They basically decide themselves. Invariably there are cross meberships in remuneration committes. May be shareholders can have a say but they rarely do.
Remuneration Committees = Scratch my back, I will scratch yours.
And in addition to AC,s reply, at the Annual General Meeting of the Company, it is put to the vote of the Shareholders whether the Directors who have served their term and are due to be re elected should be. If I remember correctly, it takes a vote of not less than 52% of the Shareholder Voting Power to unseat any of them and replace them with someone else, but first there has to be a proposed person.....