Biased beliefs and retrospective voting: why democracies choose mediocre policies

Abstract

There are two well-established empirical regularities about voters. First, they entertain systematically biased beliefs about how public policies affect economic outcomes. Second, voters vote retrospectively: they punish the incumbent for poor and reward him for good macroeconomic performance. Thus, political parties face a trade-off: offering popular yet economically harmful policies increases the chance of being elected today, but decreases the chance of re-election. We provide the first rigorous game-theoretical analysis of the trade-off. The model addresses two questions: How can biased beliefs and retrospective voting be explained consistently? What policy outcomes emerge in party competition? To micro-found persistently biased beliefs we introduce the psychological concept of mental models. Deviating from earlier studies, we allow parties to choose strategic mixtures of populist (i.e., bad yet popular) and good (but less popular) platforms. We show that retrospective voting provides a self-correction mechanism, so that parties offer strategic mixtures of policies in equilibrium rather than purely populist or purely good policy platforms. Thus, democracy is characterized by mediocre policy choices and half-hearted reforms. An incumbent bias or unclear responsibilities weaken the self-correction mechanism.

Appendix

Proof of Proposition 1

Based on (20) the first-order condition for the optimal choice of $\beta_{1}^{A}$ is given by:

(24)

It follows:

(25)

Therefore, $\beta_{1}^{A} = 0$ if f<δv(1+2v ₀)/(1+2δv) and $\beta_{1}^{A} = 1$ iff≥δv(1+2v ₀)/(1−2δv). For the optimal choice of party B we simply have to substitute $+ v_{0}^{j} = + v_{0}^{A}$ for $+ v_{0}^{B} = - v_{0}^{A} <0$ in (20). Therefore, $\beta_{1}^{B} = \frac{1}{2} +\frac{1}{4} \cdot\bigl[ \frac{f - \delta v( 1 - 2v_{0}^{A} )}{f\delta v} \bigr]$ with $\beta_{1}^{B} = 0$ if f<δv(1−2v ₀)/(1+2δv) and $\beta_{1}^{B} = 1$ if f≥δv(1−2v ₀)/(1−2δv). □

Lemma A.1

Assume a discrete number of n voters with an identical probability of voting for party j in period t given by $\pi_{it}^{j} = \varPi_{t}^{j} = p$, for all i=1,…,n. Then, function M(Π _t ) is very well approximated by:

(26)

Proof of Lemma A.1 by simulation

Assuming identical probabilities, and knowing that a party will only be the incumbent when at least n/2+1 voters support the party, we use the Bernoulli distribution (Rinne 2003: 253) to obtain as conditional vote share:

(27)

It is possible to derive the first and second derivative for M(p). Yet, the resulting expressions do not allow for a general conclusion with respect to their sign. We simulated the function and its first and second derivative for p=0 to p=1 applying n=1 000 000. Plotting the simulation results (Fig. 1) we obtain a figure depicting a functional form very close to Eq. (26). This result holds for realistic values for the number of eligible voters n.

Fig. 1

Simulated form of (a) M(p), given by (27), and (b) the corresponding M′(p) (for n=1 000 000)

 □

Proof of Proposition 2

Based on (21) the first-order condition for the optimal choice of $\beta_{1}^{A}$ is given by:

(28)

where $\varepsilon_{M( x_{t} ),x_{t}}$ is the elasticity of function M(⋅) at location x _t ={Π _t ,1−Π _t }. The Implicit Function Theorem applied to (28) reveals

(29)

where A represents $\frac{\partial \varTheta _{t}^{A}( \cdot )}{\partial \beta _{t}^{A}}$ in the optimum, that is, where A=0. We obtain:

(30)

While the sign of the nominator of (29) is clearly positive, the sign of the denominator is open a priori. Applying Lemma A.1 in (21), it is easy to show that:

(31)

Analogously, we obtain the same expression for party B, with the only difference that the term with $v_{0}^{A}$ has an opposite sign. Comparing (31) and (25), it turns out that with incumbent bias ρ ^Inc the expression increases for both parties by $\frac{1}{4}\frac{\rho}{v}$ if the party is expecting to lose the election ($\varPi_{t} < \frac{1}{2}$), or even by $\frac{1}{2}\frac{\rho}{v}$ if the party expects to win ($\varPi_{t}\ge\frac{1}{2}$). Consequently, we obtain $\frac{\partial \beta _{t}^{j}}{\partial \rho ^{\mathit{Inc}}} > 0$. □

Proof of Proposition 3

Using (23) we get $\frac{\partial \beta _{t}^{A}}{\partial k} = \frac{1}{4} \cdot[ 4\delta v \cdot E( \beta^{\mathit{ex}}) - 1 - 2\delta v ] \cdot\frac{1}{\delta vk^{2}}$. Thus,

(32)

Given that δ<1 and v<1/2, the latter restriction is fulfilled by definition. Next, we can deduce $\frac{\partial \beta _{t}^{A}}{\partial E( \beta ^{\mathit{ex}} )} = - ( \frac{1 - k}{k} ) < 0$, for all 0<k<1. □