IF you ever play the game Famous Belgians, then remember the name Joseph Auguste D’Hondt alongside Audrey Hepburn and Hercule Poirot. D’Hondt (1841-1901) was the eponymous inventor of a system of proportional representation for counting votes that will likely determine Scotland’s constitutional future. Apart from the fact he was a professor of civil law at Ghent Universit and married an English woman called Anne Clifford, Mr D’Hondt has left little by way of an historic footprint. Apart, that is, from his elegant but fiendishly complicated vote counting method.

Proportional representation became an issue the moment democracy reared its head with the American Revolution. The second US President, John Adams, summed up the issue thus: “A governing assembly should be in miniature, an exact portrait of the people at large. It should think, feel, reason, and act like them”. The problem lies in how to elect that assembly, so it reflects the electorate at large. The 19th century was devoted to a raging, disputatious debate as to how to resolveg that problem.

Essentially two broad approaches emerged – if you don’t count the absurdly simple idea of Rowland Hill, inventor of the British penny post, that voters form as many groups as they wish, with each group getting precisely one vote. The two mainstream approaches to proportional representation (PR) are the Single Transferable Vote (STV) and what we now call the D’Hondt system.

STV is used in Scottish local elections, on the grounds that every stage of democracy north of the border has to be conducted by different counting rules, the better to bamboozle the voters. STV involves multi-member constituencies in which voters rank their choices. Seat allocation works like a set of champagne glasses stacked in a pyramid. When a candidate’s glass is full (i.e. reaches a set quota of votes) their overflow (unused quota) cascades to other contenders. The math is daunting, but the outcome is clear: absolutely every vote counts.

STV is different from the D’Hondt system because it focuses on the individual candidate. Under STV, a voter can, say, tick all the women candidates regardless of party. It also yields a reasonable exact proportionality between votes cast and seats obtained. Possibly this is why the British MPs rejected the advice of an impartial Speaker’s Conference in 1917 to introduce STV for UK general elections.

READ MORE: Pro-independence parties blast Scotland in Union's 'desperate' tactical voting tool

What does the D’Hondt system have going for it? Here we need to understand why figuring out an exact proportional representation between seats and votes is more difficult than it seems. The central issue has to do with how you allocate leftover fractions of the vote. Imagine a parliament with 100 seats. Any party securing at least 1% of the vote gets a candidate elected. What could be simpler? But consider what happens if a party gets 25.5%. Does it get 25 seats or 26? If I tell you there are 21 parties standing on the regional list in Glasgow on May 6, you will appreciate why counting fractions of votes is important.

MOST of the multitude of different proportional representation systems are merely different ways of dealing with the problem of allocating these odd fractions. The D’Hondt is the most popular. It starts by trying to allocate the fractions among political parties rather than through a myriad individual candidates. This makes matters simpler, but you can instantly see the hidden assumption. The D’Hondt puts parties to the fore – the larger (in votes) the better.

It works like this. Sorry but we can’t avoid some mental arithmetic. Suppose we have a small parliament (or constituency) with 9000 voters electing nine representatives. And suppose the vote was divided by three parties – Yellow, Blue and Red. The vote goes Yellow (50%), Blue (39) and Red (11). Fractional allocation of seats is vital here. Give Yellow five of the nine seats and they are in control.

The D’Hondt system centres on allocating seats using a particular quota system to allocate the fractional leftovers. Algebraically, the quota is represented by V/(S+1), where V is the total number of voters, and S is the number of seats. Other systems use different quotas. V/(S+1) is the unique bit of the D’Hondt method, as proposed by the man himself.

Go back to our example: the D’Hondt quota is 9000 votes divided by 9+1 seats, or 900 votes. The Yellow Party polled 4500 votes, so it gets five seats. Blue received 3510 votes, but it gets only three seats despite a 39% vote share. It has 810 votes that count for nothing. Red got 990 votes overall. That yields one seat with only 90 votes wasted. In this case, Yellow gained seats proportionately as it had no odd fraction of votes unused. Technically: the bigger the party vote, the smaller the wasted fraction of votes, the more seats you get.

THIS is where folk start to pull out their hair. Why is the quota V/(S+1)? A different quota would produce a different electoral outcome. In other PR systems, the quota is a straight V/S, where V is again the number of voters, and S the number of seats. In our example, with 9000 voters and nine seats, the quota is now 1000 votes, which seems more intuitive. That immediately gives the Yellow Party four seats and the Blue Party three seats, with fractions to spare. But Red, with only 990 votes, just misses the quota. How then to allocate the last two seats? Because Yellow and Blue have big “spare” fractions of vote share unused (0.5% and 0.51% respectively), they each get an extra seat. Poor Red is still left unrepresented.

Your brain may be in a tizzy, but the implication is clear. The D’Hondt system wins over others because its method of setting the quota minimises the left-over fractions of votes to allocate. This makes seat allocation more proportional. However, it does this by slightly favouring the parties with the biggest vote share – in our example, ­Yellow had a majority under straight D’Hondt.

So far, so good. But we are about to complicate matters by mixing voting systems, as in the ­Holyrood Parliament. In establishing the Scottish Parliament in 1999, it was decided to retain one-member constituencies in order to retain the direct link between elected representatives and their electors. However, to ensure proportional representation overall, a top-up system was added. This involves extra MSPs elected on regional lists, to correct any bias from first-past-the-post (FPTP). These ­latter are elected on a variation of the D’Hondt system.

The variation concerns the way the quota is worked out. In this case, the formula for deciding the quota needed to elect a list MSP is still D’Hondt’s V/(S+1), but the actual V and S here are a bit different. For Holyrood elections, the V is the vote cast for a particular party on the regional list. The S is the number of seats already won by each party via the FPTP constituency process – so the S differs with each political party. Remember that the D’Hondt formula is only a mathematical way of allocating left-over vote fractions – it has nothing to do with politics per se.

What does this mean for the notion of a “super majority” at Holyrood, given the intent of the system is to produce a rough proportionality between votes and party seats? The D’Hondt system chosen for Holyrood was never designed to function with exclusively list parties. Rather, it was designed purely as a top-up to counterbalance excessive gains via FPTP. But in the 2021 Holyrood election, parties are standing exclusively on the list as a way of gaining extra seats for the indy cause.

THE risk in the latter course is that on a vital issue it could lead to over representation. On the other hand, in a nation struggling for independence, it is worth remembering that the D’Hondt system was imposed on Scotland not as a means of securing electoral fairness but in a deliberate attempt to stop the SNP winning a majority via FPTP. If the national movement seeks to break that barrier by gaming the D’Hondt voting mechanism, some might see that as a legitimate tactic.

In the broadly similar German system, the possibility of gaming is recognised and regulated. Regional list parties not represented in the Federal Parliament must obtain the signatures of at least one-thousandth of a state’s eligible voters. Also, for the calculation of the electoral threshold, candidate lists at a state level can be deemed as connected with the national vote of parties of a similar ideological hue – a matter decided by the Federal Returning Officer. We might speculate that such a procedure could be introduced by Westminster should a pro-indy super majority appear at Holyrood. But any such Westminster intervention to alter the existing voting rules would provoke widespread anger in Scotland.

Is a super majority actually possible in current electoral circumstances? Certainly, SNP FPTP constituency gains regularly result in very few list seats. Any SNP’s list victories accrue where it has fewer than average FPTP seats. However, there is an obvious problem for pro-indy parties in profiting from the SNP’s lack of list seats. Remember that the D’Hondt system deliberately favours the bigger parties – that includes the traditional Unionist parties – when it comes to allocating unused fractions of votes.

Gaming the D’Hondt system is not easy given its in-built bias to large, established parties. But that never stopped anyone trying.