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Can we do a quick show of hands?

Act 1: The UK

You’re at a late night AGM for the local community club. The passions are high because the stakes are low. It’s time to elect a new president. Jimmy, Paddy, and even Mary – believe it or not! – are throwing their proverbial hats in the ring.

Now Jimmy is trying to look tentative, but we all know he’s keen. Paddy’s keen too, but having a hard time holding keen in. Mary doesn’t know what she’s getting in to, but she knows Jimmy can’t tell a tab key from a spacebar. Paddy certainly would know a bar, and maybe a bar tab.

It’s already very late, but someone says “It’s getting a bit late, can we just do a quick show of hands?”. And the hands go up – 10 for Jimmy, 8 for Mary and 7 for Paddy.

And there you have it, “First Past the Post” – possibly one of the oldest forms of election – gives Jimmy the reins of power at his local community club.

Well… almost.

Act 2: France

Jimmy would have been riding high were it not for one man – the former president, no less – Mr. Tommy Byrne.

Now Tommy has been president for thirty-seven (yes, 37) years. He would have stepped down long ago were it not for reasons nobody remembers. Tommy would happily go for another spin around the sun as president; were it not for his double hip replacement, triple bypass, hernia, sore back and high blood pressure.

Tommy, like Mary, recognises that neither Jimmy nor Paddy could organise a piss-up in a brewery. If Jimmy mounts the throne, Tommy might as well throw his thirty-seven year legacy down a deep bog hole… perhaps along with that club-house photo of himself, in his hey-day, with Jackie Charlton in 1994.

So Tommy says… “Lads”… “Lads, it’s simple”… “We’re going for a second round. Jimmy and Mary there were the top scorers, so we’ll make the decision with a final show of hands.” And the hands go up – 12 for Jimmy, 15 for Mary.

And there you have it: “First Past the Post – with Two Rounds” sweeps Mary in to power. She wasn’t the most popular, but she was the least disliked!

Act 3: The Republic of Ireland

When it comes to serious matters, the Irish government has moved beyond what is done in the UK. And, yes, the French have some nice tricks – like that sneaky second round. But, the Irish have something even better – something trendy – perhaps invented only in the 1800s. We, as a 1920s new republic, were the among the early-ish adopters of Proportional Representation and the Single Transferable Vote!

And who doesn’t like representation? And if you like representation, who wouldn’t want it to be proportional?

Perhaps it’s not the best approach for an AGM, but it’s really quite simple:

  1. Voting. Let’s say we’re electing a council of 5 people, 1,200 people vote and each voter lists out their top ten candidates*.
  2. Quota Calculation*. With 1,200 votes and 5 positions to elect, divide the valid votes by the available positions plus one, and then add one**: 1,200 / (number_of_seats+1) + 1 = 201. This is called the “quota”. That’s the number of votes to get elected.
  3. First Round. In the first round, we tally up all of the votes according to the first preferences. Anyone who gets more than 201 votes is straightaway elected.
  4. Redistributing Surplus Votes. Now we get to why it’s called the “Single Transferable Vote”. Any elected candidate receiving over 201 votes has their excess votes “redistributed”. This means taking excess votes (say 199 excess votes, if an elected candidate got 400 initial votes and 201 is the quota) and looking at the number two preference on those votes. If any as-of-yet unelected candidates now cross the 201 vote mark, they too are deemed elected. This process continues until the excess votes of all elected candidates are distributed.
  5. Eliminating Bottom Candidates. You might think – at this point – we have elected all five candidates. Not necessarily. For example, there might be four elected candidates (each with 201 “quota-votes” each, accounting for 804 out of the 1200 total votes) and then six unelected candidates, each with 68, 67, 66, 66, 65 and 64 votes, respectively (including votes they earned in redistributions until this point). To fill that final seat, we move to a new set of rounds whereby the candidate with the lowest number of votes is eliminated. Each vote is transfer to the next listed candidate. If the 2nd candidate listed on a vote was already elected, that vote is re-re-distributed to the 3rd candidate on the vote, and so on. This continues until eventually a fifth candidate will reach the quota and deemed elected.

You see… Easy! Trendy!

*yes, if you pick nine terrible candidates, there’s a chance your vote gets transferred to the tenth (assuming there are at least 14 total candidates if there are five seats).

**If you have trouble understanding why the denominator has the number of positions “plus one”, it’s helpful to think of a council with just two elected positions. In that case, given 100 votes, you would need 100 / (1+1) +1 = 51 to get elected.

Act 4 – The UK, revisited

In a single-round “most votes wins” type system like the UK parliamentary elections, constituencies/districts are defined with one representative per district. To get elected, you don’t need a majority of the votes in that district. You just need the most votes. Sometimes that might be 51%, but sometimes that might be 31%.

In a naive sense, “most votes wins” does not provide representation that is proportional to votes. Rather, first-past-the-post gives all of the representation to the candidate with the most votes.

Although, this is a misleading way to frame things because it is a static perspective. Namely, both political parties and voters respond to the electoral rules.

In “most votes wins”, a losing strategy is to focus on the political views of a minority, say 30%, of the population. The reason is mathematical. Since there there are no prizes for second place, there is a huge incentive to win as high as possible of a share of the vote. Said differently, the marginal benefit of increasing the percent of the vote you win is extremely high. In proportional representation, you more smoothly win positions/seats as you increase your percentage share of the vote, which makes it more of a vote-winning strategy to not focus on catering to a majority.

Owning to these mathematics, first past the post systems tend towards two party systems, with each being pulled towards the middle to win voters and get the disproportionate rewards that come with a larger voter share. This is seen in the US with the Democrats and Republicans, and also in the UK with Labour and the Conservatives.

One long term challenge with systems of government is in avoiding lethargy and corruption. One solution to that challenge is to make it easy for the government to be replaced peacefully and completely. With first-past-the-post, parties fight for the middle-ground and earn a majority of power with a minority of representation. This allows for incumbent governments to be replaced in their entirety. It can also provides voters with two complete and competing programs for government.

Here is a chart of the recent UK parliamentary election, with number of seats on the y-axis and voting percentage won on the x-axis.

Figure 1. Seats won in the UK Parliamentary Election on the y-axis and percentage share of the vote on the x-axis. Labour is in red, conservatives in blue, Liberal Democrats in orange. Notice how about 35% of the vote can win 65% of the seats (400/650). Data taken from BBC. Notice also the upwards sloping shape of the curve, providing disproportionate benefit from trying to cater to a larger group of voters rather than a smaller segment of voters.

If you look at the UK system statically, you can say – that’s 65% of the seats for only 35% of the vote. But, if you look at the shape of that upward pointing curve, that’s what allows you to understand incentives dynamically. Dynamically – and perhaps the last decade+ of conservative governments is a counter example – this incentive structure gives winning parties the seats required to implement a comprehensive plan for government AND it allows for them to be swapped out – almost in their entirety – if they do not perform.

Act 3 Footnote: The US is a first-past-the-post voting system and has converged to a two party system. However, it’s parliament is not as autonomous as in the UK. US Government power is spread out between the house of representatives, the senate, the judiciary, and, to some degree, the president. This, and the overlapping nature of senate and house representative terms (e.g. there are two senators per state, but they are elected two years apart for a period of six years each), means that achieving a more complete change in government is difficult. And, yes, to some degree (excluding things like filibusters) this was by design and has benefits.

Act 5: France, Revisited

While labour won 65% of seats with about 35% of the vote, the party in France that won the highest percentage of the votes in the first round (~30%, or 33% including the extreme far right) – shown in yellow below – probably won’t make it into government. Why? They were unable to reach a majority, partly because – in a second round of voting – the trailing candidate out of Melenchon’s New Popular Front or Macron’s “Ensemble pour la Republique” dropped out intentionally in certain constituencies, boosting the other party’s votes won relative to the Rassemblement National (Marine Le Pen and Jordan Bardella’s party). Candidates eliminated after the second round likely benefitted Melenchon and Macron over Le Pen/Bardella as well.

Figure 2. French Parliamentary Elections. First round in yellow. Second round in orange. The y-axis is the percentage of the vote won (not seats). Data from wikipedia.

The static argument for France is: “If France had first-past-the-post, then Le Pen’s Rassemblement National would have been in power”.

The dynamic argument is that, if France had first past the post, parties would not be successful by focusing on specific segments of the population as they each did. One has to ask:

  1. Would Rassemblement have been so successful? Or, would they have been pulled much more towards the median voter, or forced to shed more of their outlying members?
  2. Would Melenchon’s party/coalition have been pulled more towards the middle? AND/OR would both Macron and Melonchon’s parties have been more willing to engage and address issues underlying increased votes for the Rassemblement?

Clearly there are many greater factors at play, but it is worth reflecting on the role of the electoral system. This is particularly true because, in France, the central government wields strong centralised power over the country. Much less power is devolved to provinces as is the case in Switzerland, or even Finland. This probably makes the national election results and the choice of electoral system too important!

Maybe you felt Macron did many great things and now you are disappointed that he will be replaced by something worse. But, perhaps everyone would be better off if so much in France didn’t hinge on the choice of central government.

Act 6 – Ireland, revisited

Statically, representation is proportional to votes.


  • The third largest party wields disproportionate power because they often bring decisive votes to form a coalition government. That third party may well be distant from the median voter’s desires. The Progressive Democrats and Green Party provide examples of small impactful parties in recent history (and I’m not judging here whether those impacts were good or bad). One might can make this case that is is good or that it is bad.
  • Since seats are proportional to representation, the margin by which coalition governments rule tends to be thin – making it hard for governments to enact much change in any new plan for government.

This is largely where Ireland is at present:

  • Three large minority parties and a very large group of independents.
  • No party can credibly claim (largely owing to electoral system reasons) that they will implement a comprehensive improved program for government – they just won’t have the electoral mandate (i.e. a strong enough majority of seats).

Whether one considers stasis to be a problem in Irish government or not, the electoral system does drive the government towards stasis.

Coda: The virtues of Representation

I’m writing strongly in favour of first-past-the-post systems – mostly because I see that position as under-appreciated. I don’t have a strong feeling on whether Ireland sticks with Proportional Representation. Given the choice, I would weakly favour moving to first-past-the-post – provided more government responsibility and taxation were moved to counties and to cities outside of Dublin. More important than the choice of PR or of First-past-the-post is the ability for a country to allow for peaceful transitions of power through elections. That lever has a bigger effect on success or failure.

Looking at electoral systems as I have is too narrow for another important reason – it omits thinking about political systems as having different scales, e.g. national versus county versus city/town. The best way to have effective representation is to have the right levels of responsibility and taxation at each level of government.

I’ll give an argument that I see as a stretch, but worth consideration… Ireland is Dublin-centric. Nearly all taxing power is in Dublin and nearly all spending power requires approval from Dublin. Maybe this is an underlying current in why we want to keep proportional representation, albeit a (small?) contributor to government stasis. Perhaps, if the Irish system of government was more like Switzerland – with more taxation and spending responsibility resting outside of the capital – then national elections would be less consequential and we would be pleased to see a completely fresh government from time to time. As I mentioned above, perhaps this is the underlying problem for France?

And I don’t say that with confidence. I just put it as a question.

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