This piece of news was mostly disregarded as just another one of Livni's foolish acts, but it does include three aspects worth paying attention to.
The first issue is that this appeal suggests that Livni is somewhat afraid to take the lead. On the one hand, public opinion polls are prompting her to return to politics (the same polls which have been known to destroy more than one successful career). On the other hand, she has stated that her goal is to replace the government.
I can already imagine the press conference after the elections, in which Peres and Livni's party wins just eight Knesset seats. Livni will make an effort to appear formal, while Peres, with drooping eyebrows, will announce that the failure was an achievement, that white is black and that Right is Left. He will congratulate the winners and declare the beginning of coalition negotiations. Each person does what they do best: When you cook oatmeal you need the master chef to provide the flavor and face the customers, and the sous chef to stir discreetly and wait.
Wait for what? It isn’t that hard to guess. Despite her great fondness for rotating premiership, we have not heard reports that Tzipi Livni demanded rotating premiership from the president. As his honor is approaching the age of 90, there is no need to include many clauses in the contract. Time, one can say tactfully, will take its course.
Quality of government
On the other hand, history shows us that you can never know. Pope John XXII was elected to the Holy See in 1316 as a compromise candidate. At the age of 72, which was considered very old at the time, the general assumption was that he had two or three years until the more serious candidates settle things between them. John controlled the Church for 18 years, causing quite a lot of damage, and died at the age of 90. It's true that Peres is supposed to launch this move at the age that John ended it, but times have changed. If you're waiting for Peres to vacate his seat for you, you had better bring a book. It'll take a while.
The third issue is the most important. Suggesting that the president quit his job and jump back into politics without a cooling-off period may be kosher (I assume Livni and her advisers looked into this issues), but doesn't exactly smell of roses. Indeed, this isn’t an inconceivable move as far as Peres is concerned. When he left the Labor Party behind and joined Kadima, Peres wasn't a marginal member of his party, but its leader. But as far as anyone who cares about "quality of government" is concerned, this is an extremely harmful move, which will make the boundaries between the national and the factional even more indistinct. The president should be above factional politics, and even if he cannot be stopped from resuming his political career, it must be done after a particularly long cooling-off period.
The appeal to Peres was driven by a cynical attempt to misuse the support he receives as the representative of the State; as the person who is finally disassociated with tricks in which the generators of votes are not asked too many questions, and there are definitely no quandaries regarding the long-term consequences of vote-generating moves. Next time you hear Livni talk about a different kind of politics, you should remember her presidential move.