In the face the forthcoming constitutional haggling that appears set to follow Thursday's election, the identity of the next Secretary of State for Scotland has more than a hint of the parochialism of the "Titanic sinks: North-east man lost at sea" headline.

Nevertheless, if the polls are correct and the SNP win more than 50 seats, the question does present some interesting options.

The simplest possibilities first. If there is a continuing Conservative-Liberal Democrat coalition government, the logical likelihood is that Alistair Carmichael remains in post (or, if the Conservatives win more than one Scottish seat, potentially one of them would take over but let's not complicate things too much yet). Similarly, if Labour end up governing, the likelihood is that they'd nominate one of their remaining Scottish Labour MPs. So far, so straightforward.

However, if the SNP sweep the board in Scotland (and some polls last week suggested this is a possibility) there would obviously be no Scottish Labour, Conservative or Liberal Democrat MPs. So if you are Prime Minister Cameron or Miliband, who becomes your Scottish Secretary?

The Cabinet Manual suggests it is "convention" that ministers are Members of the House of Commons or the House of Lords. Nothing says the Scottish Secretary has to represent a Scottish constituency (indeed, the Northern Ireland Secretary tends not to represent a Northern Irish constituency). However, the problem for either of the large UK parties is that, if they have just been defeated rather heavily in Scotland, would an MP from elsewhere in the UK have any legitimacy as Scottish Secretary? Legitimacy of a different kind would also hamper the Lords from providing the role, though there may be some candidates there (former First Minister Jack McConnell, or Annabel Goldie?). Rather radically, might the job be offered to an MSP, like the increasingly popular Scottish Conservative leader Ruth Davidson? Unconventional, but a possibility in these rather changed political times.

Failing those options, might a minority Labour government offer the role to an SNP MP, potentially Alex Salmond? Both parties have been quick to rule out a formal coalition, but a deal that put the SNP in charge of the brief might make some sense: it would recognise the SNP won the election in Scotland, help to rebuild relations between the parties - and also pass off the difficult decisions to the SNP. Though would the SNP accept such a role? It would make more difficult their claims that Edinburgh was being constrained by Westminster politics.

Potentially the most likely option, irrespective of the colour of government, is the abolition of the post entirely, and the creation of a Secretary of State for Devolution. This would remove the immediate problem of legitimacy while emphasising the importance of the constitutional reform process going forward. This is an idea that has been discussed at several points in the past, though the election's outcome might force the government to make such a change.

At this point, all bets are off.

Dr Harvey is a research fellow at the Centre on Constitutional Change and the University of Aberdeen.