Sarah Silverman has offered Sheldon Adelson ‘traditional lesbian sex’ if he gives the $100 million he has pledged to help elect Mitt Romney to Barack Obama instead. In 2008, Silverman focused a similarly mock-serious campaign on Florida’s blue-haired bloc. Then, the comedian's worry was that latently racist elderly swing-state voters could have denied Obama victory; now, the fear is that a single septuagenarian billionaire can do it on his own.

Obama himself, although he looks set to exceed the record $745 million he raised in 2008, has fretted that he may be the first sitting president to be outspent in his re-election campaign – and the candidate with the most money wins 98 per cent of the time.

Campaign finance has changed since 2008 because of a new kind of organisation known as a Super PAC, created by a 2010 Supreme Court ruling which held that restrictions on political contributions by corporations and unions violated their right to free speech. Removing limits on individual donations has unsurprisingly given more of a boost to Republicans: Restore Our Future, which backs Romney, has spent more than three times as much as the Obama-supporting Priorities USA Action. Many of Obama’s wealthy donors have soured on him; others won’t contribute to Super PACs because they disapprove of them on principle (though Silverman’s video was paid for by one, the Jewish Council for Education and Research).

Super PACs are allowed to raise unlimited funds from any source, as long as they don’t make direct contributions to candidates’ campaigns or parties. So most of their money is spent on attack advertising: more than $137 million so far.

In June, Romney raised more money than Obama for the second month in a row and looked set to benefit from anaemic economic news. The Super PACs spent $30 million between them, but the slew of ads petered out with Obama increasing his lead: of the voters who told a USA Today poll that the ads had convinced them to change their minds, 76 per cent had done so in favour of the president.

Super PACs may not be the malignant threat to democracy that their opponents fear precisely because they spend the vast majority of their money on attack ads. Newt Gingrich, whose Super PAC collected $16.5 million from Adelson, might have done better had he been able to spend the money on employing strategists and ground staff of the sort who helped Rick Santorum win the Iowa primary with far less money.

Only 8 per cent of respondents to the USA Today poll changed their minds after seeing the ads. That’s enough to make a difference in battleground states, but the torrent of advertising means the numbers are likely to drop with each passing barrage. In any case, attack advertising is most memorable when the target’s chances of winning are already slim, as with Johnson’s ‘Daisy’ ad suggesting Goldwater would start a nuclear war, or Bush’s portrayal of John Kerry as an effete Massachusetts liberal with no core convictions.

Super PACs have got most of their money from wealthy individuals currying favour with candidates rather than from the expected corporations, who have shown less interest in spending more and more money to win over fewer and fewer voters. Instead, the smart money is going to bodies classified as ‘social welfare’ organisations which don’t have to disclose who their donors are. We may not know who has given what – and what effect it has – for some time.