Ishanu Chattopadhyay PRO
ML Data Science Biomedicine Social Science Faculty
Ishanu Chattopadhyay
Modeling Opinion Dynamics
with validated predictive capability
University of Chicago
Feb 2 2023
what are we trying to do?
Understanding complete worldview of individuals or groups from partial information
Predicting how opinions change and belief shift in society
Calculate optimal trajectories from one worldview to another
Results in validated deployable tools
Algorithmic Lie Detector
what are we trying to do?
How is it done today?
Lack of validation
Opinion vectors: Possibly partial responses to a survey like GSS
How do we measure the difference between opinion vectors?
What is the right "distance" function?
?
\( x\)
\( y\)
How are we doing it?
Opinion vectors: Possibly partial responses to a survey like GSS
How do we measure the difference between opinion vectors?
What is the right "distance" function?
\theta(x,y) \propto Pr(x \rightarrow y)
\( x\)
\( y\)
Intrinsic distance that scales with the probability of spontaneous jump
How are we doing it?
The intrinsic distance actually emerges from inferring dependencies between opinions/beliefs
- Small distance: switch possible
- Large shifts CAN happen but via hops
Estimation of worldview from partial responses
Will online bluster lead to IRL action?
\Phi_i:\prod_{j \neq i} \Sigma_j \rightarrow \mathcal{D}(\Sigma_i)
1. Qnets
Data-inferred hidden dependencies between beliefs
- Recursive forest of conditional inference trees, constructed from survey responses.
- No prior assumption of dependency structure
Recursive expansion
The q-distance Metric: Why Is This a Natural Metric?
\textrm{items } X_1, X_2, \cdots , X_{i-1},X_{i+1}, \cdots, X_N
a
b
c
d
e
X_i
Similar opinion vectors can spontaneously switch:
Our intrinsic metric quantifies the odds of this spontaneous switch
Three fundamental equations:
\Phi_i:\prod_{j \neq i} \Sigma_j \rightarrow \mathcal{D}(\Sigma_i)
1. Qnets
\theta(x,y) \triangleq \mathbf{E}_i \left ( \mathbb{J}^{\frac{1}{2}} \left (\Phi_i^P(x_{-i}) , \Phi_i^Q(y_{-i})\right ) \right )
2. Q-distance
\mathbb{D}^P(x,i)\triangleq 1 - \Phi^P_i(x_{-i})\vert_{x_i}
3. Dissonance
Data-inferred hidden dependencies between beliefs
Canonical distance between belief vectors
Quantifying the notion of dissonance /surprise
Belief vectors define a metric space; close beliefs are ones that can spontaneously change to or jump across
| GSS variable | actual (masked) | Reconstructed |
|---|---|---|
| spkcom | allowed | allowed |
| colcom | not fired | not fired |
| spkmil | allowed | allowed |
| colmil | allowed | not allowed |
| libmil | not remove | not remove |
| libhomo | not remove | not remove |
| reliten | strong | no religion |
| pray | once a day | once a day |
| bible | inspired word | word of god |
| abhlth | yes | yes |
| abpoor | no | no |
| pillok | agree | agree |
| intmil | very interested | very interested |
| abpoorw | always wrong | not wrong at all |
| godchnge | believe now, always have | believe now, always have |
| prayfreq | several times a week | several times a week |
| religcon | strong disagree | disagree |
| religint | disagree | disagree |
| comfort | strongly agree | neither agree nor disagree |
Reconstruction
Example 1
| GSS variable | actual (masked) | Reconstructed |
|---|---|---|
| spkcom | allowed | allowed |
| colcom | not fired | not fired |
| libmil | not remove | not remove |
| libhomo | not remove | not remove |
| gunlaw | favor | favor |
| reliten | no religion | no religion |
| prayer | approve | approve |
| bible | book of fables | inspired word |
| abnomore | yes | yes |
| abhlth | yes | yes |
| abpoor | yes | yes |
| abany | yes | yes |
| owngun | no | no |
| intmil | moderately interested | moderately interested |
| abpoorw | not wrong at all | not wrong at all |
| godchnge | believe now, didn't used to | believe now, always have |
| prayfreq | several times a week | several times a week |
| religcon | strongly agree | agree |
| religint | strongly agree | not agree/dsagre |
Reconstruction
Example 2
Left and Right Polar Vectors
GSS variable,R-pole,L-pole
-----------------------------------------------------
abany,no,yes
abdefctw,always wrong,not wrong at all
abdefect,no,yes
abhlth,no,yes
abnomore,no,yes
abpoor,no,yes
abpoorw,always wrong,not wrong at all
abrape,no,yes
absingle,no,yes
bible,inspired word,book of fables
colcom,fired,not fired
colmil,not fired,not allowed
comfort,strongly agree,strongly disagree
conlabor,hardly any,a great deal
godchnge,"believe now, always have","don't believe now, never have"
grass,not legal,legal
gunlaw,oppose,favor
intmil,very interested,not at all interested
libcom,remove,not remove
libmil,not remove,remove
maboygrl,true,false
owngun,yes,no
pillok, agree,strongly agree
pilloky,strongly disagree,strongly agree
polabuse,no,yes
pray,several times a day,never
prayer,disapprove,approve
prayfreq,several times a day,never
religcon,strongly disagree,strongly agree
religint,strongly disagree,strongly agree
reliten,strong,no religion
rowngun,yes,no
shotgun,yes,no
spkcom,not allowed,allowed
spkmil,allowed,not allowed
taxrich,about right,much too low
viruses,definitely true,definitely not true
37 dimensional polar baseline
Extreme Left
- questions on key social issues
- questions that are unambiguously tied to liberal/conservative ideologies
Out-of-sample validation
GSS data
Out-of-sample validation
Eurobarometer data
Primary outcome:
Estimate worldview from partial knowledge
Secondary outcome:
Validate geometric theory of belief shift
Future Work: Validation in Survey Experiments in the wild
Sep 2 2021
YouGov
Primary outcome:
1. Estimate worldview from partial knowledge
Secondary outcome:
1. Predict belief shift
2. Validate mechanism (emedding geometry is more important to nature of interactions)
highly consequential !
TruthNet:
Algorithmic Lie Detector
- Make Cognet model from responsedatabase
- As subject continues to respond, the Cognet model predicts response distributions
- "Lies" would produce consitently high "surprise"
Impossible to "hack" or "beat"
Prequisite: Questions are from a standard database, for which earlier respondants were recorded
Darpa_Arthur_Joeanna_Jan2023_ishanu
By Ishanu Chattopadhyay
Darpa_Arthur_Joeanna_Jan2023_ishanu
Opinion dynamics and belief shift using recursive decision forests
