Re: I don't understand any of this
If Apple buys back shares from the shareholders, does the board exercise the voting rights of those shares or do the remaining shareholders get proportional rights over the votes of the Apple-held shares?
In a nutshell, when a company buys back its shares, they are added to the pool of authorized, but unissued stock shares[1]. While in this pool, NO ONE has the voting rights for that stock. They can be subsequently sold in the future by the company if more 'investment' is required.
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[1] Example: Fuster Cluck Co, has authorized the issuance of 1 million shares of common stock, but has sold only 800,000 shares. That means that there is still 200,000 shares available to sell if the company needs more capital if it ever becomes necessary. Until those shares are actually sold, they have no voting rights.
Now, contrast that with this example, Fuster Cluck Co, has sold all one million shares, and still needs capital. It might persuade the current stockholders to authorize the issuance of more shares, at the prospect of diluting the ownership percentage one share represents. With 1 million shares authorized, each share represents 1/1,000,000th of the company. If the stockholders authorize another million, then one share represents 1/2,000,000th of the company. Also, stock in the authorized, but unissued pool do not receive dividends, those dividends are paid only to those who own qualifying shares. One last thing, not all shares in some companies are created equal. There are various classes of stock with differing rights (such as 'Common' vs 'Preferred').