Revisiting the Theory of the Calculus of Voting Ching 1

Revisiting the Theory of the Calculus of Voting Outline  Research Question  The EITM Framework  Hypotheses  Data and Measurement  Empirical Evidence  Conclusions Research Question  The calculus of voting (Downs 1957; Riker and Ordeshook (1968):  R = PB – C + D 1) R: the reward gained by the voter from voting in a given election. 2) P: the probability that her marginal contribution to the election is decisive. 3) B: the individual’s benefits if her preferred candidate actually wins. 4) C: the cost of voting (informational, physical, opportunity, etc.). 5) D: the sense of citizen duty, goodwill feeling, psychological and civic benefit of voting.  The voter turns out to vote if R > 0 and abstains if R ≤ 0. Research Question  Fiorina (1976): expressive components (D) 1) Civic duty. 2) Psychological support.  This study attempts to employ an empirical implication of theoretical models (EITM) framework to reexamine the calculus of voting and expect to provide more insight into the D term in the model developed by Downs (1957) and Riker and Ordeshook (1968). The EITM Framework  Three-Step EITM Framework (Granato et al. 2010): Step 1: Identify a theoretical concept of human behavior of interest and relate it to a statistical concept. Step 2: Develop behavioral (formal) and statistical analogues. Step 3: Unite the theoretical and statistical analogues in testable theory. Step 1: Identify a theoretical concept of human behavior of interest and relate it to a statistical concept  The baseline model: R = PB – C + D (1) 1) D: civic duty (i.e., O) and affinity for candidate (i.e., A). 2) C: small and constant (Niemi 1976; Aldrich 1993; Tullock 2000; Riker and Ordeshook 1968)  U(V) = PB + O + A (2)  where U(V) is the utility of voting; PB is the benefit of voting; O is civic duty; A is the voter’s affinity for candidate. 1) If U(V) > 0, then an individual will choose to vote. 2) If U(V) ≤ 0, then an individual will abstain from voting. Step 1: Identify a theoretical concept of human behavior of interest and relate it to a statistical concept  The EITM relation: 1) Theoretical concept: decision making (U(V) = PB + O + A). 2) Applied statistical concept: discrete choice (turnout - a dichotomous action). Step 2: Develop behavioral (formal) and statistical analogues  U(V) = PB + O + A (2) 1) PB: party differential (i.e., Pd) (Downs 1957). 2) A: the difference in affinity for competing candidates (i.e., Ad).  U(V) = Pd + O + Ad (3) Step 2: Develop behavioral (formal) and statistical analogues  An individual i will vote if at least one of the three components is greater than zero: 1) Pdi > 0, Oi > 0, and Adi > 0. 2) Pdi > 0, Oi = 0, and Adi = 0. 3) Pdi = 0, Oi > 0, and Adi = 0. 4) Pdi = 0, Oi = 0, and Adi > 0. 5) Pdi > 0, Oi > 0, and Adi = 0. 6) Pdi = 0, Oi > 0, and Adi > 0. 7) Pdi > 0, Oi = 0, and Adi > 0.  An individual i will abstain from voting if Pdi = 0, Oi = 0, and Adi = 0. Step 2: Develop behavioral (formal) and statistical analogues  Assume that the true values of an individual’s party differential, civic duty and affinity for candidate are conditioned on her observed values, 𝑃𝑑𝑖 , 𝑂𝑖 and 𝐴𝑑𝑖 .  The probability that an individual vote is: Pr(yi = 1| 𝑃𝑑𝑖 , 𝑂𝑖 , 𝐴𝑑𝑖 ) = 1 – Pr(Pdi = 0| 𝑃𝑑𝑖 ) Pr(Oi = 0| 𝑂𝑖 ) Pr(Adi = 0| 𝐴𝑑𝑖 ) (4) 1) Pr(Pd) = Φ(𝛼𝑃𝑑 + 𝛽𝑃𝑑 𝑃𝑑 ), 2) Pr(O) = Φ(𝛼𝑂 + 𝛽𝑂 𝑂) 3) Pr(Ad) = Φ(𝛼𝐴𝑑 + 𝛽𝐴𝑑 𝐴𝑑 ).  The familiar property of the standard normal cumulative distribution function: 1 – Φ(z) = Φ(–z). Step 2: Develop behavioral (formal) and statistical analogues Equation (5) is simply a conventional probit regression setup with several interaction terms. Step 3: Unite the theoretical and statistical analogues in testable theory  Probit(Turnout) = δ0 + δ1(Party differential) + δ2(Civic duty) + δ3(Affinity for candidate) + δ4(Party differential × Civic duty) + δ5(Party differential × Affinity for candidate) + δ6(Civic duty × Affinity for candidate) + δ7(Party differential × Civic duty × Affinity for candidate) (6)  It is expected to find that δ1, δ2, and δ3 are positive.  But how are δ4, δ5, δ6 and δ7 ?