One element that explains part of the leftist governments decline in the polls is the media situation in Iceland.
It largest media corporation by far is 365 Mišlar which is primarily owned by the wife of Jon Asgeir Johannesson, one of the "financial vikings" from the boom era. Its well known that Jon Asgeir has been using his influence to change stories about him, but he has also used it against politicians he perceives as "unfriendly to investors" (read leftists) .
The second large media corporation in Iceland is the one centered around Morgunbladid, which used to be the only daily in Iceland and has strong ties to IP. Its dominant shareholder is Gudbjorg Matthiasdottir, who is one the Top 5 of the richest persons in Iceland. She owns a large fishing enterprise and a lot of valuable fishing quota. Editor in chief is no other than Mr. David Oddson, ex IP prime minister, ex governor of the central bank, and generally viewed as more responsible for the banking crash than any other politician in Iceland. All though nominally independent conservative this translates as Independence Party conservative and the paper is highly biased against the government.
Its of course not uncommon that rich right wingers own the media, but in a small country like Iceland the effect becomes stronger.
Basically your bog-standard Murdoch type oligarch then?