Rationality and Political Participation

POLSCI 240 / PSY 225: Political Psychology

January 13, 2025

Questions for this section

Why do (some) people engage with politics?

  • Why do they vote?
  • Why do they consume political media?
  • Why do they argue with others?
  • Why do they protest?

In many cases, there is a puzzle: (most) people don’t have a large marginal influence on political outcomes

Our general path of investigation

  1. Identify a phenomenon we want to understand
  2. Build a simple, “rational” model of that phenomenon
  3. Observe how reality deviates from that model’s predictions
  4. Add realism, “psychological” components to the model
  5. Iterate 3-4

Simple: a good place to start

Relatively few assumptions and model components; parsimonious

  • Easier for humans to understand and use
  • Hard to know what piece of a complex model went wrong
  • Fewer assumptions -> more general

It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.
- Einstein (1934)

Rational: a good place to start

As a general rule, initially assuming others are reasonable people is a nice thing to do

Even if assumption is wrong, it may capture a lot of behavior:

  • People generally pursue their own interests
  • They respond to incentives
  • They are pretty smart!

What is rational choice?

Sparse definition:

  • People have preferences and beliefs
  • Rational people combine their preferences and their beliefs to choose the alternative that is best for them, all things considered
  • They prefer options that maximize expected utility

Expanded definition (sometimes used, but more contentious assumptions):

  • Have full and accurate information relevant to choice
  • Act as-if they can perform even complex computations
  • Preferences = material self-interest (e.g., max income)

Goals for today


  1. Unpack this notion of maximize expected utility
  2. Set up a simple, expected utility model of turnout in elections
  3. Explore the implications of this model for turnout across contexts

Utility

Utility: the subjective value of something - for example:

Other possible utility functions

There are an infinite number of possible functions - different properties have very different implications!

Uncertainty

  • If choice leads directly to outcome, rational choice is easy: choose alternative with highest utility

  • If connection between acts and outcomes is uncertain, need to take into account multiple possible outcomes

Expected value (EV), in general

  • In general: the EV of a choice is the probability-weighted average of the potential outcomes of that choice
  • Take all the different possible outcomes, multiply by their probs, and sum

 [1] 11.462263  9.119826 11.301137  9.333183  9.790929  9.193792 11.814229
 [8] 10.051982 10.662539  8.860903  9.724786  9.581735 11.336260  9.895899
[15] 10.140371 10.289712 12.456323  8.966063  9.690482  9.504979 10.035954
[22]  9.587791 10.714244 10.128861 10.657525

Expected utility

Expected utility is the expected value of the utility

  • Consider the following example:

You currently have $1,000 in total wealth. I flip a fair coin. If it comes up heads, you win $100. If it comes up tails, you lose $100.

  • What is the value to you of this gamble?
  • Would you choose to play?

Find expected utility

To find the expected utility of an action, (1) find the utility of each possible outcome of that action, (2) multiply these utilities by their associated probabilities, (3) add all these products up

  • If you value money at its nominal dollar amount, i.e., \(\text{U}(\$1,100) = 1,100\)
0.50*(1000 + 100) + 0.50*(1000 - 100)
[1] 1000

If you value money at the square root of its nominal dollar amount, i.e., \(\text{U}(\$1,100) = \sqrt{1,100}\)

0.50*sqrt(1000 + 100) + 0.50*sqrt(1000 - 100) - sqrt(1000)
[1] -0.03965265

Turnout

A simple, rational model of turnout (intuition)

People turn out to vote when the benefits of doing so are greater than the costs, in expectation

Let’s use example of two-candidate election (e.g., 2024 Pres):

If I vote

  • Pay some utility cost, \(C\), to vote (time, gas, childcare, learning, etc.)
  • My preferred candidate, \(T\), wins with some probability, \(p_1\)
  • My non-preferred candidate, \(H\), wins with probability \(1 - p_1\)

If I don’t vote

  • My preferred candidate, \(T\), wins with some probability, \(p_2\)
  • My non-preferred candidate, \(H\), wins with probability \(1 - p_2\)

A simple, rational model of turnout (formal)

Expected utility if I vote (\(\text{EU}_V\)):

\[ \begin{align} &= p_1 \times \text{U}(T) + (1 - p_1) \times \text{U}(H) \space - \space C \\ &= p_1 \times \left( \text{U}(T) - \text{U}(H) \right) + \text{U}(H) - C \end{align} \]

Expected utility if I don’t vote (\(\text{EU}_{DV}\)):

\[ \begin{align} &= p_2 \times \text{U}(T) + (1 - p_2) \times \text{U}(H) \\ &= p_2 \times \left( \text{U}(T) - \text{U}(H) \right) + \text{U}(H) \end{align} \]

Difference in expected utility between voting and not voting:

\[ \begin{align} \text{EU}_{V} - \text{EU}_{DV} &= (p_1 - p_2) \times \left( \text{U}(T) - \text{U}(H) \right) - C \\ &= \quad \quad p \quad \space \times \quad \quad \quad B \quad \quad \quad - C \\ &= pB - C \end{align} \]

A simple, rational model of turnout (formal)

A person should turn out to vote when:

\[ \begin{align} pB - C &> 0 \\ pB &> C \end{align} \]

  • \(B\): the “candidate (or party) differential”: the difference in utilities under one’s preferred candidate relative to the alternative

  • \(C\): the opportunity costs in utility of voting

  • \(p\): the probability of being decisive

    • One’s marginal influence
    • The probability that the outcome changes when you vote (vs don’t vote)

Is it rational to vote for President in NC?


  • What about in other places?
  • What about in other kinds of elections?
  • What about in proportional representation systems?

Applied to other contexts

The model is quite general, e.g.,

  • Voting in proportional representation systems
  • Information gathering
  • Organizational membership
  • Protest

In all such cases, we can think about (1) benefits of preferred outcome relative to others, (2) marginal influence of one’s action on outcome that obtains, and (3) personal costs of acting

BREAK

Goals for today


  1. What does simple, rational model get right and wrong?
  2. What if we allow for mistaken beliefs about \(p\), \(B\), and \(C\)?
  3. What if we allow for different kinds of preferences (besides just changing the outcome to get a good candidate)?

Model predictions

Static

  • Little time consuming political information
  • Little knowledge of politics
  • Weak attitudes and commitments
  • Low turnout
  • Little participation in political organizations and direct action

Dynamic

  • Increase in engagement as alternatives move further apart
  • Increase in engagement as decisiveness increases
  • Decrease in engagement as costs increase

What’s your assessment of the model’s predictions?

Assessment of simple, rational model

It gets a lot right!

  • Most people devote little time to politics
  • Political ignorance is widespread, attitudes weak and conflicting
  • Political movements are hard to sustain
  • People respond to costs, benefits, and closeness

But, seemingly, a lot wrong…

  • Lots of people do engage deeply with politics, even when they have little influence, and when the costs are high (sometimes very high)
  • People do not seem to be as responsive as we would expect
  • How can we understand this seemingly irrational political behavior?

Modifying the simple, rational model

\[ \begin{align} pB &> C \\ pB - C &> 0 \end{align} \]

Two general modification strategies that can produce more participation:

  1. People have simple, rational preferences (this model is true), but their beliefs about \(p\), \(B\), and/or \(C\) are mistaken

  2. People have preferences that are not captured by this simple, rational model

Mistaken beliefs about \(p\)

People tend to be insensitive to large changes in probability

  • Overweight small probabilities
  • Underweight large probabilities

Mistaken beliefs about \(B\)


Levendusky and Malhotra (2016)

Mistaken beliefs about \(C\)


  • In general, people tend to forget about opportunity costs
  • Do poor job calculating all the costs associated with an action
  • Nonetheless, the actual cost of voting is quite low
  • (But this doesn’t count the cost of becoming informed!)

Expand preferences: the calculus of voting (intuition)

\[ \begin{align} pB &> C \\ pB - C &> 0 \end{align} \]

The so-called “calculus of voting” model (Riker and Ordeshook) posits new preferences rather than mistaken beliefs

  • The simple, rational model predicts low engagement because of \(p\)
  • Perhaps there are benefits to participation that don’t depend on changing the outcome - that are intrinsic to the act of participation

The calculus of voting (formal)

The calculus of voting model makes one small change:

\[ \begin{align} pB + D &> C \\ pB + D - C &> 0 \end{align} \]


  • What did we do here? What is \(D\)?
  • Isn’t that…cheating?

Civic duty

What if everyone did that?

Intrinsic and extrinsic

We can extend this model slightly to capture an important conceptual distinction between intrinsic and extrinsic

\[ \begin{align} pB + D_I + D_E &> C \\ pB + D_I + D_E - C &> 0 \end{align} \]

  • intrinsic: you get it from performing the act, full-stop
  • extrinsic: you get it from others knowing you performed the act

A classic study

Green, Gerber and Larimer (2008)

A classic study

Green, Gerber and Larimer (2008)

Treatment effects on proportion voting

Green, Gerber and Larimer (2008)

Another example

Bond et al. (2012)

Aytaç and Stokes: costly abstention

\[ \begin{align} P &= A - C + D_E, \quad \\ A &= f(B[1 + \gamma]), \quad f'(\cdot) > 0. \end{align} \]

  • \(A\): the costs of abstention
  • \(\gamma\): the competitiveness of the election
  • \(f'(\cdot) > 0\) means \(A\) is always increasing in \(B\) and \(\gamma\)

she can experience straight-up disutility from not taking part, and the desire to avoid such disutility can induce her to participate.

How costs of abstention change

The effects of difference between candidates/parties and closeness depend on each other!

  • The effect of each is bigger when the other is at a high value

BREAK

Goals for today


  • Conceptual distinction between instrumental & expressive forms of utility from choice
  • Brennan & Lomasky: consumer vs political choice contexts
  • Caplan’s rational irrationality
  • Politics as entertainment, and political hobbyism
  • Good citizenship as a public good

Instrumental vs expressive behavior


  • Instrumental: acting as a means to bring about the best outcome
  • Expressive: acting as a signal to self or others

image source

“individuals do not necessarily participate in collective action in order to produce outcomes, but instead often do so in order to express who they are by attaching themselves to such outcomes” (Schuessler 2000)

Consumer vs political choice

You get what you choose!

What you get is weakly related to what you choose!

Brennan and Lomasky model (intuition)

The move from consumer to political choice is a move from decisive to non-decisive action

  • Instrumental expected utility is a function of decisiveness
  • Expressive utility is accrued regardless of decisiveness

As one’s ability to change the outcome decreases, the proportion of overall behavior determined by expressive motives increases

Brennan and Lomasky model (formal)

The voter prefers candidate 1 if the following is true, otherwise they prefer 2:

\[ pB_1 + E_1 > pB_2 + E_2 \]

  • \(B\) as the benefits of electing the respective candidate
  • \(E\) is the benefits of expressing a preference for the respective candidate
  • \(p\) is the probability the voter is decisive

In ideal-type consumer choice, \(p=1\) and they are weighed equally, while in ideal-type political choice, \(p \sim 0\) and expressive benefits dominate choice

Predictions for political behavior

Learning

  • Seek info about alternative’s symbolic meaning
  • Care a lot about what close/important others think (and what they think about what others think, and so on…)

Action

  • Express preferences for things you don’t prefer (can often see this clearly, e.g., parents)
  • Difference in behavior that is private vs public
  • Care more about public exposure of act than policy impact
  • Change in behavior as one becomes more decisive/influential

Sequence of Caplan’s argument

  1. Classic public choice: \(p \sim 0\) implies “rational ignorance” and democratic failure

  2. But maybe ignorance doesn’t doom democracy?

    • “miracle of aggregation”
    • heuristics
    • skepticism of elites

  3. So “rational ignorance” isn’t the problem, but you remain skeptical of democratic outcomes?

    • That’s because people are not rational - more precisely, they are rationally irrational in the political realm
    • RI means having preferences over beliefs when there is no cost for being wrong

Rational irrationality

What is “irrationality” here? Beliefs that are systematically biased because of our preferences

  • make us look good/nice/moral
  • make our “enemies” look bad/mean/immoral
  • help us fit in
  • are simple / require little effort
  • etc.

Politics as entertainment

Political hobbyism

a degraded form of politics that caters to the voyeurism of news junkies and the short attention spans of slacktivists…it is the Facebooker who argues with friends of friends he does not know;…the news sharer willing to spread misinformation and rumor because it feels good; the data junkie who frantically toggles between horse races…What is really motivating this behavior is hobbyism — the regular use of free time to engage in politics as a leisure activity.

Negative externalities of expressive behavior

Decisiveness implies that one must internalize the costs of one’s choice (you get what you choose)

  • In consumer choice, people pay the costs of poor decision making
  • In political choice, no one person pays the cost of their own behavior - rather, we suffer as a collective for the aggregated consequences of the behavior of individuals

Good citizenship as a public good