A guest post from Richard Laird. Richard is a Politics graduate from the University of Dundee and past parliamentary candidate for the Scottish National Party who tweets as @Richard_Laird.

Those of you who saw last night’s Newsnight Scotland will have seen Professor John Curtice raise the possibility of altering the system used to elect the Scottish Parliament. Specifically, Professor Curtice suggested changing the way regional MSPs are elected by replacing the D’Hondt formula with the Sainte-Laguë equivalent.

Named after French mathematician André Sainte-Laguë (left), and used in numerous countries as a form of proportional representation, the Sainte-Laguë method uses the same process as D’Hondt with one change: the formula. In Scotland under D’Hondt, regional seats are allocated to parties (or Independents) by dividing their regional votes by one more than the number of seats they have already won. Under Sainte-Laguë, the process is the same except the regional votes are divided by one more than double the number of seats won. In practice, this means that instead of the vote being divided by 1, 2, 3, 4, etc., it is divided by 1, 3, 5, 7, etc. Let’s look at a worked example.

Here is the (condensed) result from the West Scotland region in last week’s election:

This result meant Labour won three regional seats, the Nationalists won two, and the Conservatives also won two. If Sainte-Laguë had been used, here is how the count would have played out:

As you can see, the Conservatives retain two seats while the Greens and LibDems each win one seat with Labour and the SNP losing out accordingly. A similar story transpires across Scotland producing a Parliament which looks like this:

Because it removes the bias towards larger parties, Sainte-Laguë would have seen the Greens and Lib Dems benefit at the expense of the SNP and Labour. It would also have seen George Galloway elected in Glasgow. The reason for this is that Sainte-Laguë makes it easier for a smaller party to win a first seat, but increasingly difficult to win additional ones. Only Central Scotland would be without a Green MSP with the SNP losing its top-up seats in Mid Scotland & Fife and North-East Scotland. Overall, the regions would now look like this:

Obviously, the changes in membership would have ramifications for the functioning of the Parliament. The increase in Green MSPs would see the party given with a seat on the Parliamentary Bureau (which determines what business the Parliament will conduct) and would likely see the Greens and LibDems posing questions to the First Minister on alternating weeks, as the Greens and SSP did between 2003 and 2006. Crucially, the SNP would be one seat short of a majority and would require the support of at least one other MSP to get motions and Bills through. However, the balance of pro- and anti-independence MSPs would remain the same with five Nationalists swapped for five Greens.

In his remarks on Newsnight, Professor Curtice addressed the fact that the SNP won a majority of seats on a minority of the vote and how the Holyrood electoral system was supposed to prevent this. His suggestion of a switch from D’Hondt to Sainte-Laguë would indeed have prevented this (just!), but would not have stopped pro-independence parties winning a comfortable majority. A move to Sainte-Laguë would improve the proportionality of Holyrood, but what really distorts the outcome is the existence of constituencies electing by First-Past-the-Post and the fact that these constituencies elect a majority of MSPs. If you want a purely proportionate parliament, change that instead.

Despite the crushing referendum result last week, there is one place AV will never be displaced – when politicians choose one of their own. It’s not just Labour – even the Tories do it. Sure – it’s often done differently, round by round, to allow some very sophisticated game-playing (although that doesn’t work when the membership get a say). When the Tories chose between IDS, Ken Clarke and Michael Portillo, the IDS crowd lent their first round votes to Clarke because they knew a) that their guy would make the next round and b) Ken Clarke couldn’t win.

And you can see why they use it. Candidates with a narrow support base (like Clarke in 2001) would come through the middle, especially if two similar candidates stand. You get to express all your preferences. You can vote sincerely throughout (although as above, spreading it out over several separate ballots allows a bit more gaming to come in).

Today Holyrood will use the same system to elect a Presiding Officer. We have three candidates who could almost have been designed to demonstrate this principle. Two fierce SNP women, Christine Grahame and Tricia Marwick, plus Hugh Henry, a dry but impressive former Labour minister. Christine declared first, and without iterated run-offs, that would surely have kept Tricia out. Instead she’s surely going to win.

Assuming for the sake of argument a degree of voting by party, which is unfortunately pretty likely even for a notionally non-partisan role, and assuming the rest of the tattered Yoonyonisht Conshpirashy back Hugh, it’s easy to see how he could win. Yet there can be few in the Chamber with a first preference for either of the SNP candidates and a second preference for Hugh.

The fact remains, as the AV campaign should have said, preferential voting remains the only sensible way to indicate opinion and count votes when electing a single candidate (fans of various obscure Condorcet mechanisms please take it up in the comments). And as should be obvious, there’s no good way to elect single candidates and achieve proportionality.