Once upon a time, I worked for a high-tech division (Bell Laboratories) of a company. Within the company, the technical people knew what the pay scale was on a statistical basis. Each level of promotion was paid the square root of two, on average, times the average pay of the level below. Thus, my department head (the manager of my manager) would, on average, be paid twice the amount that someone at my level, on average, would get paid. This went up at least four levels. It did NOT go to the very top (more on that later) but it did go up a ways.
There were sub-levels to which the square root of two did not apply. For example, the equivalent of a SW Engineer I versus a SW Engineer II did not connect to the ratio of the square root of two. But, in general, people knew what type of average deltas existed between levels (and even sub-levels, to a point). I keep saying "on average" because, as was (and still is) true for most companies, the monetary amount for each level was not publicly discussed -- neither the average nor the range.
This worked well. The precise amount did not matter too much. Maybe each level could have increased by the square root of three rather than two. It couldn't be a lot more than that, however, and still be considered "fair". It was known, and understood, that each level had more responsibility than the previous but -- beyond a certain ratio -- pay ratios could get out of whack (no longer at a reasonable point). Perception of fairness depended on two things -- visibility of ratios and a translation of that to a delta of responsibilities and duties.
How high up in the hierarchy did this pay ratio between levels apply? I don't know. As stated earlier, it made it four levels up. Beyond that, I don't know except that it did NOT apply to the highest executive levels. Thus, at some point, the ratios were discarded.
This discrepancy, or abandonment, of fairness at the higher layers was a topic of discussion. Most of the time it was just something in the background as we were doing OK within the company and system. One year, however, the CEO doubled their salary while doing a pay freeze for the rest of the employees. That did not go down well but it was known that most of the people were there because they could do the work they wanted to do -- not primarily for the money. But the perception of fairness never returned and morale never quite made it back to the same levels.
So, how should a CEO be paid? What is fair? If you used the formula I mentioned at the beginning here, then a CEO of a huge corporation should be paid about 16 times that of a regular worker. Is that close to the reality? Nope. Not even in Poland, where a CEO gets about 28 times that of a regular worker. If we used the (straining the "fairness" doctrine) square root of three (rather than two) ratio, it would mean that a CEO of a huge corporation would be paid 81 times that of a regular worker.
What is it like in the United States? About 354 times that of a regular worker -- it continues to go up and up. The highest in Europe is a ratio of about 148 to 1 in Switzerland. An article with more numbers is here.
So, once again, what is fair? More important, what meets the PERCEPTION of fair? Perception of fairness goes hand in hand with perceived mobility. If I can work hard and get that golden apple, that brass ring of the merry-go-round, that round-the-clock money mill then almost anything can be perceived as fair. Dreams of winning the lottery just don't allow reality and statistics to interfere.
Note that there are two categories of CEOs -- those who are heads of private corporations and those who are heads of public corporations. The CEOs of private corporations often have relatively low salaries because they have large amounts of equity (ownership) and recognize that putting money back into the company (if successful) will give them a higher eventual rate of return. Taking out a lower salary allows the money to be used to actively grow the company. When I was "Vice President of Engineering" of a company that I co-founded, my salary was only a little (not even the square root of two
The CEOs of public corporations have salaries, perks, "golden parachutes", and so forth determined by the board of directors. They will have equity as part of their compensation but their salaries have no direct interaction with the equity. In other words, a lower salary does not translate into higher potential equity and a higher salary does not mean less equity.
So, how is the compensation package of the CEO of a for-profit (non-profit is similar but generally has a ceiling beyond which people won't tolerate) public corporation determined? First, please note that public corporations (those which have had a successful Initial Public Offering (IPO)) are going to be beyond the small scale of most private corporations. Saying, as an example, that an average employee's compensation package (salary, taxes, benefits, physical overhead, etc.) is $50,000/year this would indicate an average U.S. CEO salary of $17.7 Million/year. Obviously, a company grossing $15 Million/year cannot pay this. Probably a company would have to start reaching a $500 Million/year gross income before their board of directors would even consider a $17.7 Million/year compensation package for the CEO.
The above referenced study actually indicates the average CEO salary in the U.S. is approximately $12.3 Million/year (less than that $17.7 Million/year of the example calculation). I have not seen a distribution graph of CEO salaries. However, the highest paid CEO in the U.S. for 2017 is $236 Million/year. My suspicion (not verified by any hard data) is that the distribution does not follow a standard bell curve. I think that there are a lot of lower salaries from smaller companies that bring down the average from the higher paid ones. But, since the average still exists at 354 times average worker, there also has to be a lot of very highly paid ones.
These highly paid CEOs are not really in the salaried employee category. They are Rock Stars, Professional Sports First Draft Picks, Celebrity Panelists, and so forth. Their compensation packages are based on competition between boards of directors which keep inflating compensating packages in order to "win" -- show that they have a better CEO because they are paid more. There is no tie between company performance and package and most have such extensive separation packages that someone can be hired as a CEO, do a horrible job, and leave with enough money to support 1,000 (or more) families for a year.
Boards of directors are theoretically determined by the stockholders -- but stockholders care primarily about quarterly results and, with the mega corporations, even effective losses of hundreds of millions of dollars, don't affect the bottom line much. If that is so, does it really matter what the CEOs are paid? Some say no, it doesn't. Personally, I think (like the situation from my earlier career days) it poisons morale. And, whether it affects the stockholder's value or not, that $236 Million/year is paid for by at least $1000/employee in the one company. In other companies, it may affect the "average" employee even more. But it is still all part of the package of valuation of employees at companies -- not just the CEO's compensation package.