Judged purely on that measure, however, it seems from this week's events that the party which Mr Blair led for 13 years still has a way to go.
There was a point, 18 months or so ago, when it looked as though the former Hartlepool MP had finally managed to win his way into the hearts, as well as the minds, of the party faithful.
But all the goodwill engendered by his return from Brussels to stand at Gordon Brown's side during his government's most difficult days has been dissipated at a stroke by his decision to publish a trashy account of the New Labour years.
In the past, many Labour people who found Lord Mandelson's style of politics distasteful have nevertheless forgiven him on the grounds that he was a loyal party man with Labour literally running through his veins.
But the publication of his book 'The Third Man' this week has surely demolished that defence once and for all.
It has oft been said of Peter Mandelson that he was always better at guiding the fortunes of the party and its leaders than he ever was at managing his own career.
But the lack of judgment that resulted in at least one of his two Cabinet resignations seems to have returned with a vengeance in his apparent eagerness to cash in on the lucrative summer 'beach read' market.
It is not even as if any of the revelations in the wretched book tell us much that we didn't know already.
Much of the focus of attention has inevitably been on whether or not Tony Blair called Gordon Brown "mad, bad and dangerous" and likened him to a "Mafia don."
Well, "mad" is one of those words that gets thrown around a little too loosely these days. It can mean anything from clinical insanity to having a bit of a temper on you.
It is hardly surprising, though, that Labour's opponents in the media have put the worst possible construction on it, with Mr Brown's reputation taking a further battering as a result.
But in my view, the book is far more damaging to Mr Blair's historical reputation than to his successor's.
It confirms what many have long suspected, namely that he did indeed promise Mr Brown in 2003 that he would not fight a third general election, but went back on it.
It is impossible to over-estimate the impact of this on subsequent Labour history. Had Mr Brown been Labour leader up against Michael Howard in 2005, he would have won that election with at least as good a majority as Mr Blair managed.
He would then, in all likelihood, have retired with dignity mid-way through the last Parliament, giving Labour a chance to renew itself in office under a new generation.
As it is, Mr Brown is currently being subjected to all sorts of indignities, with his government's record being trashed by the Con-Lib coalition on an almost daily basis.
But I wonder whether when people realise what the coalition is really doing to our public services – privatising the NHS by the back door being its latest wheeze – they might start to feel some sympathy for the former Prime Minister.
Either way, the Labour Party will doubtless in time come to love Gordon in the way it does all its old leaders – particularly the unsuccessful ones.
One thing it will never now do, though, is to learn to love Peter.