Ishanu Chattopadhyay
Modeling Opinion Dynamics
with individual-level predictive capability
University of Chicago
Nov 18 2022
cognet 0.0.193 lates version
Learning dependency structure between opinions from data
Using Learned structure for prediction
Estimate worldview from incomplete information
Learning dependency structure between opinions from data
Using Learned structure for prediction
Estimate worldview from incomplete information
Learning polarization dynamics
1. Qnets
Data-inferred hidden dependencies between beliefs
Recursive expansion
Three fundamental equations:
1. Qnets
2. Q-distance
3. Dissonance
Data-inferred hidden dependencies between beliefs
Canonical distance between belief vectors
Quantifying the notion of dissonance
Belief vectors define a metric space; close beliefs are ones that can spontaneously change to or jump across
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
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
Out-of-sample validation
GSS data
Out-of-sample validation
Eurobarometer data
Modeling societal polarization
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: ML For Survey Data Validation
&
Identification of Adversarial Responses
University of Chicago
Algorithmic Lie Detector
QNet: Interrogating Structure of Survey Responses
Nodes Hyperlinked to Trees
click on nodes to change trees
"Mass tells space-time how to curve, and space-time tells mass how to move."
-- John Wheeler
I think here "mass" (concentration of people) modulates the geometry,
which then drives the belief shifts.
Future Work: The "why" question
Symmetry breaking in opinion formation: Towards the physics of opinion change
Symmetry breaking in opinion formation: Towards the physics of opinion change
"mass" distribution:
Z-axis: local density of samples
A
B
C
D
Opinion mass creates "gravity" wells
perturbation causes opinions to shift towards its closest "gravity" well
Explains Chris Bail's observation
Dissonance more at ideological boundaries
Red and gray represent high and low dissonance on the GSS variable "bible"
Red and blue represent conservative-leaning and liberal-leaning populations
Predicting worldviews
from partial observation
reconstruct
response
random
mask
collect data
construct qnet
reconstruct worldview
predict belief shifts
Summary
Towards A Mechanistic Theory of Belief Shift Dynamics: Peaks Attract
Towards A Mechanistic Theory of Belief Shift Dynamics: Peaks Attract
A
B
C
D
A
B
C
D
current opinion
Shifted belief
local density gradient
embedded versions
A
B
C
D
current opinion
Shifted belief
Proven property of q-distance
Theorem (conjectured)
Eurobarometer is a series of public opinion surveys conducted regularly on behalf of the European Commission and other EU Institutions since 1973. These surveys address a wide variety of topical issues relating to the European Union throughout its member states.
Reconstruction Error Distribution
Eurobarometer 4
GSS
Eurobarometer 4
EC Membership good, bad, neither?
Future:
1. Survey expt
2. Statistical Physics of Opinion Change
theorem
symmetry breaking
The q-distance Metric
Collection of all such conditional inference trees is the recursive forest, answering the following question:
The q-distance Metric
The q-distance Metric: Why Is This a Natural Metric?
a
b
c
d
e
Similar opinion vectors can spontaneously switch:
intrinsic metric quantifies the odds of this spontaneous switch
Theorem: q-distance is "natural"
Theorem 1.
Sanov's Theorem & Pinsker's Inequality
Assume that one question $$X_i$$ is unanswered.
a
b
c
d
e
Distribution of responses to this item given remaining responses
Given this distribution the probability that "b" is the answer
From first principles:
Distance metric such that log-likelihood of jump scales as the distance
theorem
Summarizing
1. Qnets
2. Q-distance
3. Dissonance
Qnet