This week, 4 eurozone countries announced a coordinated ban of short selling of some bank stocks. This move is designed to stabilize prices and prevent "market manipulation". In reality this is a bad policy. The overwhelming evidence from careful academic research shows that short selling increases pricing efficiency and allows information about the true value of assets to be more rapidly incorporated into those asset prices. If anything, eliminating short selling will increase volatility rather than reduce it.
There is an argument made that naked shorting (short selling without borrowing the stock) can have real economic effects, particularly when employed on financial stocks. I think that this may have some merit in that if naked shorting could drive down a bank's stock price, that lower price might lead creditors of the bank to withdraw funding which might precipitate a bank run. In reality, however, this is very unlikely because the total amount of naked shorting is tiny, as for most market participants it is illegal.
Naked shorting can be achieved by purchasing a credit default swap (CDS) however. A CDS allows the holder to basically bet against the value of the debt issued by the underlying stock. For a bank which is typically very highly levered, a CDS is really a tool for shorting the bank stock. The "naked" feature of the CDS is that the holder doesn't have to actually hold the underlying debt of the bank. Unsurprisingly, the eurozone regulators did not ban this type of shorting.