# What is Fair Pay for Executives? An Information Theoretic Analysis of Wage Distributions

## Abstract

**:**

## 1. Introduction

## 2. Towards a Rational Quantitative Framework for Determining Relative Value of Employees

## 3. An Information Theoretic Framework

_{min}) received by the lowest employee, often fixed by the minimum wage law, and (iv) the maximum salary (S

_{max}) cannot exceed M. This may not seem like much, but even this partial knowledge can help us a great deal by narrowing the choices, as we shall show, since the value distribution is constrained by this information. In practice, one might have more information but at the very least one would possess this data set.

_{i}of any employee i as:

_{i}= C ln S

_{i}

_{i}is his or her total annual salary including bonuses and other benefits, and C is a constant of proportionality which we set equal to one. We choose the natural logarithm for mathematical convenience.

_{i}?”

_{max}– V

_{min}

_{max}– ln S

_{min}= ln M – ln S

_{min}

^{2}

^{2}] = σ

^{2}?”

^{2}. In other words, the maximally fair distribution salaries is lognormal while that of values is normal.

## 4. What is Fair Pay for CEOs?

_{CEO}) on the bell curve and computing the corresponding salary for it. Adjustments to this ideal pay package can be made as needed, to account for individual talents and accomplishments, by relating them to both short term and long term performance targets.

_{CEO}upper bound for which the outside area under the bell curve (i.e. under the far right tail) equals 1/N, where N is the total number of employees in the company. For example, for Motorola which has about 64,000 employees, 1/64000 = 0.0000156 corresponds to a position on the bell curve that is 4.16 standard deviation (i.e., σ

_{CEO}= 4.16σ) away to the right of the mean, thereby fixing the ideal CEO salary. We emphasize that these are only rough estimates, as we lack detailed salary distribution data which are needed to estimate the μ, σ, and σ

_{CEO}more accurately. Once we have the actual pay distribution, one can apply much more rigorous statistical methodologies to better estimate these parameters and the CEO’s pay.

## 5. Conclusions and Recommendations

^{2}] = σ

^{2}, which a teleological system must satisfy. As for the second law, Shannon and Jaynes liberated entropy from its narrow thermodynamic view to a broader information theoretic interpretation as a measure of uncertainty. In our contribution, we propose the use of entropy as a measure of fairness [38] in economic systems. Thus, maximizing entropy is the same as maximizing fairness collectively in economic systems. Economic equilibrium is reached under this condition when the participants feel they have received a maximally fair deal given the constraints. As we all know, fairness is a fundamental economic principle that lies at the foundation of the free and efficient market system. It is so vital to the proper functioning of the markets that we have regulations and watchdog agencies that breakup and punish unfair practices such as monopolies, collusion, and insider trading. Thus, it is eminently reasonable, indeed reassuring, to find that maximizing fairness, i.e. maximizing entropy, is the condition for achieving economic equilibrium.

## Acknowledgments

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**MDPI and ACS Style**

Venkatasubramanian, V.
What is Fair Pay for Executives? An Information Theoretic Analysis of Wage Distributions. *Entropy* **2009**, *11*, 766-781.
https://doi.org/10.3390/e11040766

**AMA Style**

Venkatasubramanian V.
What is Fair Pay for Executives? An Information Theoretic Analysis of Wage Distributions. *Entropy*. 2009; 11(4):766-781.
https://doi.org/10.3390/e11040766

**Chicago/Turabian Style**

Venkatasubramanian, Venkat.
2009. "What is Fair Pay for Executives? An Information Theoretic Analysis of Wage Distributions" *Entropy* 11, no. 4: 766-781.
https://doi.org/10.3390/e11040766