Why don't companies pay dividends on a graduated scale?

[cemanuel]

Shares dictate ownership of a company. Two people with the same amount of ownership need to have the exact same rights, and get the same amount of shareholder distributions.

Is this correct? If I buy a stock as part of its IPO I will almost certainly have a lock-up period where I will be unable to sell shares - usually several months. But if I buy the stock on the first day it's publicly traded I can sell it tomorrow. I own shares, the IPO participant owns shares, those shares stipulate the same relative ownership of the company, but our rights are different.

So long as a company is clear about what it does why can't it make a stipulation regarding dividend eligibility?