# Information Use and the Condorcet Jury Theorem

## Abstract

**:**

## 1. Introduction

## 2. Related Literature

## 3. Model

#### 3.1. Setup

**Definition**

**1**

**Definition**

**2**

**Definition**

**3**

#### 3.2. Nash Equilibrium

**Proposition**

**1.**

**Proof.**

**Corollary**

**1.**

**Proof.**

#### 3.3. Optimal Committee Size

#### 3.3.1. Expected Performance

#### 3.3.2. Existence Condition

**Proposition**

**2.**

**Proof.**

**Corollary**

**2.**

**Proof.**

#### 3.3.3. Direction of Strategic Interactions

**Corollary**

**3.**

#### 3.4. Comparative Statics

## 4. Extensions

#### 4.1. Median-Voting Rule

**Corollary**

**4.**

**Proof.**

#### 4.2. Common Signal

## 5. Application: Monetary Policy by Committee

#### 5.1. Macroeconomic Model

#### 5.2. Interest Rate Setting by Committee

#### 5.3. Equilibrium Dynamics and Macroeconomic Volatility

**Corollary**

**5.**

#### 5.4. Optimal Size and Positive Implication

#### 5.4.1. Optimal Size of the Monetary Policy Committee

**Corollary**

**6.**

- (i)
- Under the average-voting rule (34), there exists a finite optimal size of the monetary policy committee if and only if $r>\frac{1}{5}$ and $\frac{{\sigma}_{\xi}^{-2}}{{\sigma}_{e}^{-2}}<\frac{5r-1}{{(1-r)}^{2}}$.
- (ii)
- Under the median-voting rule (35), there exists a finite optimal size of the monetary policy committee if $r>\frac{\pi}{\pi +8}$ and $\frac{{\sigma}_{\xi}^{-2}}{{\sigma}_{e}^{-2}}<\frac{(\pi +8)r-\pi}{\pi {(1-r)}^{2}}$.

#### 5.4.2. A Positive Implication

## 6. Discussion

## 7. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Lemma**

**A1.**

**Proof of Lemma**

**A1.**

## Appendix B. Derivation of (17)

## References

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**Figure 1.**The relationship between committee size and expected performance ($r=0.4$, $\omega =1.25$, $\beta =1$).

**Figure 2.**The relationship between degree of coordination motive and optimal size ($\omega =1.25$, $\beta =1$).

**Figure 3.**The relationship between precisions of private signals and optimal size ($r=0.4$, $\omega =3$).

**Figure 4.**The relationship between precisions of common information and optimal size ($r=0.4$, $\beta =2$).

**Figure 5.**The regions below the blue and red curves are the parameter regions that satisfy the sufficient conditions for the existence of optimal committee size under the average and median voting rules, respectively. The former contains the latter.

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Morimoto, K.
Information Use and the Condorcet Jury Theorem. *Mathematics* **2021**, *9*, 1098.
https://doi.org/10.3390/math9101098

**AMA Style**

Morimoto K.
Information Use and the Condorcet Jury Theorem. *Mathematics*. 2021; 9(10):1098.
https://doi.org/10.3390/math9101098

**Chicago/Turabian Style**

Morimoto, Keiichi.
2021. "Information Use and the Condorcet Jury Theorem" *Mathematics* 9, no. 10: 1098.
https://doi.org/10.3390/math9101098