You don’t really need a 50% shareholding to make an impact on a company. Anything above 25% and you have an effective veto on most important business. You will also guarantee yourself an ability to get at least one or two of your chosen people elected to a board.
I should point out – Stiglitz is not advocating outright state ownership through shares. He is advocating an increased state influence on companies through shareholding. A five or ten percent stake in a company or a group of companies can allow you to have great influence on their business strategy.