lydia l. chen instructor: robert axelrod ps793 – complexity theory 30-jan-16 jan-16 lydia l. chen...

Lydia L. ChenInstructor: Robert AxelrodPS793 – Complexity Theory

May 3, 2023

05/03/23 Lydia L. Chen <[email protected]>

Seeking Consistent StoriesSeeking Consistent StoriesBy Reinterpreting or Discounting Evidence: By Reinterpreting or Discounting Evidence:

An Agent-Based Model^An Agent-Based Model^

CSCN Presentation

05/03/23 Lydia L. Chen <[email protected]> “Seeking Consistency” - 2

AgendaAgenda

1. The Phenomenon2. Agent-Based Model (ABM) Primer3. The Model4. Sample Run5. Experiments


Research InterestsResearch Interests Goal: psychology, law, computational modeling

persuasion and decision making

law classes => persuasion techniques storytelling narrative coherence metaphors

Story model of jury decision making (Pennington & Hastie, 1986)


Real-Life Scenario: Bench TrialReal-Life Scenario: Bench TrialProsecution () Defense Lawyer

“Guilty!

”“Innocen

t!”


Sequential Evidence – What’s NormativeSequential Evidence – What’s Normative

Evidence 1

…

Evidence 2

Evidence 3

Evidence N

Official Deliberatio

n

Story/ Verdict


Empirical Literature on JDMEmpirical Literature on JDM Form “coherent” stories that support option/verdict

(Pennington & Hastie, 1988) Confidence in option/verdict increases with “coherence”

(Glockner et al., under review) Decision threshold: “sufficiently strong” (supported by many

consistent evidence) or “sufficiently stronger” than other stories (review by Hastie, 1993

Narrative coherence: consistency causality completeness

“Consistency” aspect of “good” stories consistency between evidences in a story consistency of evidence with favored story


Example Case (Pennington & Hastie, 1988)Example Case (Pennington & Hastie, 1988)

Scenario: Defendant Frank Johnson stabbed and killed Alan Caldwell Evidence := facts or arguments given in support of a story/verdict

Facts— “Johnson took knife with him” ; “Johnson pulled out his knife” Arguments—”Johnson pulled out knife because he wanted revenge” vs. “Johson pulled

out knife because he was afraid”

Story := set of evidence supporting a given verdict Same evidence can be framed to support multiple verdicts/stories!

P DDesired Verdict

“Guilty” “Innocent”

Story “Premeditated murder”

“Self-defense”

Interpretation of Evid

“Johnson was angry”

“Johnson was afraid”


Sequential Evidence – More DescriptiveSequential Evidence – More Descriptive

Evidence 1

Compare, Deliberate, Interpret

…

Evidence 2

Evidence 3

Evidence N


n

Story/ Verdict

Premature Story/

Verdict @ Evid n < N

(Brownstein, 2003; Russo et al., 2000)


How People Deal with Incoming EvidenceHow People Deal with Incoming EvidencePeople don’t just take evid @ face value, but

are selective!

Possible Reactions to New Evid in Light of Old: “reinforce” each other

“reinterpret” less plausible one (Russo et al., etc.); e.g., misremember the info

“discount” less plausible one (Winston)

actively “seek” more evidence (not modeled here)

Existing evidence A: “Johnson was not carrying a knife.”

New evidence B1: “Johnson is nonviolent.”

Inconsistent new evid B2: “Johnson pulled a knife.”

Reinterpret B2: “Johnson grabbed a knife from Caldwell.” (i.e., explain it was Caldwell’s knife, not Johnson’s)

Discount B2: “Witness must be mistaken.”

Judge asks layers follow-up questions


AgendaAgenda



What is Agent-Based Modeling?What is Agent-Based Modeling? agents + interactions^

start simple; build up^

Key terminology agents system dynamics

agent births and deaths interactions/competitions

parameters


Contributions ABMs Can MakeContributions ABMs Can Make Symbiotic

relationship:

Behavioral Experiments

ABM

parsimony: demo emergence of seemingly complex

phenomen from small set of simple rulespredictions:

new observations/predictions

understanding: study processes in detail

Test

Inputdescription: informs base assumptions


(Other Models (Hastie, 1993))(Other Models (Hastie, 1993))


(Contrast with Bayesian & Algebraic Models)(Contrast with Bayesian & Algebraic Models)

Algebraic (additive), Bayesian (multiplicative): “single meter” of overall plausibility

ABM allows: revisiting and reconsidering previously-

processed evidence interaction/competition between new

evidence and individual pieces of previous evidence (not just conglomerate)


Contrast with Story Model & ECHOContrast with Story Model & ECHO Explanatory Coherence Model := Thagard’s Theory

of Explanatory Coherence (TEC) + Story Model

Only implemented discounting, not reinterpretation

ABM enforces lower evidence-agent-level consistency, as opposed to higher story-level consistency

Unlike previous ABMs, model agents within individual as system


MotivationsMotivations1. Study emergence of consistent stories via

reinterpretation, discounting, reinforcement mechanisms

2. Adaptive? aid consistency? speed-accuracy tradeoff? avoid indecisiveness

increases convergence rates? order effects hurt accuracy?


AgendaAgenda



GoalGoal Model consistency-seeking process in story

formation

Present evidence-agents to judge-system

Judge-system compares evidence-agents => keep, reinterpret, or discount evidence (agents “interact” & “compete”)

Until sufficiently strong/stronger story emerges


Evidence-agents, composed of “features”

Operationalize consistency /b/ agents: “similarity” in abstract features (Axelrod’s culture ABM,

1997) “inverse Hamming distance” := % feature matches

AgentsAgents

Gxx

89%

Evid 1Nxy

34%

Evid 2

…

Verdict (“G”,”N”,…)Abstract

features (binary)Plausibility

index (0%-100%)

Nxx

14%

Evid 1


ParametersParametersParameter Variabl

eBase

# agents to present- Initial A0 3- Additional A 20

# possible verdicts V 2# features/evidence (excluding verdict) F 2% feature matches for:

Sufficiently consistent C 100%Close enough for reinterpretation N < C 50%

# interactions /b/ evidence-agent births I (A0+A -1)

Change rate of agent plausibility (increase upon winning, decrease upon losing)

D 0.1

Rule(s) and threshold(s) for winning story-- “sufficiently strong” and/or “sufficiently stronger”

S, Sd Both — 0.5, 0.2


(Java GUI)(Java GUI)


System & Agent BirthsSystem & Agent Births Judge-system represents judge’s mind

Evidence presentation = “agent birth”:

Initialization of N0 Agents: Set up randomly-generated agents, OR…

uniform distributions—even for plausibility index due to prior beliefs (Kunda, 1990) or knowledge (Klein, 1993)

User-specified


(Topology)(Topology)results\sysout_081118_0455.log

Printing 8 agents:

01 02 03 04 05 06 07 08

N G I G N I N N

y y y y y y y y

y y y y y y y y

100% 100% 100% 100% 100% 100% 100% 80%

Dead/Rejected Evidence--Printing 9 agents:

01 02 03 04 05 06 07 08 09

I G G I G I N N N

y y x x y x x x y

y x x x y x x y y

00% 00% 00% 00% 00% 00% 00% 00% 00%

To keep track of evidence-agents and their order of presentation:

lists of agents in order of birth/presentation to the system.

latest-born agent always appears at the end of a list.

no geographical “topology”


StoriesStories:= {evidence-agents supporting a verdict} Consistency = inverse Hamming distance amongst evidence

(:= evidencePairs # feature matches / # evidencePairs / F ) Plausibility Index (“Strength”) = average of plausibility indices

Gxx

89%

Evid 1Nxy

51%

Evid 2

Nxx

14%

Evid 1

Story promoting

“Guilty” verdict

Story promoting “Innocent”

verdict

strength = 89%

strength = 99% / 3= 33%

Nyy

34%

Evid 3


Births & InteractionsBirths & Interactions1. If time period t = k * I, where k is some constant, birth new agent.

2. Random selection of agent to compare with newest-born.

3. Compare agents and compute consistency. If consistency… = C, both agents are "winners“; increase both agents' plausibility

indices by D < C, "inconsistency conflict“ => competition.

higher plausibility index => "winner" (“draw” if indices identical). If consistency…

= N, "loser" is salvageable by “reinterpreting” one of its inconsistent features to match winner’s

< N, discount (decrease plausibility by D) Agents with plausibility = 0% => death & removal from system

4. Gather stories in system. Check strengths.

“Winning story found” if 1 ! story with strength >= S and/or |strength-strength | >= Sd for all competing stories; stop run early.


Operationalizing Consistency--ExamplesOperationalizing Consistency--ExamplesPossible Reactions to New Evid : Completely consistent (e.g., 100%

features match) => “reinforce” both; “reward consistency”

Inconsistent… but salvageable (50% features

match) => “reinterpret” less plausible “loser”; “increase inconsistency”

not salvageable (0% features match) => “discount” “loser”; “punish inconsistency”

=> plaus(Evid1) > plaus(Evid2) => Evid2 “loser”

xy

51%

Evid 1

xy

34%

Evid 2

xy

61%

Evid 1

xy

44%

Evid 2

xy

51%

Evid 1

yy

34%

Evid 2

xy

51%

Evid 1

xy

34%

Evid 2

xx

51%

Evid 1

yy

34%

Evid 2

xx

51%

Evid 1

xy

24%

Evid 2


AgendaAgenda



Sample Output^Sample Output^ Live Evidence--Printing 8 agents:

01 02 03 04 05 06 07 08

N G I G N I N N

y y y y y y y y

y y y y y y y y

100% 100% 100% 100% 100% 100% 100% 80%


01 02 03 04 05 06 07 08 09

I G G I G I N N N

y y x x y x x x y

y x x x y x x y y

00% 00% 00% 00% 00% 00% 00% 00% 00%

3 stories found:

-Verdict N supported by 4 evidence, with 1.00 consistency => 0.48 strength

-Verdict G supported by 2 evidence, with 1.00 consistency => 0.25 strength

-Verdict I supported by 2 evidence, with 1.00 consistency => 0.25 strength

*** Found winning story! Verdict N supported by 4 evidence, with 1.00 consistency => 0.48 strength


Judge-System can get Stuck…Judge-System can get Stuck…results\sysout_STUCK.log

Live Evidence--Printing 17 agents:

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

N G G I G I I I I N I G G N N N G

x x x x x x x x x x x x x x x x x

y y y x y y y y y y y y y y y y y

100% 100% 100% 90% 100% 100% 100% 100% 100% 100% 84% 100% 79% 100% 100% 98% 100%


01 02 03 04 05 06 07 08 09 10

I I I I N I I G N G

y x y y y y y y y y

y x x x x x x y x x

00% 00% 00% 00% 00% 00% 00% 00% 00% 00%

3 stories found:

-Verdict N supported by 5 evidence, with 1.00 consistency => 0.29 strength

-Verdict G supported by 6 evidence, with 1.00 consistency => 0.34 strength

-Verdict I supported by 6 evidence, with 1.00 consistency => 0.34 strength

No winning story found.


Output of a Run^Output of a Run^

GGG GGGGGGGG GGGGGGG GG

5 10 15 20

04

8

N N N N N N N N N N N N N N N N N N N N

5 10 15 20

04

8

Supporting Evidence (#)

Time (presentation of agents)

GGGGGGG GGGGGGG GGGGGG

5 10 15 20

0.0

0.6

N N NN N N N N N N N N N N N N N N N N

5 10 15 20

0.0

0.6

Plausibility (%)


GG GGGGGGG

G GGGGGGG GG

5 10 15 20

0.0

0.6

N NN N N

N N N N N N N N N NN N

N N N

5 10 15 20

0.0

0.6

Consistency (%)



5 10 15 20

0.0

0.4

0.8


5 10 15 20

0.0

0.4

0.8

Strength (%)



AgendaAgenda



5 Experiments5 Experiments Experiment 1: Emergence of

consistency

Decision Speed Experiment 2: Speedup Experiment 3: Accuracy tradeoff

Decision Accuracy—Order Effects Experiment 4: Emergence of order effects Experiment 5: Extending deliberation


Obtaining Consistent Stories – Q1Obtaining Consistent Stories – Q1

Q1: Evidence-level consistency sufficient? Which of the 3 mechanisms?

Implementation: No rules

DV: Consistency of stories


Obtaining Consistent Stories – Q1 ResultsObtaining Consistent Stories – Q1 Results

Reinforce Reinterpret Discount Median consistency

0.9 0.8

0.7 0.6

0.6 0.6

0.5

Reinterpret > Discount > Reinforcement


Speed-Accuracy Tradeoff – Q2Speed-Accuracy Tradeoff – Q2

Q2: Reinterpretation & Discounting increase speed?

Prediction: Reinterpretation & Discounting allow much faster convergence

DV: Time to Converge, Max nEvid (Max Consistency)

Implementation: Both rules; all cases have reinforce


Speed-Accuracy Tradeoff – Q2 ResultsSpeed-Accuracy Tradeoff – Q2 Results

Results of 10 Runs—Time to First Convergence, Maximum Number of Evidence,

Maximum Story Consistency

Run1 2 3 4 5 6 7 8 9 10

W/o Reinterp, W/o Discount results/sysout_081215_1938.log

NoC160.5

NoC130.5

NoC12

0.5

NoC120.5

NoC120.5

NoC14

0.5

NoC150.5

NoC12

0.5

NoC120.5

NoC130.5

W/o Reinterp, W/ Discountresults/sysout_081215_1937.log

NoC9

0.8

64

1.0

1811

0.6

NoC9

0.6

NoC100.5

NoC14

0.5

NoC110.6

NoC11

0.7

178

1.0

NoC9

0.5

W/ Reinterp, W/o Discountresults/sysout_081215_1935.log

NoC131.0

NoC120.8

NoC14

0.6

54

1.0

86

1.0

NoC12

0.6

NoC130.8

NoC12

0.9

21140.9

54

1.0

W/ Reinterp, W/ Discountresults/sysout_081215_1946.log

NoC100.8

NoC131.0

43

1.0

NoC8

0.8

126

1.0

43

1.0

NoC8

0.8

86

1.0

NoC9

0.8

19101.0


Speed-Accuracy Tradeoff – Q2 ResultsSpeed-Accuracy Tradeoff – Q2 Results

Medians of 10 Runs—Time to First Convergence, Maximum Number of Evidence,

Maximum Story Consistency

Reinterpret > Discount > Reinforcement only

W/o Discounting W/ DiscountingW/o Re-interpretation Converged 0% of runs

nEvid = 12.5 (0.5)

Converged 30% of runs, time = 17,

8(1.0)

W/ Re-interpretation Converged 40% of runs, time = 6.5, nEvid = 5

(1.0)

Converged 50% of runs, time = 8

6 (1.0)


Speed-Accuracy Tradeoff – Q3Speed-Accuracy Tradeoff – Q3 Q3: What would happen if allow process to continue even after having

found winner? Any point to "holding off judgment" until all evidence presented?

DV: Which story wins? (Strength) Prediction: Leader will only be strengthened; competing stories never

get a foothold. Implementation: Allow system to continue running even if found winner

Run 1 2 3 4 5 6 7 8 9 10Winner once conditions met (G/N)

Winner after additional evidence presented (G/N)

Changed winner? (Y/N)


Speed-Accuracy Tradeoff – Q3 Results^Speed-Accuracy Tradeoff – Q3 Results^

Over 20 runs, # runs same winner:# runs different winner = 15:1 => Good heuristic to stop deliberation, for less time & effort


5 10 15 20

04

8


5 10 15 20

04

8Supporting Evidence (#)



5 10 15 20

0.0

0.6


5 10 15 20

0.0

0.6

Plausibility (%)


GG GGGGGGG

G GGGGGGG GG

5 10 15 20

0.0

0.6

N NN N N

N N N N N N N N N NN N

N N N

5 10 15 20

0.0

0.6

Consistency (%)



5 10 15 20

0.0

0.4

0.8


5 10 15 20

0.0

0.4

0.8

Strength (%)


Figure 2. Example run where winner switches


Order Effects – Q4Order Effects – Q4Heuristic may be ok only if randomized evidence…what if biased

evidence?

Q4: Is there an Order Effect?

Took {20 randomly-generated evidence} and then “doctored” it; % D win = “accuracy”

IV: Presentation order--P goes first, followed by D vs. interwoven evidence

Prediction: earlier, weaker side (e.g., P) beats out later, stronger side (e.g., D); "Accuracy" of D…P… > PDPDPD… > P…D…

DV: Time to Converge, (Projected) Winner


Order Effects – Q4 ResultsOrder Effects – Q4 Results


5 10 15 20

04

8


5 10 15 20

04

8



GGGGGGG G

GGGGGG GGGGGG

5 10 15 20

0.0

0.6


5 10 15 20

0.0

0.6

Plausibility (%)


G

GG GGGGGGGG GGGGGGG GG

5 10 15 20

0.0

0.6 N N N

N N N N N N N N N N N N N N N N N

5 10 15 20

0.0

0.6

Consistency (%)



5 10 15 20

0.0

0.4

0.8


5 10 15 20

0.0

0.4

0.8

Strength (%)


Figure 3. Sample random presentation order run.



5 10 15 20

04

8


5 10 15 20

04

8




5 10 15 20

0.0

0.6


5 10 15 20

0.0

0.6

Plausibility (%)


GGG GGGGGGGG GGGGG

GG GG

5 10 15 20

0.0

0.6

N N

N N N N N N N N N N N N N N N N N N

5 10 15 20

0.0

0.6

Consistency (%)



5 10 15 20

0.0

0.4

0.8

NN

N N N N N N N N N NN N N N N N N N

5 10 15 20

0.0

0.4

0.8

Strength (%)


Order Effects – Q4 ResultsOrder Effects – Q4 ResultsFigure 4. Sample D…P… biased presentation order run.


Order Effects – Q4 ResultsOrder Effects – Q4 ResultsFigure 5. Sample P…D… biased presentation order run.


5 10 15 20

06

12


5 10 15 20

06

12



GGGG

GGG GGGGGGG GGGGGG

5 10 15 20

0.0

0.6

NN N N N N N N N N N N N N N N N N N N

5 10 15 20

0.0

0.6

Plausibility (%)


GGGG

GGGGGGG GGGGGGG GG

5 10 15 20

0.0

0.6 N N N N N N N

N NN N N N N N N N

N N N

5 10 15 20

0.0

0.6

Consistency (%)


GGG

GGGG GGGGGGG GGGGGG

5 10 15 20

0.0

0.4

0.8


5 10 15 20

0.0

0.4

0.8

Strength (%)



Order Effects – Q4 ResultsOrder Effects – Q4 Results

Table 4. Results of 10 Runs Varying Presentation Order of Evidence

Presentation Order

Median Time to Converge% Runs that Defense Won

% Runs Resulting in Switch in Winner

PDPDPD… 7D won 90%, NoC 10%

0%

D… P… 5D won 90%, NoC 10%

0%

P... D… 8P won 80%, NoC 20%

30%

• Strong primacy effect• Exper3 conclusion no longer holds; longer deliberation DOES help!


Increasing Deliberation – Q5Increasing Deliberation – Q5

Q5: Can deliberating more often between births reduce order effects (i.e., increase "accuracy")?

Implementation: Use P…D… model from Exper4

IV: Varied I (I = 0 => wait till end to deliberate)

DV: % runs that P wins


Increasing Deliberation – Q5 ResultsIncreasing Deliberation – Q5 Results

Run 1 2 3 4 5 6 7 8 9 10 % P Wins

I = 0.8 * (# agents – 1)

60%

I = 1.0 * 80%I = 1.2 * 100%

Too much lag time during trials can be detrimental!


Summary of Key FindingsSummary of Key Findings Why reinterpret and discount evidence?

1. Maximizes consistency (Experiment 1)2. Hastens convergence on decision (Experiment 2)

Reinterpret > Discount > Reinforcement

Speed-accuracy tradeoff? Yes… Accuracy ok if evidence balanced (Experiment 3) Not ok/primacy effect if biased (Experiment 4) => Important to interweave evidence, like in real trials!

Can reduce primacy effect by decreasing premature deliberation (Experiment 5)

All achieved by modeling consistency @ evidence level, not story level


(Future Expansions)(Future Expansions) Q6: What happens when introduce bias toward certain

verdicts? Prediction: Verdict-driven process takes less time to converge DV: Time to Converge (Consistency of Stories) Implementation: Add favoredVerdict

Q7: In general, what conditions lead to indecision?


BACKUPS


AgendaAgenda



Sequential Stream of Evidence…Sequential Stream of Evidence…

Evidence 1

Compare, Deliberate, Interpret

…

Evidence 2

Evidence 3

Evidence N


n

Story/ Verdict

Premature Story/

Verdict @ Evid n < N


A Variant of “Biased Predecisional Processing”^A Variant of “Biased Predecisional Processing”^

“leader” / “favored option”

Pre-Decisional SpreadingA

B,C,D,...switch to A DECISIONne

gativ

eposit

ive

Post-Decisional Spreading

Confi

denc

e or

Per

ceiv

ed S

uppo

rt

A

B,C,D,...DECISIONne

gativ

eposit

ive

Time


Tests (DV: Time to converge; stories’ consistency)

Model 0 P Model 1

Reinterpretation Speeds Process: W/o interpretation/discounting

> With reinterpretation/discounting

Primacy Order Effects:Weaker stories presented earlier beat stronger stories presented laterE.g., Defense is disadvantaged since it presents evidence after Prosecution!

> for

Introduce Bias Toward Certain Verdicts (Kunda motivated reasoning, 1999; Thagard emotional coh, 2003)Lifetime of features and agents that differ from those initially (& arbitrarily) associated with favored verdict:

Data-driven process (stories emerge and compete w/o intervention)

> Verdict-driven process (e.g., “defendants tend to be guilty”):

Tests & PredictionsTests & Predictions


(2 Levels of Plausiblity & Consistency)(2 Levels of Plausiblity & Consistency)

Plausibility1. Plausibility of evidence2. Plausibility (“strength”) of story

(composed of evidence)

Consistency1. Consistency /b/ 2 evidence2. Consistency among evidence @ story

level


(Notes)(Notes) “fast learning” with constant D with every

winner/loser

100% & 0% are absorbing states for plausibility indices

Does not take into account innoculation effects as predicted by cross-cultural differences (Nisbett et al.)


Other Simplifying AssumptionsOther Simplifying Assumptions Features

Any combination of abstract features can be framed (e.g., by the lawyers) to support a verdict. All evidence are automatically categorizable into a verdict.

Interactions Interactions only take place between the newest agent and another agent

(as opposed to having two older agents interact and compete).

Computing Consistency Verdict feature neither considered nor included in interactions

Comparing Stories judge forms 1 story / verdict If only 1 story is found at time t, use the "sufficiently strong" rule as

opposed to the "sufficiently stronger" rule. (i.e., no “holding out” by judge) Which layer drives consistency-seeking?

consistency at the individual agent interaction level, AND/OR consistency at the story level


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Kuhl, J. (1994). Motivation and volition. In G. d'Ydevalle, P. Bertelson, & P. Eelen (Eds.), Current advances in psychological science: An international perspective (pp. 311–340). Hillsdale, NJ: Erlbaum.

Kuhl, J. (1984). Volitional aspects of achievement motivation and learned helplessness: Toward a comprehensive theory of action control. In B. A. Maher (Ed.), Progress in experimental personality research (Vol. 13, pp. 99-171). New York: Academic Press.

McCaul, K. D., Ployhart, R. E., Hinsz, V. B., McCaul, H. S. (1995). Appraisals of a consistent versus a similar politician: Voter preferences and intuitive judgments. Journal of Personality and Social Psychology, 68, 292-299.

Peng, K., & Nisbett, R. E. (1999). Culture, dialectics, and reasoning about contradiction. American Psychologist, 54, 741-754.

Simon, D., Krawczyk, D., & Holyoak, K.J. (2004). Construction of preferences by constraint satisfaction. Psychological Science, 15, 331-336.

lydia l. chen instructor: robert axelrod ps793 – complexity theory 30-jan-16 jan-16 lydia l. chen...

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