Every four years, radicals in America face a dilemma. Should they vote Democrat to keep out the Republican? Or should they vote for a candidate who offers change? (some, of course, don’t believe in voting – but this presents less of a dilemma).

In some elections, this isn’t a very tough choice: often there isn’t really any credible candidate to the left of the Democrat. But not so this election. Perhaps as a result of the Occupy movement, or maybe because of the broader collapse of the financial system, there are two candidates standing for president who offer platforms to the left of the Democrats, and who have secured their places on enough ballots to win – Green party candidate Jill Stein and, if you include write in access, former Salt Lake City mayor Rocky Anderson of the newly formed Justice Party.

I don’t intend to discuss the differences between the two here – the case for voting for one or other is relatively similar, and their policy positions are pretty close. There is a case that Anderson, as former mayor of a major city, is more credible. There is an opposite case that Stein – on the ballot in significantly more states – is. Below, I will talk about Stein, but for most of the arguments, you could equally read Anderson.

Of course, she is not going to win. But getting on the ballot is an impressive feat in itself. And Stein has run a campaign which has been more prominent than that of any third party candidate of the left I can remember. You need to go back to Ralph Nader in 2000, for example, to find another third party candidate who raised enough funds in primary season to secure FEC match funding.

Further, the issues she addresses are not as much those of the fringe left as some American Greens have been known for. She is an activist not for 9/11 truth commissions, but for free education and full employment. She says she decided to run when Obama accepted Congress’ deal on the debt ceiling – allowing massive cuts to America’s already threadbare welfare state. She makes an articulate case for significant changes in America’s economic system which would otherwise not be on the ballot paper in many states – a case which I imagine most readers of this blog would support.

There is a simple case for voting for her: if you don’t vote for what you want, you’ll never get it. By voting Green in America, you are playing a long game, contributing to the building of a credible third party. The bigger the Green vote this time, the bigger the Green voice in the media next time. If it reaches 5%, then the rules start to change – they begin to get more significant federal funding. This would be a good thing: America needs change, and neither Democrats nor Republicans offer it.

There is also perhaps a slightly more complex case. At the moment, all swing voters in American politics are on the centre right of their spectrum – between the right of the Democrats and the left of the Republicans. Those on the left are seen as solid Democrats and so ignored. To be noticed – to shift American politics to the left – these voters need to be seen as swing voters. If there was a credible risk that those who believe in free education, for example, would not vote for Obama, then perhaps Obama would shift his platform in their direction. Only if you are willing to play hard to get with your own side can you stop it copping off with your opponents.

Independents don’t actually hold the key to victory. In the three closest elections since exit polls began, the candidate who won amongst independents lost the White House. The people who do hold the key to victory are the solid Democrats or Republicans. But because the only thing they can do if they don’t like their candidate is not turn out, they don’t ever make any active statement about what they would like. They don’t show what candidates need to do to win them back. If their way of playing hardball is to remain silent, they will continue to be ignored.

On the other hand, if, for example, Democrats believe that they lost in 2000 because a few voters in Florida couldn’t stomach Gore and so voted Nader, how did they change their platform in 2004 and 2008 to win those voters back? What would they have run on if they hadn’t suffered that loss? We will never know, but I suspect that somewhere, in some strategy meeting, this was at least briefly discussed. And I suspect that a significant vote for Jill Stein in swing states – whether or not it costs Obama the White House – would force them to ask these questions again.

The case for voting for Obama is also clear. It can be summed up in two words: Mitt Romney. Despite all of the criticisms quite rightly levelled at Obama, there is a choice in this election. It is a choice between two capitalist candidates, yes. But those who see no difference between Obama and Romney won’t be on the rough end of Romney’s welfare cuts. The idea of this man with his finger on the nuclear button is enough to keep me awake at night. Obama, on the other hand, for all his many, many flaws, has been the best president since Carter.

The American system is not the same as the British system in two key ways. In the UK, if you vote Green, particularly in some of the party’s strongholds, there is a credible chance this will build a vote which will secure an MP within this generation – Brighton went from less than 3% in ’97 to a Green MP in 2010. In the UK, this Green MP, though not the government, can represent you, and can help change politics day in, day out. On the other hand, Labour losing one seat is unlikely to cost them Number 10.

In American presidential elections, you get no such result from your vote. You don’t get an MP, it’s all or nothing – president or not. The notion Greens will win president this generation seems extraordinary (though, of course, history is littered with tales of the extraordinary). Similarly, if you live in a swing state, there is a genuine chance that your state could swing the whole election in a way one constituency just won’t.

The second key difference is the primary system. One of the (many) reasons I am not in the Labour party is that I do not see how by joining I could expect to change it. Pressure from the outside seems a much more viable option. This isn’t the case to the same extent in the Democrats. If we take the job of president, then I could have an active role in choosing a new party leader through an open primary process every four (or, if there is an incumbent, in practice, eight) years.

Where does this leave us? In some states, it is easy. Where Obama is certain to win, or Romney is certain to win, Americans may as well vote Green. This will bring them one vote closer to the magic 5% mark, and it will secure them one more votes worth of media coverage next time round. But, in another sense, this is pointless. The best reasons for voting Stein I listed above apply most of all in swing states. If the point is to play hardball, then you have to be tough. And that means following through, even if you live in Ohio… and that means risking Romney’s finger on the big red button.

American voters have a tough choice on Tuesday. They can vote for the managed decline of Barack Obama. Or they can vote for a better future and risk the disaster of Mitt Romney. The decision they have to make will impact on the whole world, and I don’t envy it.