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3.2 — Voting II: Ignorance & Irrationality

ECON 410 • Public Economics • Spring 2022

Ryan Safner
Assistant Professor of Economics
safner@hood.edu
ryansafner/publicS22
publicS22.classes.ryansafner.com

Major Players in a Liberal Democracy

  • Voters express preferences through elections

  • Special interest groups provide additional information and advocacy for lawmaking

  • Politicians create laws reflecting voter and interest group preferences

  • Bureaucrats implement laws according to goals set by politicians

  • Judges interpret laws to settle individual disputes

Two Questions for the Next Few Weeks

  1. What incentives does each type of player face?

    • How is this affected by the specific rules & institutions we set up?
  2. How does this explain actual policy outcomes & behavior we see in the world?

Voters in a Liberal Democracy

  • Voters express preferences through elections

  • Voters as economic agents:

  1. Choose: < a candidate/policy >

  2. In order to maximize: < utility >

  3. Subject to: < constraints? >

Constraints of Voting: An Inconvenience Store

  • Recall the spatial model of voting:
    • Each candidate represents a bundle of policy positions
    • Voters vote for candidate closest to their ideal point

Rational Ignorance

The Collective Action Problem of Democracy

  • Citizens vote in politicians to enact various laws that citizens prefer — and vote politicians out of office if they fail to deliver

  • A collective action problem: citizens need to monitor the performance of politicians and bureaucrats to ensure government serves voters’ interests

The Collective Action Problem of Democracy

  • Voting is instrumental in enacting voters’ preferences policy

  • Good governance is a public good: an individual citizen enjoys a small fraction of benefit created

  • Additionally, policies & elections depend on many millions of people

  • Individual bears a private cost of informing self and participating

  • Hence, a free-rider problem

The Rational Calculus of Voting

  • A rational individual will vote iff: p(B)+W>C

  • B: perceived net benefits of candidate (or policy) X over Y

  • p: probability individual vote will affect the outcome of the election
  • W: individual's utility derived from voting regardless of the outcome (e.g. civic duty, “warm glow,” etc)
  • C: marginal cost of voting

The Rational Calculus of Voting

  • A rational individual will vote iff: p(B)+W>C
  • p0

    • Outcome requires many votes
  • B is a public good

    • Get small fraction of total benefit
  • C>0

    • Cost of informing oneself and voting informed

The Rational Calculus of Voting

  • A rational individual will vote iff: p(B)+W>C

  • If citizens are purely rational, W=0

  • Citizens then vote if p(B)>C

  • Prediction: rational citizen does not vote

Voter Turnout: Presidential Elections

Year Turnout of Elligible Voters
2020 62.0%
2016 54.8%
2012 53.8%
2008 57.1%
2004 55.7%
2000 50.3%
1996 49.0%
1992 55.2%

Sources: Wikipedia, U.S. Census Bureau, Bipartisan Policy Center

The Rational Calculus of Voting

  • A rational individual will vote iff: p(B)+W>C

  • Now suppose, W>0

  • Citizens then vote if W>C

  • More importantly, the voter votes regardless of the positions of the candidates!

  • Vote for non-rational reasons: “more presidential looking,” “I’d have a beer with him,” “a better temperament,” etc.

The Rational Calculus of Voting

  • Many do vote, even at significant personal cost!

  • “Expressive voting”: people vote to express identity, solidarity, tribalism, preferences, etc

  • Voting as a pure consumption good, not an instrumental investment to achieve policy preferences

Rational Ignorance

  • Model predicts rational ignorance

  • Not necessarily no voting, but

    • Less than maximum turnout
    • Voting not for instrumental, ’rational’ reasons, but for non-rational reasons

Rational Ignorance

Winston Churchill

1874-1965

“The best argument against democracy is a five minute conversation with the average voter.”

Rational Ignorance

Somin, Ilya, 2014, Democracy and Political Ignorance

Rational Ignorance

Somin, Ilya, 2014, Democracy and Political Ignorance

Rational Ignorance as Positive, not Normative

  • Just so we’re clear, rational ignorance is not a normative claim: that you should/not vote, or that you are a good/bad person if you do/don’t vote/vote rationally

  • It’s a positive explanation of the outcomes we see in the world

Rational Irrationality

The Miracle of Aggregation

  • Miracle of Aggregation: under the right conditions, large groups can pick reach the optimal outcome, even if each individual is unlikely to choose the optimal outcome

The Miracle of Aggregation

  • Miracle of Aggregation: under the right conditions, large groups can pick reach the optimal outcome, even if each individual is unlikely to choose the optimal outcome

The Miracle of Aggregation

  • Some basic statistics of sampling:
    • Central Limit Theorem: With large enough n, distribution of outcomes is approximately normal
    • Extreme “errors” on either side of the mean cancel out such that the sample mean is, on average, an unbiased estimator of the truth

The Miracle of Aggregation

  • If there are systematic biases, or individuals are all likely to be wrong in the same way, the mean is no longer unbiased!

The Miracle of Aggregation: Juries

  • Why do we have trial by jury instead of an expert judge decide most cases?

The Miracle of Aggregation: Juries

  • Suppose an expert judge is correct 90% of the time Pr(J=Wrong)=0.10

The Miracle of Aggregation: Juries

  • Suppose an expert judge is correct 90% of the time Pr(J=Wrong)=0.10

  • Suppose each individual juror, i, is just slightly better than random Pr(i=Wrong)=0.49

The Miracle of Aggregation: Juries

  • Suppose an expert judge is correct 90% of the time Pr(J=Wrong)=0.10

  • Suppose each individual juror, i, is just slightly better than random Pr(i=Wrong)=0.49

Pr(All i=Wrong)=12i=10.49=0.4912=0.0002

The Miracle of Aggregation: Juries

  • The decision rule for criminal cases at common law is unanimous consent of a jury beyond a reasonable doubt
    • Minimize external costs of false conviction of innocents

Pr(All i=wrong)<Pr(J=wrong)

Condorcet Jury Theorem

Marquis of Condorcet

1743--1794

  • Suppose there is a correct outcome (e.g. innocent or guilty) and a group wishes to reach a decision by majority rule

  • Each voter has an independent probability pi of voting for the correct decision

  • How many voters should we include in the group?

M. Le Marquis de Condorcet, Essai Sur L'Application de L'Analyse a la Probabilite des Decisions Rendues a la pluralite des voix

Condorcet Jury Theorem

Marquis of Condorcet

1743--1794

  • Condorcet Jury Theorem: if pi>0.50, then as n, p(Correct)1

    • Adding more voters increases the probability of the correct outcome
  • Note: if pi<0.50, adding more voters decreases the probability of the correct outcome!

    • Optimal jury consists of n=1

M. Le Marquis de Condorcet, Essai Sur L'Application de L'Analyse a la Probabilite des Decisions Rendues a la pluralite des voix

The Miracle of Aggregation and MVT

  • Applied to mass election:

  • Even if individual voters are rationally ignorant, individual votes on either side of optimum cancel out

  • Socially optimum policy remains at the median, and is thus, the winning policy enacted

The Miracle of Aggregation and MVT

  • Applied to mass election:

  • Even if individual voters are rationally ignorant, individual votes on either side of optimum cancel out

  • Socially optimum policy remains at the median, and is thus, the winning policy enacted

  • ...so long as there are not systematic biases

The Miracle of Aggregation and MVT

  • If there are systematic biases, the median (winning) policy platform will not be the socially optimal policy

Systematically-Biased Beliefs

  • People do have systematically biased beliefs?

  • Caplan:

    1. Anti-market bias
    2. Anti-foreign bias
    3. Make-work bias
    4. Pessimistic bias

Systematically-Biased Beliefs

  • Think about your own experience taking economics classes!

  • They probably have disabused you of some things you thought before taking them!

Rational Irrationality

Bryan Caplan

1971-

  • Irrationality is a consumption good that protects our comforting beliefs from reality or scrutiny

  • Many biases are costly to indulge: anti-vaxx, faith healing, quack medicine, etc

    • have to face tradeoffs between maintaining belief and suffering a cost

Rational Irrationality

Bryan Caplan

1971-

Caplan, Bryan, 2001, "Rational Ignorance versus Rational Irrationality," Kyklos 54: 3-26

Rational Irrationality

Bryan Caplan

1971-

  • But in many areas (politics, religion, astrology), the "cost" of irrationality is zero!

  • Irrationality in politics: beliefs that are non-falsifiable, false, or biased

  • Voting often signals an identity and membership in a particular tribe (ideology, identity politics, etc)

  • Having your biases questioned is painful!!

Caplan, Bryan, 2007, The Myth of the Rational Voter

Social Desirability Bias

  • Choosing public preference often affected by Social desirability bias

  • People say and do things they don't believe because its what think others want to hear

    • Saying something because "it sounds good"

Social Desirability Bias

  • Examples from Wikipedia
    • Personal income and earnings, often inflated when low and deflated when high
    • Feelings of low self-worth and/or powerlessness, often denied
    • Patriotism, either inflated or, if denied, done so with a fear of other party’s judgement
    • Bigotry and intolerance, often denied, even if it exists within the responder
    • Intellectual achievements, often inflated
    • Indicators of charity or "benevolence", often inflated

Social Desirability Bias and Economics

  • Economists and your economics courses force you to fight a lot of social desirability bias:

  • "We should protect American workers from foreign competition"

  • "We should only buy American"
  • "We should save the [declining X] industry"
  • "We should raise minimum wages"
  • "We should put people ahead of profits"
  • "We should tax the rich more"
  • "Corporations are making too much profits"
  • "We should spend more on healthcare"
  • Not saying there are no good arguments for these, but most people agree with them only because they sound good

Social Desirability Bias

Social Desirability Bias

Social Desirability Bias

  • Social desirability bias may be connected with Framing effects:

"Given humanity's great tradition of exploration, do you favor continued funding for space flight?"

vs.

"In order to cut government waste and refocus our national priorities, should we fund things more important than space flight?"

Rational Irrationality: Implications

Bryan Caplan

1971-

  • It's rational for individuals to maintain irrational (objectively wrong) beliefs about politics

  • Actual policies are not necessarily bad because of corruption, special interests, backroom deals, etc

  • Voters might be getting exactly what they want!

    • “The median voter is a moderate National Socialist”

Caplan, Bryan, 2007, The Myth of the Rational Voter

Rational Irrationality: Implications

H.L. Mencken

1880-1956

“Democracy is the theory that the common people know what they want, and deserve to get it good and hard.”

Mencken, H. L, 1926, Notes on Democracy

Major Players in a Liberal Democracy

  • Voters express preferences through elections

  • Special interest groups provide additional information and advocacy for lawmaking

  • Politicians create laws reflecting voter and interest group preferences

  • Bureaucrats implement laws according to goals set by politicians

  • Judges interpret laws to settle individual disputes

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