memory starts to fail causing value to be under estimated
Within a sample, the values of the instances differ
The further an instance is from choice, the less important the contribution
Samples of increasing numbers of instances reach an asymptotic representation of the entire scheduleSlide45Slide46
46
Procedure
Many studies have measured discrimination between reinforcement densities (e.g. Commons, 1979, Commons, 1982)
A sample presents five possibilities for reinforcement for pecking- four on the center key and one on the left or right keys
The center key pecks are reinforced on either a rich or a lean schedule
Each center key peck during a cycle had a certain probability of reinforcement
Rich schedules had a 0.75 probability, and lean schedules had a 0.25
After the cycles in a sample, pigeons pecked either a left or right key
A right key peck was reinforced if the sample was a rich schedule, and a left key peck was if the sample was a lean schedule
A small number of probe trials consisted of randomly assigned instances in which the length of time of an instance increased by certain factors
The multiples were 2 or 3 for pigeons 30, 84, 102 and 995Slide47
47
Results
The first three figures show how the pigeons dealt with delay
Figure 2 shows that the perceived value of reinforcers adds
It also shows pigeons are mostly sensitive to relative rates of reinforcement
Figure 3 also shows support that relative rate of reinforcement as an explanation for what controls choice
Pigeons estimated a sample as being less rich when there were temporary increases in time between possible reinforcers
Figure 4 shows reinforcers were discounted hyperbolically
Figure 5 show relatively little discounting over absolute timeSlide48
48
Reinforcer Values Simply Add
Figure 2 shows the effects of delay
The first difference equation of value
The
perceived richness of the sample is on the y-axis
Number of reinforcers in the sample are on the x-axis
With the probe multiple as one, the number of reinforcers predict choice
The perceived value of the reinforcers simply add together
As probe multiple increases, the slopes decrease
When the cycle length is doubled, reinforcers are valued around half as much
This is because
pigeons are mostly sensitive to relative rates of reinforcement
Pigeons are effectively insensitive to timePigeons from Commons, Woodford and Trudeau 1991Figure 2: The perceived value of a samples is plotted against the number of reinforcers in the sample. Circles represent cycle lengths of two seconds, triangles three and squares four. As one can see, the cycle length has very little effect. Slide49
49
Figure 3 shows risk
Risk is the second
difference equation
of value with respect to time
Slopes from linear regression of perceived value versus number of reinforcers Figure 2 were plotted against the multiple of cycle of time
The red lines represent the expected slope of the perceived values as a function of the multiple values
High r-values and the close fit to the predicted slope support relative rate of reinforcement as an explanation for what controls choice
Second
difference equation
of Value: Momentarily Increasing Cycle Time Had a Large Effect on Perceived Risk
Figure 3: The slopes from Figure 2 are plotted against the probe multiples. Bird 102 is excluded because its slopes were negative and thus incompatible with hyperbolic regression.
Pigeons estimated a sample as being less rich when there were temporary increases in time between possible reinforcers
This is because the pigeon have learned that previous samples’ reinforcers are packed more densely
Closer together in timeSlide50
50
The First Difference
Equation
of Value
The data are from pigeons 27, 29, 31 and 85 (Commons 1979)
There was just one reinforcer in the sample to be discriminated
On the x-axis, the number of cycles between the single reinforcer in the sample and choice. This is delay
The y-axis shows the perceived value of the sample as rich (Probit transformed)
This result provides empirical evidence for Commons/Mazur’s Equation
Commons and Mazur predict hyperbolic discounting over time
Reinforcers closer to choice will be valued significantly more than those far from choice (Commons, Woodford & Ducheny, 1982; Mazur 1987)
This decreasing hyperbolic function is a negative power function
Figure 4: The perceived value of a sample is plotted against the distance in number of cycles that reinforcer is away from the choice period.Slide51
51
Testing The Second Difference Equation Of Value: Possible Contributions To Perceived Risk
Perceived risk as represented by the slopes from linear regression of perceived value versus number of reinforcers
The possible contributions were examined to perceived risk by
Probe multiple
Cycle length
Total time = Probe multiple * Cycle length in seconds
For probes, the
r
(178) = .864,
p
= .000
Cycle length had no systematic effect on perceived risk,
r
(178) = -.033,
p = .660Total time was very collinear with both probe multiple and cycle length as would be expected Therefore with probe, cycle length and total time, the r(176) = .868, p = .000, an insignificant change Slide52
52
Conclusion
A unified theory of value, its time difference equations, and their effects on discounting were found to describe the data
The theory also accounts for the difference equations of value with respect to delay, risk and change in risk
The assumptions were rather simple
Individual events were shown to be processed with respect to a background rate of reinforcement
The value of these events was shown to be simply summated after discounting
A set of experiments tested the theory
The experiments supported additivity, hyperbolic discounting for the first difference equation, control by relative rates, and risk as a second difference equation.
A time based model rather than a probability based utility model may reflect how organisms perceive reinforcers delivered over timeSlide53
53
There are other possible formulations for discounting both the simple delay and of risk
Studies with more cycles need to be run
We have to formulate why the
k
i
are differentSlide54
3. An Integrative Account of Stage and Value as Determinants of Action
MICHAEL LAMPORT COMMONS (Harvard Medical School) Abstract: Accounts of stage and moral action have not integrated behavioral, developmental and quantitative paradigms. This presentation integrates the three by using a mathematical model of value obtained from developmental action and from stage, as in the Model of Hierarchical Complexity. The result is a behavioral-developmental account of stage and action, rather than a mentalistic one. Both value and stage are necessary for determining actions. Each consists of a matrix. The Value matrix has a number of vectors. For humans, there are 6 Holland Code variables in the value vector. The second vector is discounting-difference ratio between change in the overall value vector and change in time. The third vector is the change in differences in value over time, or risk. The second matrix is Stage, which measures performance in meeting difficulties produced by the order of hierarchical complexity of particular tasks, as discussed in the earlier talks. A mathematical account of the value and the stage matrices and their interaction terms are used to predict moral behavior. Example from predicting forensic expert bias and from peddlers income based on the order of hierarchical complexity will be given.
54Slide55
3. How Stage and Value can be Incorporated to Predict Behavior
Michael Lamport CommonsHarvard Medical SchoolCommons@tiac.netTimothy Barry-Heffernan
Harvard University
timothy.barryheffernan@gmail.comSlide56
Introduction
This presentation is about a behavioral-developmental account of stage and action that integrates the three paradigmsBehavioral paradigmDevelopmental paradigmQuantitative paradigmA mathematic technique for predicting an organism’s behavior would be extremely valuable and widely applicable to a range of organisms and behaviors
Such predictions may variabilize diagnosis in mental illness, replacing symptom based
diagnoses
Prediction by the technique that follows relies only on proper weighting of various scoresDifficulty of tasks accomplishedPreference for outcomes of tasks accomplished in terms of
Overall value in a domain
Discounted value
Risk
56Slide57
Implications of a Stage and Value Model to Predict Behavior Personality Disorders
A theory of personality disorders:Personality disorders may be rooted in low social perspective-taking skill and an inappropriate estimation of discounted value and of riskThe two categories of people with personality disorders (i.e. SAD, and BAD) fit this ruleMAD should be on the spectrum of the psychotic disorders
A psychopath, from the BAD category, may imitate a high stage of behavior and may
Overestimate the loss of value due to delay of reinforcement
Underestimate risk in their own behaviorPsychopaths may consequently appear unemotional and apatheticSlide58
Implications of a Stage and Value Model to Predict Behavior Personality Disorders
People with autism spectrum disorders do not read emotions or gestures from other peopleConsequently do not value these thingsPeople with borderline personality disordersFeel abandonedFear more abandonment, thus overvaluing “companionship”
People with SAD disorders have been beaten down over a period
They have developed methods of coping like compulsions
Dependent personalities are megalomaniacs who value abuse as attentionSlide59
Implications of a Stage and Value Model to Predict BehaviorSelections for Employment
A model that predicts successful task completion would be applicable to the workplaceOne could determine who is fit to work at what position by means of a test or by means of observation and mathematic evaluationSince this model takes into account ability, motivation, difficulty and reinforcement, it is applicable to numerous scenarios
P
articularly, careersSlide60
Purpose and Outline of Paper
The purpose of this paper is to examine the interplay of Model Hierarchical Complexity derived stage scores and valuation of reinforcers in predicting behaviorTheoretical mathematics will be used acquire a “Behavior Matrix” This matrix will predict the likelihood of successful task accomplishment in an experiment where
j
types of reinforcers are administered i times
To predict behavior reasonably, one must consider:
Delay
Risk
An organism’s predisposition to different forms of reinforcement
A reinforcer’s value in different domainsSlide61
First Step: Acquiring a Preference Column Matrix
Any prediction must begin with valuation Valuation is rooted in value
Suppose all
n
categories in which reinforcement is valuable were indexedCategories would include:
Basic biological ones
Food
Sex
Other areas in which an organism’s behavior may be reinforced
Ones related to interest as measured by the Holland scales
Realistic
- practical, physical, hands-on,
tool-oriented
Investigative
- analytical, intellectual, scientific, explorativeArtistic - creative, original, independent, chaoticSocial - cooperative, supporting, helping, healing/nurturingEnterprising - competitive environments, leadership, persuadingConventional - detail-oriented, organizing, clericalSlide62
First Step (continued): Acquiring a Preference Column Matrix
A scalar Qi expresses an organism’s valuation of a specific form of reinforcer
i.e
.
A food-deprived bear would have a high value in the food categoryWe assign to an organism a column matrix, or vector [Q
], which contains scalar numbers {
Q
1
, Q
2
,…Q
n
}
Each scalar corresponds to the organism’s preference for the corresponding form of reinforcementSlide63
Second Step: Acquiring a Reinforcer Value Matrix
Take a reinforcer, and associate with it a row matrix, or dual space map [P]Matrix expresses the reinforcer’s value in different domains, with the same n domains as ordered in the column matrix [
Q
]
[P] contains real numbers {P1, P2,… P
n
}, where each number expresses the reinforcer’s value in a particular domain
P
i
and
Q
i
refer to the value and valuation, respectively,
in the same domain
i
i.e. A piece of meat would have a high food value to a food-deprived bear, and very low values in other domainsSlide64Slide65Slide66Slide67Slide68
Fifth Step: Acquiring a Proxy for Likelihood of Successful Completion
Difficulty must be accounted for if one is to successfully predict whether an organism will complete a taskOne can express the likelihood of completion of a reinforcer’s corresponding task with its degree of difficulty, task’s order of hierarchical complexity
OHC
ij
The weighting technique depends on the sensitivity of the behavior prediction one intends to obtain
An example difficulty measure is the task’s order of hierarchical complexity
;
equals a task’s order of hierarchical complexity.
One can estimate the likelihood of successful completion by dividing an organism’s weighted stage score,
u
, by the weighted degree of difficulty of the task
Slide69Slide70
Conclusion and Thoughts on Testing
To test the model, data need to be obtained from people varying in personal interestsPersonal interests may be represented by factor scores obtained from the Holland factors
In a test of the model, discounting would be measured by a perceived value experiment in which the length of delay would be varied on probe trials
In the case where behavior may be related to task completion for reinforcement, it should be possible to predict behavior mathematically with the methods just outlined
The variables mentioned in the presentation are defined loosely so that one can apply the technique for predicting behavior in a broad contextSlide71
Works CitedCommons, M. L. (1979).
Decision rules and signal detectability in a reinforcement-density discrimination. Journal of Experimental Analyses of Behavior, 32, 101-120.Commons, M. L. & Pekker, A. (In preparation). A New Discounting Model of Reinforcement, under review.
Commons, M. L., Woodford, M., & Ducheny, J. R. (1982).
How Reinforcers are Aggregated in Reinforcement-Density Discrimination and Preference
Experiments.Commons, M. L., Woodford, M., & Trudeau, E. J. (1991). How Each Reinforcer Contributes to Value: "Noise" Must Reduce Reinforcer Value Hyperbolically
.Slide72
4. How Stage and Value Explain the Morally Questionable Basis Expert Witnesses
This paper is an empirical study where it is shown that the stage of behavior required by a situation is related to perceived biasing of a situation. When experts are hired to give an opinion in a court, for example, the ideal is that they be unbiased when issuing their option. In the current study, forensic experts were asked to what extent various situations that experts might find themselves in could cause the resulting opinions of the expert to be biased. This paper is an empirical test of part of the stage and value model, because it uses the hierarchical complexity of the items to empirically predict moral action. In addition, the degree of bias that was perceived and the stage requirements of the items that reflected perceived bias are related. The moral question is, how do expert witnesses perceive the possible biases of their fellow expert witnesses? Participants, who were attendees at a workshop at the American Association of Psychiatry and the Law, were asked to rate for their biasing potential a number of situations that might affect the behavior of an opposing expert. A Rasch Analysis produced a linear scale as to the perceived biasing potential of these different kinds of situations from the most biasing to the least biasing. Working for only one side in both civil and criminal cases had large scaled values, which means that they were seen as highly biasing; they were also the first factor in a factor analysis. In interesting contrast, a) an opposing expert also serving as the litigant's treater and b) an opposing expert being viewed as a "hired gun" (supplying an opinion only for money) were two situations viewed as not very biasing. In a regression analysis, the order of hierarchical complexity of an item predicted the perceived bias of the items from the 1st, 2nd and 3d factors.
72Slide73
How Do Forensic Expert Witnesses Perceive The Possible Biases Of Their Fellow Expert Witnesses?
Patrice Marie Miller, Ed.D.Thomas Gordon Gutheil, MD Michael Lamport CommonsHarvard Medical SchoolSlide74
Expert witness is a person with education or training in his or her area of expertise and whose opinion is regarded to be worthy rely upon in a legal case
The objectivity that an expert witness brings to the legal system is the most valued quality of an expertOne of the most challenging but necessary ideals for expert witnesses to uphold, therefore, is dealing with “expert bias”
Expert bias
is seen as a deviation from the “ideal” neutral balanced assessments, judgments and the like
74Slide75
In our previous work on expert bias, we showed that expert witnesses in our survey perceived the existence of a good deal of such bias
Perceived bias here is operationally defined as how strongly biasing the study participants found certain situations to beThis did allow a conclusion that some situations were perceived by experts to be actually more biasing than others, but there was no way to ascertain specifically how much more or how much less biasing each situation was perceived to
be
75Slide76
The purpose of the current study is to find out how potentially biasing each of the situations is perceived to be on a ruler-like scale that jurors may readily understand, using a technique called Rasch analysis
We hoped that forensic experts might benefit from being informed as to the perceived degree of seriousness of various biasing situationsWith such information, forensic experts can consider altering their own behavior and/or informing the jury of the seriousness of biases which the other side may hold
76Slide77
46 participants
81.4% (35 out of 43) M.D.’sThe average number of years in forensic practice were 11.34 (SD = 9.32)
Annual number of forensic cases was 48.82 (SD = 79.07)
Data was analyzed using Rasch Analysis
77Slide78
The Model of Hierarchical Complexity classifies
tasks as to their complexityA task action is defined as more hierarchically complex when the higher order action:
Is defined in terms of two or more actions from the next lower order
Organizes these lower-order actions
Organizes these lower-order actions
78Slide79
A task is at a higher order if:It is defined in terms of two or more lower order task actions
It organizes lower order task actionsThis organization is non-arbitrarySlide80
Instrument
In a questionnaire, subjects were asked to think of recent cases in which they had served as expert witnesses as they answered the questions
These
snipids
from the cases were rated on six point
scales as to how biasing they were
The
first series of queries,
were on the
issue of an expert’s influence on case outcomes and the subjects’ emotional reactions to those outcomes
Next
series of queries asked subjects to identify potentially biasing factors, from least biasing to most biasing, such as money, prestige, high profile cases, etc.
The
final series of queries focused on expert attitudes towards bias and biasing factors, such as money, prestige, high profile cases
The majority of questions were asked in regards to
“opposing experts” 80Slide81
Rasch Analysis Ranked Factors That Participants Rated As Potentially Biasing
The most biasing situations:The frequency with which a respondent will turn down cases that evoke personal discomfort (Rasch score -1.55)
Certain expert witnesses testified consistently for
Only
one side (e.g. plaintiff-only civil-case, -.89;
Prosecution-only criminal-case -.87
Defense-only
criminal-case, -.
83
Defense-only
civil-case, -.
79
81
Order
n + 2Action 1Order n + 1 Action 1Order n + 1Action 2Order nAction 1Order nAction 2Order nAction 3Order nAction 4Order n + 2Action 1Order n + 1 Action 1
Order n + 1Action 2Order nAction 1Order nAction 2Order nAction 3Order nAction 4Slide82
The least biasing situations:
The opposing expert had been the examinee’s treater (1.99)The respondent had assessed the expert witness on the opposite side to be a hired gun (1.6)Respondents’ assessment of their own degree of happiness in a given case in which they had testified “appropriately,”
but that side of the case lost with a probably unjust outcome "Possibly unjust outcome" as used in the instrument may itself be subject to interpretation bias (.97
)
82Slide83
Situations that do not fit:
The respondent was asked whether they had ever decided to take action after concluding that an expert witness on the side opposite from the respondent's had acted unprofessionally during the course of a case
83Slide84
Stage Of Pricing Strategy Predicts Earnings:
A Study Of Informal EconomicsLucas A. H. Commons-MillerHudson Fernandes GolinoMichael Lamport Commons
Dare Institute
Universidade Federal de Minas Gerais
Harvard Medical SchoolSlide85
Abstract
This is the first cross cultural study of stages of development on economic tasksStudying informal economies across cultures allows us to test the stage of pricing strategies used by people of varying levels of education ranging from no schooling to completion of college, and at different stages of development ranging from primary operations to meta-systematic
We found that the hierarchical complexity of their pricing strategies correlated with how much they earned and the assets they accumulatedSlide86
Method
Interviews of 51 peddlers and carters were conducted:33 (64.7%) were from Rio De Janeiro and Belo Horizonte, Brazil.18 (35.3%) were in Richmond, California, and Dorchester, Massachusetts
There were 35 (68.6%) who were male
There were 14 (27.5%) who were female.
The gender of two subjects was not recorded (3.9%)
Participants ages ranged from 17 to 85 with M = 47.1 (SD = 14.13)Slide87
Procedure
Participants were asked questions such as: “How do you set your prices”“Do you earn more now than you did in the past”“Do you know what others charge?
Participants were also asked questions about their health and habits and some data was inferred by the experimenter through observationSlide88
Pricing Strategy Scoring Manual
At the Primary stage, peddlers do not control their pricesEither someone sets the price for them
Or they take whatever someone offers
At the
Concrete stage, they set their price by adding an amount to the price they paid, or by negotiating with the buyerAt the
Abstract stage,
they set their prices based on norms
They know what others are charging and they match or beat that price
At the
Formal stage
, they set prices based on a proportional markup
They add a proportion of what they paid for the goods to the price.
Most people who employ this strategy use numerical percentages
One participant had a formal concept of proportionality based on magnitude and estimationSlide89
Pricing Strategy Scoring 2
At the Systematic stage, people use multiple factors to set prices. They usually have a marketing strategy
They understand how the markets they sell in work
They especially understand about the markets in which they trade
At the
Metasystematic stage
, pricing strategies involve being able to compare and choose between different business models
The one metasystematic performing participant, did not sell his wares on the street, he traveled from city to city
He had a complex business model
He understood what niche of the jewelry industry his business was fillingSlide90
Results
Stage Country Education Earnings Category Stage r
1 .196 .258 .506(**)
Sig. (2-tailed) . .182 .091 .000
N 48 48 44 45
Country
r
1 .575(**) .581(**)
Sig. (2-tailed) . .000 .000
N 51 45 45
Education
r
1 .568(**)
Sig. (2-tailed) . .000
N 45 41
Earnings Category 1Sig. (2-tailed) . N 45 ** Correlation is significant at the 0.01 level (2-tailed)Slide91
Results
In the correlation analysis Stage alone predicted earnings significantly r = .506fig. 1: earning category by stage
Stage, however, did not perform much differently than the other two predictors on their own, and this difference was not significant:
Country:
r = .581Education:
r = .568
7
8
9
10
11
12
Stage
1
2
3456
E
a
r
n
i
n
g
C
a
t
e
g
o
r
i
e
s
1= 0-4 $ p/day
2= 4-16 $ p/day
3= 16-64 $ p/day
4= 64-256 $ p/day
5= 256-1024 $ p/day
6= 1024-4096 $ p/day
Earnings Categories:Slide92Slide93Slide94
Results
Model
Unstandardized
Coefficients
Standardized
Coefficients
t
Sig.
Collinearity Statistics
B
Std.Error
Beta ToleranceVIF
1Constant-2.4071.105 -2.178.036 Stage.388.122.367
3.192
.003
.930
1.075
Country
.881
.339
.353
2.601
.013
.667
1.499
Education
.254
.130
.270
1.961
.057
.647
1.544
A multiple linear regression of the 3 main predicting variables, Stage, Country, and Education showed that while all three predicted earnings, with an
r
value of:
r
(37) = .738,
p
= .000
Stage was a little better than the other two factors
;
the betas of were:
β
=
.
367
(Stage)
β
=
.
353
(Country)
β
=
.
270
(Education)
The multiple regression is shown in the table below (
Fig. 6
)Slide95
Discussion
The stage of pricing strategy predicted earningsIt did so better than the other two main variablesCountry
Education
The
r = 575
between country and education probably indicates that it is easier to obtain an education in the United States than in Brazil
This shows some co-linearity
Stage, country and education all predicted earnings slightly better than stage alone
Country predicted education
Country and education did not predict stage
This further supports that stage was the main predicting factor in earnings
This is the first study showing a stage effect in behavioral economics
This is further evidence that the stage is applicable in a number of fields and across culturesSlide96
96