Could a limited company decide to pay dividends only to certain individuals, e.g., those who hold 50% or more of the outstanding shares? If not, do dividends have to be paid out proportionately to all shareholders?
Yes and no. You have to pay dividends for each class of shares evenly.
For example you could chose to only pay class A shares but not class C. You couldn't however only pay some of the class A shareholders
No, company can't decide to pay dividends only to certain individuals. One of the rights of every sharesholder, is right to get a dividend (share of profit), ofcourse if majority of shareholders decide to pay dividends at all (depends on type of limited company though)
It's true, that each share might not be justified to equal size of dividend, because of different types of shares (preference shares, cumulative shares, convertible preference shares...). To simplfy: when someone buys a particular type of share, he should be able to know what he can expect in case of profit sharing (paying out dividends).
Lets suppose I have 51% of shares of company and you have 49%. It wouldn't be really fair if I could decide to pay dividends only to me and not to you aswell.