A Model of Stage and Value to
Predict Behavior
Michael Lamport Commons
Harvard Medical School
Commons@tiac.net
Presented to the Department of Psychology, University of Minho
Thursday, July 4th, 2012, Braga, Portugal
© 2012 Dare Association, Inc., Cambridge, MA
1. Measuring the A Priori Difficulty of a Task
Contingency Using Order of Hierarchical Complexity
• The Model of Hierarchical Complexity is a quantitative behavioraldevelopmental theory that suggests an objective way of determining the a
priori difficulty of a task's contingencies. The model explains why stagelike 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).
2
1. Measuring the A Priori Difficulty of a Task
Contingency Using Order of Hierarchical
Complexity
Michael Lamport Commons
3
The Model of Hierarchical Complexity
• The Model of Hierarchical Complexity is a quantitative
behavioral-developmental theory
• It 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 of Hierarchical Complexity
• Behavior can be analyzed by the difficulty of tasks that an
individual successfully address
• We 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 complexity
– Commons’ 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 complexity
 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 actions
• This organization is non-arbitrary
16 Orders of Hierarchical Complexity
Order
Name Complexity
8
Concrete
0
Calculatory
9
Abstract
1
Sensory & Motor
10
Formal
2
Circular Sensory-motor
11
Systematic
3
Sensory-motor
12
Metasystematic
4
Nominal
13
Paradigmatic
5
Sentential
14
Crossparadigmatic
6
Preoperational
15
Meta
Crossparadigmatic
7
Primary
7
The Model of Hierarchical Complexity
• Task sequences form a hierarchy from simpler to more
complex
• Task-Performance should always follow that certain
(developmental) order
• Under the above conditions, development occurs in stages
reflecting the necessity to coordinate lower level action
Empirical Studies
• The Model of Hierarchical Complexity 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 usually Preoperational order 6 up to
Metasystematic order 12
• Tasks were generated in several domains
– Reinforcement contingencies (economic)
– Mathematical, scientific
– Moral, political, and social domains
The Laundry Instrument
 The Laundry Instrument consists of isolation of Variable
problems
– Inhelder and Piaget (1958) developed the pendulum and chemicals
tasks
• Participants 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 questions
Laundry Instrument Example:
Abstract Order 9
• This is the first order in which
participants are required to see what
the operative variable is
Laundry Instrument Example:
Formal Order 10
• Higher order
problems added
more ingredients to
the mixture
• Also make
deduction more
difficult by
including many
more possible
operative variables
• They also included
multiple possible
relationships among
the variables such as
And/Or scenarios
The Laundry Instrument
Participants
• 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 studies
• Here, we will briefly describe
– The characteristics of each separate sample
– The 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
Subsample 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
The Laundry Instrument
Procedure
• Participants filled out the questionnaires either on paper or online
• The 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 data
Rasch Model
• Under the Rasch model these linear measures are
– Item-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 variables
– Sum 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 measure
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 reversals
– No 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
•
•
•
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
instruments
Item Stage Score Versus Item Order of
Hierarchical Complexity
r2
= .804
• The item stage score
plot shows how the
items performed
– Items with a
hierarchical complexity
of 10 would be expected
to have a stage score of
10
• This plot shows that
this trend is followed
Social and Behavioral Tasks
 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 person
– Each vignette represented each order of Hierarchical Complexity
20
Helper-Person Problem

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 Helper
Figure 2a. Method
Figure 2b. Inform
Figure 2c. Guide
21
Politician-Voter Problem
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 Politicians
Figure 3a. Method
Figure 3b. Inform
Figure 3c. Vote
*** Each data point represents an average of all 3 items at each stage***22
Item Order of Hierarchical Complexity Predicted
Item Rasch Scaled Scores
•
•
•
•
•
•
Helper-Person
Politician-Voter
Anti-Incest Reporting
Anti Death Penalty
Pro Death Penalty
Jesus Stoning Dilemma
r(3) = .967, r(3) = .978, r(3) = .973
r(3) = .920, r(3) = .895, r(3) = .900
r(3) = .898, r(3) = .850, r(3) = .834
r(3) = .854, r(3) = .801
r(3) = .849, r(3) = .758, r(3) = .875
r(3) = .539, r(3) = .564
• The measured difficulty reflects the theoretical difficulty
• (Order of hierarchical complexity)
23
**Overall
Figure 9a. Overall
Best
Figure 9b. Helper-Person
Inform
Next Best
Figure 9c. Politician-Voter
Inform
24
Summary
• The Model of Hierarchical Complexity measures the a priori
difficulty of tasks, a new approach to Behavioral
Developmental Analysis
• Empirical studies show that the
– Order 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 development
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 = Σvi 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
= ΣΔAm. The value of an instantaneous reinforcer is ΔAm. 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
Vi (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.
26
2. Can Perceived Value Be Explained
by Schedules of Reinforcement?
Nicholas Hewlett Keen Commons-Miller, Tufts University
Michael Lamport Commons, Harvard Medical School
Robin 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 University
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 reinforcement
Delayed 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 nonoccurrence 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
28
Issue This Research Resolves
This presentation addresses five unresolved issues that should
allow for an integration these issues
1. To relate the micro to the molecular what needs to be known is
how well do samples from schedules approximate the overall
schedules
2. The integration should also to address what events from the
micro analysis are accumulated, and how
3. Do reinforcers, after being discounted, simply add together?
4. Is a pigeon’s perception of the discounting of value based on
relative rates of reinforcement and delay of reinforcement?
5. 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?
29
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
30
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?
31
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, SR+, 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 (SR+) of a sample of equal probability possible reinforcer
events at instances, i, is the product
EV = Σip(SR+) * Vi (SR+)
i = the instance being examined;
(1)
Vi(SR+) = value of reinforcer, SR+ , i;
p(SR+) = probability of obtaining a reinforcer immediately after time i
32
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, Vi , at instance i.
• This has been a general tenet of both older and even more
modern learning theories
• Our model goes beyond this simple formulation to show that
how an organism assigns value is also a function of other
parameters
33
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 time
34
• Commons-Miller et al. (2010) proposed a model for choice
that includes three variables, and their associated parameters
• The first variable is reinforcement
– Its associated parameter is sensitivity to reinforcement.
• The second variable is delay
– Along with its associated parameter, sensitivity to delay
• There is risk and sensitivity to risk
35
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.
• Am = ΣΔAm (1)
36
• 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:
o m = the mth delivered reinforcer in a sequence of reinforcing events
• ΔA1, > ΔA2, > ΔA3 .... > 0
37
Total Value
• The total value, Am , is the total value of all the reinforcers
delivered with no delay
– When total satiation has occurred and ΔAi 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, ΔAi also varies with personal interests, culture and genes.
38
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, ΔAi, 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, ΔAi with respect to
time, Δdi, 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.
39
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 risk
• k2 = is for sensitivity to delay
• Consider the case of ΔAi /(1+ k2d) with d = 0, no delay
• This makes 1+ k2d = 1, then ΔVi = ΔAi
40
• In contrast, taking the long view, means being relatively
insensitive to delay
• It should be reflected in a small value for k2, the delay
parameter
• To successfully address high order of complexity scientific
tasks, one has to have long term goals that allow for a large
delay of reinforcement
• Most discoveries take multiple years to achieve.
41
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(ΔAi/ Δd)Δd = Δ(ΔAi/(1+ k3d))/Δd (3)
• k3 = is sensitivity to risk, the change in value with respect to
change in delay
42
• 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
43
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 schedule
44
Procedure
• Many studies have measured discrimination between reinforcement
densities (e.g. Commons, 1979, Commons, 1982)
• A sample presents five possibilities for reinforcement for peckingfour 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 995
46
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
time
47
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
Figure 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.
Pigeons from Commons,
Woodford and Trudeau 1991
•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
time
48
Second difference equation of Value: Momentarily Increasing Cycle
Time Had a Large Effect on Perceived Risk
•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
Figure 3: The slopes from Figure 2 are plotted against the probe multiples.
reinforcement as an explanation for what
Bird 102 is excluded because its slopes were negative and thus
incompatible with hyperbolic regression.
controls choice
•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 time
49
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.
50
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 = .660
• Total 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
51
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 time
52
• 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 ki are different
53
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.
•
•
•
54
3. How Stage and Value can be Incorporated
to Predict Behavior
Michael Lamport Commons
Harvard Medical School
Commons@tiac.net
Timothy Barry-Heffernan
Harvard University
timothy.barryheffernan@gmail.com
Introduction
• This presentation is about a behavioral-developmental account of
stage and action that integrates the three paradigms
– Behavioral paradigm
– Developmental paradigm
– Quantitative paradigm
• A 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 scores
– Difficulty of tasks accomplished
– Preference for outcomes of tasks accomplished in terms of
• Overall value in a domain
• Discounted value
• Risk
56
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 risk
– The two categories of people with personality disorders (i.e. SAD, and
BAD) fit this rule
– MAD 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 behavior
– Psychopaths may consequently appear unemotional and apathetic
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 people
– Consequently do not value these things
• People with borderline personality disorders
– Feel abandoned
– Fear 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 attention
Implications of a Stage and Value Model to Predict Behavior
Selections for Employment
• A model that predicts successful task completion would be
applicable to the workplace
– One could determine who is fit to work at what position by means of a
test or by means of observation and mathematic evaluation
• Since this model takes into account ability, motivation,
difficulty and reinforcement, it is applicable to numerous
scenarios
– Particularly, careers
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 behavior
 Theoretical 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 domains
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 indexed
− Categories 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, explorative
Artistic - creative, original, independent, chaotic
Social - cooperative, supporting, helping, healing/nurturing
Enterprising - competitive environments, leadership, persuading
Conventional - detail-oriented, organizing, clerical
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 category
• We assign to an organism a column matrix, or vector [Q],
which contains scalar numbers {Q1, Q2,…Qn}
– Each scalar corresponds to the organism’s preference for the
corresponding form of reinforcement
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,… Pn}, where each number expresses
the reinforcer’s value in a particular domain
– Pi and Qi 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 domains
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 task
 One can express the likelihood of completion of a reinforcer’s
corresponding task with its degree of difficulty, task’s order of
hierarchical complexity OHCij
− 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
Dij = OHCij; OHCij 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
Conclusion and Thoughts on Testing
 To test the model, data need to be obtained from people
varying in personal interests
− Personal 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 context
Works Cited
• Commons, 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.
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.
72
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 Commons
Harvard Medical School
 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 expert
 One 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
74
 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 be
 This 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
75
 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 situations
 With 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
76
 46 participants
‒ 81.4% (35 out of 43) M.D.’s
‒ The 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
77
 The Model of Hierarchical Complexity classifies tasks as to
their complexity
 A 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
78
 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 actions
• This organization is non-arbitrary
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”
80
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
 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)
82
 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
83
Stage Of Pricing Strategy Predicts
Earnings: A Study Of Informal
Economics
Lucas A. H. Commons-Miller
Hudson Fernandes Golino
Michael Lamport Commons
Dare Institute
Universidade Federal de Minas Gerais
Harvard Medical School
Abstract
• This is the first cross cultural study of stages of
development on economic tasks
• Studying 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 metasystematic
• We found that the hierarchical complexity of their pricing
strategies correlated with how much they earned and the
assets they accumulated
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)
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 observation
Pricing Strategy Scoring Manual
• At the Primary stage, peddlers do not control their prices
– Either 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 buyer
• At 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 estimation
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 filling
Results
Stage r
Sig. (2-tailed)
N
Country r
Sig. (2-tailed)
N
Education r
Sig. (2-tailed)
N
Earnings Category
Sig. (2-tailed)
N
Stage
1
.
48
Country
.196
.182
48
1
.
51
Education
.258
.091
44
.575(**)
.000
45
1
.
45
Earnings Category
.506(**)
.000
45
.581(**)
.000
45
.568(**)
.000
41
1
.
45
** Correlation is significant at the 0.01 level (2-tailed)
Results
•
•
In the correlation analysis
Stage alone predicted earnings
significantly r = .506
– fig. 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 = .581
– Education: r = .568
E
a
6
r
n
5
i
n
g
4
C
a
3
t
e
g
2
o
r
Earnings Categories: 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
1
i
e
s
7
8
9
10
Stage
11
12
Results
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)
Unstandardized
Coefficients
Mode
l
1
B
Constant
Stage
Country
Education
Std.Error
-2.407
1.105
.388
.122
.881
.254
Standardized
Coefficients
Beta
Collinearity Statistics
t
Sig.
Tolerance
VIF
-2.178
.036
.367
3.192
.003
.930
1.075
.339
.353
2.601
.013
.667
1.499
.130
.270
1.961
.057
.647
1.544
Discussion
• The stage of pricing strategy predicted earnings
– It did so better than the other two main variables
• Country
• 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 cultures
96