Belief Updating & Persuasion
POLSCI 240 / PSY 225: Political Psychology
February 5, 2025
Learning about politics
We have talked a lot about the nature of opinions and how they may be constructed
- How do they evolve and change in response to a changing world?
- Started talking about this a bit with Zaller…
Why do we care?
- Holding representatives accountable
- Making good policy
- Promoting a healthy discourse
Goals for this section
Explore rational theories for how people should update their beliefs about politics
Explore (some) ways in which actual people deviate from these models
- Biases in information search
- Biases in evidence evaluation
In subsequent weeks, we will continue to explore sources of such biases
Rational theories of choice
Three components:
- Optimal information search
- Optimal belief updating (given 1.)
- Optimal decision making (given 2.)
We have talked about 3. (max expected utility) - what about 1. and 2.?
Selection of sources: a brief detour on persuasion
Under what conditions can someone change your mind? (i.e., persuasion)
Cheap talk
Persuasion is harder than we think, because of speaker incentives to lie
Even if S is believed to be knowledgeable, how can we trust them?
Of course they will say we can trust them, but why should we believe that?
This is the problem of cheap talk
- If S shares our interests, then they will be truthful in saying \(X\) is good for us
- If S does not share our interests, they will lie and say \(X\) is good for us
- So if S sends the same message no matter what, M conveys no information at all
Is (rational) persuasion possible?
Lupia and McCubbins say yes! If and when there are “institutions” or background conditions that create incentives for S to be trustworthy (incentive compatibility)
- Verification
- Penalties for lying
- Observable, costly effort
- What do these look like in the real world? Are they sufficient?
In the absence of incentive compatibility…
People need some way to determine whom to trust, but this is difficult and ripe for bias
- Confirmation bias
- Conformity to majority behavior (coming soon)
- Conformity to in-group norms (coming soon)
In the absence of incentive compatibility…
People need some way to determine whom to trust, but this is difficult and ripe for bias
- Confirmation bias
- Conformity to majority behavior (coming soon)
- Conformity to in-group norms (coming soon)
- Overgeneralization of trust
Overgeneralization of trust
Politicians are typically highly constrained: well-described by left vs right ideology
- But citizens are not!
- Perceptions of shared values on 1 dimension may be (over-)generalized to unrelated dimensions
- Related: using partisanship or ideology as a cue may not be a good strategy
In the absence of incentive compatibility…
People need some way to determine whom to trust, but this is difficult and ripe for bias
- Confirmation bias
- Conformity to majority behavior (coming soon)
- Conformity to in-group norms (coming soon)
- Overgeneralization of trust
You might say: “just trust the experts!”
- But how do you determine who is an expert? And don’t they have their own interests?
Optimal stopping rules
How do you decide when to stop gathering information?
Very hard problem b/c of potential for infinite regress
It is inevitable people will need to rely on “heuristics” (rules of thumb)
- Are their rules of thumb good ones? What kinds of biases creep in?
Moving the goal posts
A confidence threshold is the amount of information you need before you are willing to make a decision (or form an opinion, judgment, etc.)
- But we often raise or lower when information is inconsistent or consistent with prior opinions
- More generally, we are often overconfident: hold stronger beliefs than are warranted by the information on which they are based
In sum
Optimal information gathering is a very hard problem!
- Need to trust others in politics, but incentive compatibility is rare
- Full-information is not possible, need to decide when you have enough info and how confident you should be
Ultimately, we rely heavily on heuristics (rules of thumb), which often have systematic biases
Optimal belief updating
To help us think it through, we will start with a very simple general situation:
- A proposition \(X\)
- A person with a prior (pre-existing) belief about the truth of \(X\): \(p(X)\)
- A piece of new information (“data”) relevant to \(X\): \(D\)
- A posterior (updated) belief about \(X\) after the person integrates the new information: \(p(X|D)\)
Rational updating as Bayesian updating
Theories of rational belief state that people should update using Bayes’ Rule
- one’s posterior belief after viewing information about a claim is equal to their prior belief in that claim, multiplied by the probability of seeing the information if the claim is true, divided by the total probability of seeing the information regardless of what’s true
\[
p(X|D) = p(X) \frac{p(D|X)}{p(D|X)p(X) + p(D|\neg X)p(\neg X)}
\]
\(\text{updated belief} = \text{prior belief} \times \frac{\text{prob of data if X is true}}{\text{total prob of data}}\)
Another way to look at it
Use frequencies instead of probabilities:
1 in 10,000 people have the disease
If you test 10,000 people:
- ~500 people without the disease will test positive (5%)
- ~1 person with the disease will test positive
If you test positive, what is probability you have the disease?
- 1 out of 500! (approximately)
Political example
- \(X\): “The average rate of inflation during the year 2024 was less than 3%”
- \(p(X) = 0.25\)
- Person sees MSNBC headline: \(D=\) “2024 Inflation comes in at 2.9%”
- What should the person’s updated belief be? What is \(p(X|D)\)?
Reasons we might be concerned…
We might be skeptical people (can or do) perform these calculations, even implicitly
Even if they try, there may be systematic biases relative to optimality
Even if people have priors about \(X\), they usually need to construct the probability of the data - both conditional (\(p(D|X)\)) and unconditional (\(p(D)\))
- How do they construct these in practice? What kinds of biases might be introduced?
Can or must?
Galef suggests we have two modes of confronting new information:
When that information is consistent with our prior opinion:
When that information is inconsistent with our prior opinion:
Motivated skepticism
People use more rigorous standards for evaluating information inconsistent with their preferred beliefs
- Inconsistent information is evaluated with fine-tooth comb
- Consistent information is accepted without much consideration
What kinds of biases are these?
Cognitive: problems of information processing, judgment - examples:
- Faulty calculations (e.g., w/ Bayes’ rule)
- Faulty heuristics (e.g., majority is always right, overgeneralization of trust)
- Memory (e.g., spreading activation -> recall prior-consistent considerations)
Motivational: people have preferences over beliefs
