Will Australia succeed America as the world's leading society?
I've never been to England, but by all accounts the level to which it has sunken would have appalled the Victorians, who saw the country at its most influential politically and culturally. Although they don't appear to be destined for the gutter, they are never going to recover those glory days. In this they join the post-Roman Italians, the modern-era French, the Turks, Celts, Mongols, Persians, Arabs, and other once-powerful cultures.
America held things up pretty well after the English could no longer hold themselves so strongly together, but for at least the past 20 years the signs of our plateau-ing or perhaps decline have been there for anyone with eyes to see. There's no one else in sight behind us for now, so we'll probably ride out a decadent phase for maybe another half-century. It might still be a nice place to live, but it will never regain the influence that it had from roughly the Kennedy through Reagan eras.
So then, who's going to take our place? We can rule out any pre-industrial society, including China and India.
The Chinese have been designed by natural selection for intensive agriculture, which has no high risk / high reward opportunities that would fit them for even a proto form of capitalism. That's why their so-called progress is only being kept afloat by a gigantic state-funded bubble. (The Japanese only settled down from a nomadic way of life a couple thousand years ago, unlike the Chinese who were one of the first groups to enslave themselves with agriculture.)
Pastoralism and nomadism are proto-capitalist ways of life, since unlike farmland their livestock multiply just as an investment earns compound interest. Also unlike farmland, it is possible for a pastoralist to raid the livestock of another, run off with them quickly, and get rich quick. This selects for greater risk-taking among herders. However, the livestock, the guard animals, and most importantly the rival herder himself are not going to just sit there and take it. So, the expected push-back selects for a more cautious, not reckless, form of risk-taking.
Related to this is the greater religiosity among pastoralists, especially a strong emphasis on upholding morality personally: there is no central state to police the would-be rustlers, so herders do not outsource the enforcement of morality to distant third parties. An obsession with trusting and being trustworthy also pervades herder religion, again because trust plays a larger role when there are no neutral third parties to settle squabbles. The canonical examples here are the three major monotheistic religions, each founded by groups of Near Eastern pastoralists, and the off-shoots of the religion of the Proto-Indo-Europeans, another highly nomadic herder group.
Lacking these elements of morality, the Chinese cannot hope to attain global influence. Others can tell when someone doesn't try to live a personally moral life, which makes the person seem shady. (Chinese morality is mostly about filial piety.) And the absence of trustworthiness will keep others from being drawn to them. One other central aspect of pastoralist life is the focus on proper guest/host relations, in which the host offers a lot and the guest does not refuse very much. This culture of hospitality is a great way to make more friends and gain greater influence. But type in to google, "why are chinese..." or "why are the chinese..." and it will auto-suggest that they are "so rude."
India is too much of a sprawling mess, and like China it has already had its day in the sun as a major civilization. There is enough of a history of pastoralism that if they along with some farmers broke off into their own country, and waited several hundred years for the society to cohere, they could do all right. But for the next century or two, they aren't going anywhere near the top.
Having cleared up some confusion about the two countries that everyone has their eyes on, what about within the developed world? That is the obvious place to look. All of Europe has reached whatever maximum potential it had, so it won't be them. America will be done for as the first-place country before too long, and that means our dorky little brother Canada too. The first-world pockets in Latin America are still a couple hundred years away from being at a European level.
Funny as it sounds, I think Australia has a good shot at taking the torch from us. They're an Anglo society, and we have hundreds of years of proof that those work. They've got lots of open land to develop. They've got the mix of pastoralist cautious risk-taking combined with the farmers' penchant for slaving away, just like other European-descended groups. They're moral, pragmatic, suspicious of silly fads (relative to other Western countries anyway), they're rambunctious rather than wimpy, they're more informal and not authoritarian, they contributed a good amount to rock music, and they export Celtic super-babes. In other words, they're not so different from our own Scotch-Irish. And since they've never reigned at the global level, they haven't been retired yet.
All they need is a strong and very alien enemy to make them pull together. This is Peter Turchin's idea of ethnogenesis along a meta-ethnic frontier, where the two peoples on either side look different, talk different, believe different, and act different. The American settlers, pioneers, frontiersmen, and so on, had the various Indian tribes to unite against. Even though the middle strip of the country does have greater solidarity than the west coast or eastern half of the country, still it is not so high and is declining for want of a common enemy.
Who would the Australians' Indians be? Not the Aborigines, as they pose no threat. But Australia is surrounded by all sorts of non-European countries where the appearance, speech, beliefs, and customs are all radically different. If one of them should try to unite and prove hostile, that might just do the job to rally Australians to the cause of upholding civilization. My guess is that the Chinese would be the ones to try this, as they are already strongly nationalistic and have the military to try it.
Right now Australia is heavily invested in the Chinese bubble, which is why they have been spared the worst effects of the recession that we've seen elsewhere in the West. But sooner or later that house of cards will fall down, and it could be the first in a series of sour relations between the two countries.
Since this is all at least 50 to 100 years off, who knows even roughly how things will unfold? (Maybe it will be New Zealand instead of China that tries to take over the region.) Still, looking around the world I don't see a stronger contender.