Electoral systems compared

ballot paper photo
Photo by david-gilmour
We use four different electoral systems in Scotland (FPTP, AMS, STV and d’Hondt), and a few years ago there was a referendum on using the AV system for Westminster elections. Another possible system is the one used in Denmark. Most people discussing these tend to focus on one or two at a time, so to make it all a bit clearer, I decided to compare all these systems in one post.

What I’ll do in the following is that I’ll test the various systems on a hypothetical council area contain five wee towns: Auchterclyde, Balclyde, Carclyde, Dunclyde and Ellanclyde. Only four parties are standing: The SNP, the Conservatives, Labour and the Greens. Here are the candidates and the number of local supporters they have:

Constituency CON GRN LAB SNP Voters
Auchterclyde North Caitlin (790) Gabriel (190) Lachlan (456) Samantha (1009) 2445
Auchterclyde South Caleb (732) Gabriella (275) Lana (333) Samuel (1465) 2805
Auchterclyde West Callum (718) Gary (290) Lara (592) Saoirse (1339) 2939
Balclyde North Calvin (538) Gavin (254) Layla (349) Sarah (1083) 2224
Balclyde South Cameron (551) Gemma (317) Leigha (568) Scarlett (1112) 2548
Balclyde West Caoimhe (717) George (238) Lennox (422) Scott (1543) 2920
Carclyde North Casey (558) Georgia (306) Leo (452) Sean (1327) 2643
Carclyde South Catherine (675) Georgina (387) Lewis (311) Sienna (905) 2278
Carclyde West Charles (640) Gertrude (300) Liam (485) Simon (1435) 2860
Dunclyde East Charlotte (647) Giovanni (316) Lily (456) Skye (871) 2290
Dunclyde North Chloe (416) Gloria (237) Logan (308) Skylar (1424) 2385
Dunclyde South Christian (781) Gordon (399) Lola (549) Sophie (953) 2682
Dunclyde West Christopher (713) Grace (253) Louis (395) Stanley (1343) 2704
Ellanclyde East Clayton (407) Grayson (341) Lucy (331) Stephen (1522) 2601
Ellanclyde North Cole (678) Gregor (255) Lukas (514) Struan (1097) 2544
Ellanclyde South Conor (786) Greta (305) Luke (535) Stuart (1596) 3222
Ellanclyde West Curtis (559) Gus (261) Lyle (392) Szymon (1081) 2293
All 10906 4924 7448 21105 44383

FPTP (the Westminster system)

Under FPTP (First Past The Post) each of the 17 areas elect one candidate, and that’s simply the person who gets the most votes. You cannot transfer votes, rank the candidates, or vote for a candidate standing elsewhere.

Here is an example of a completed ballot paper:

Ballot Paper for the Auchterclyde North Constituency

Caitlin (CON) ☐
Gabriel (GRN) ☐
Lachlan (LAB) ☐
Samantha (SNP) ☒

Here are the results of the election:

Constituency CON GRN LAB SNP Result
Auchterclyde North 790 190 456 1009 Samantha (SNP)
Auchterclyde South 732 275 333 1465 Samuel (SNP)
Auchterclyde West 718 290 592 1339 Saoirse (SNP)
Balclyde North 538 254 349 1083 Sarah (SNP)
Balclyde South 551 317 568 1112 Scarlett (SNP)
Balclyde West 717 238 422 1543 Scott (SNP)
Carclyde North 558 306 452 1327 Sean (SNP)
Carclyde South 675 387 311 905 Sienna (SNP)
Carclyde West 640 300 485 1435 Simon (SNP)
Dunclyde East 647 316 456 871 Skye (SNP)
Dunclyde North 416 237 308 1424 Skylar (SNP)
Dunclyde South 781 399 549 953 Sophie (SNP)
Dunclyde West 713 253 395 1343 Stanley (SNP)
Ellanclyde East 407 341 331 1522 Stephen (SNP)
Ellanclyde North 678 255 514 1097 Struan (SNP)
Ellanclyde South 786 305 535 1596 Stuart (SNP)
Ellanclyde West 559 261 392 1081 Szymon (SNP)

The result is thus that the SNP wins all 17 constituencies, although they didn’t have a majority in most of them. Many of the SNP candidates would therefore have been vulnerable to tactical voting.

First Past The Post works great when there are only two candidates. As soon as the number increases, the number of wasted votes goes up, and it becomes more important to vote tactically for a candidate that can win instead of the one you actually prefer – one might argue that the best thing to do is to vote for your biggest enemy’s most popular enemy.

Advice for pro-independence voters: Vote for the SNP candidate – voting for any other party is a wasted vote.

  • Simplicity: ✔✔✔✔✔ (it doesn’t get any simpler than this)
  • Proportionality: ✔ (it doesn’t get any less proportional)
  • Voter engagement: ✔✔ (if you live in a swing seat, you’ll get a lot of attention, and your vote really matters, but otherwise you’ll get ignored, and you might as well stay home on the couch)

AMS (the Holyrood system)

Under AMS (the Additional Member System), the number of FPTP constituencies is reduced from 17 to 10, and the remaining 7 seats get distributed using d’Hondt (see below for details on this system).

To make this work, every vote has to fill out two ballot papers, one for the constituency and one for the region:

Ballot Paper for the Auchterclyde North and South Constituency

Caleb (CON) ☐
Gabriella (GRN) ☐
Lana (LAB) ☐
Samuel (SNP) ☒

Ballot Paper for the Auchterclyde–Balclyde–Carclyde–Dunclyde–Ellanclyde Region


The regional vote doesn’t allow the voter to prioritise candidates. Instead, the parties create party lists ranking them. For instance, in this example the Green party lists is as follows:

  1. Gabriella
  2. Gemma
  3. Georgina
  4. Gloria
  5. Grace
  6. Gregor
  7. Gus

This means that Gabriella gets the first Green seat, Gemma the second one, and so on. Poor Gus doesn’t have realistic chance of getting in.

Here are the results of the constituency vote:

Constituency CON GRN LAB SNP Result
Auchterclyde North and South 1522 465 789 2474 Samuel (SNP)
Auchterclyde West 718 290 592 1339 Saoirse (SNP)
Balclyde North and South 1089 571 917 2195 Sarah (SNP)
Balclyde West 717 238 422 1543 Scott (SNP)
Carclyde North and South 1233 693 763 2232 Sienna (SNP)
Carclyde and Ellanclyde West 1199 561 877 2516 Szymon (SNP)
Dunclyde East and North 1063 553 764 2295 Skylar (SNP)
Dunclyde South and West 1494 652 944 2296 Stanley (SNP)
Ellanclyde East and North 1085 596 845 2619 Stephen (SNP)
Ellanclyde South 786 305 535 1596 Stuart (SNP)

The regional election results are as follows:

Party Share of vote Seats gained Candidates elected
LAB 17% 2 Lana, Leigha
GRN 11% 1 Gabriella
CON 25% 4 Caleb, Cameron, Catherine, Chloe
SNP 48% 0

Note that no SNP candidate gets elected because the party already got more than their fair share on the constituency ballot – the d’Hondt result would have been 8 SNP members instead of 10, and Labour and the Greens would both have benefitted from this.

In some other countries using AMS (Germany and New Zealand), they elect more members to prevent this from happening – in this case extending the number of elected representatives from 17 to 20 would have allowed a “correct” d’Hondt result, namely SNP 10, CON 5, LAB 3, GRN 2.

The fact that this doesn’t currently happen in Scotland means that it’s both very tempting and very dangerous to vote tactically, as many pro-independence voters found out last year.

Advice for pro-independence voters: Cast your constituency vote for the SNP, and use the list vote to support your favourite party. Tactical voting is dangerous.

  • Simplicity: ✔ (having two ballot papers is bad enough, but explaining the system to all voters is practically impossible)
  • Proportionality: ✔✔✔✔ (the result is quite proportional, but it gets skewed when one party is much larger than the rest)
  • Voter engagement: ✔✔✔ (voters have a fair amount of influence, but it suffers from the same defects and FPTP and d’Hondt)

STV (the council election system)

Under STV (the Single Transferable Vote) there are a number of multi-member constituencies, and the voters rank the candidates. In this case we have created one constituency per town.

Here is an example of a completed ballot paper:

Ballot Paper for the Auchterclyde Constituency

Caitlin (CON) ⑩
Caleb (CON) ⑪
Callum (CON) ⑫
Gabriel (GRN) ④
Gabriella (GRN) ⑤
Gary (GRN) ⑥
Lachlan (LAB) ⑦
Lana (LAB) ⑧
Lara (LAB) ⑨
Samantha (SNP) ①
Samuel (SNP) ②
Saoirse (SNP) ③

An STV election starts with every voter’s first choice, and then goes through the following steps:

  1. A candidate who has reached or exceeded the quota (the minimum number of votes) is declared elected.
  2. If any such elected candidate has more votes than the quota, the excess votes are transferred to other candidates. Votes that would have gone to the winner go to the next preference.
  3. If no-one new meets the quota, the candidate with the fewest votes is eliminated and those votes are transferred to each voter’s next preferred candidate.
  4. This process repeats until either a winner is found for every seat or there are as many seats as remaining candidates.

This is obviously a rather laborious process, and it’s best done by computer.

Here is a graphical illustration showing how Samantha, Caitlin and Samuel got elected in the Auchterclyde constituency, assuming transfers from Green to SNP and from Labour to Conservative, and within a party to the person who comes first alphabetically:

Here are the full results:

Constituency Seats Elected candidates
Auchterclyde 3 Samantha (SNP), Caitlin (CON), Samuel (SNP)
Balclyde 3 Sarah (SNP), Cameron (CON), Scott (SNP)
Carclyde 3 Sean (SNP), Catherine (CON), Simon (SNP)
Dunclyde 4 Charlotte (CON), Skylar (SNP), Stanley (SNP), Lily (LAB)
Ellanclyde 4 Stephen (SNP), Stuart (SNP), Lukas (LAB), Cole (CON)

Note that the Greens didn’t manage to get a single seat, and Labour only managed to win one in the four-member constituencies. This is because STV at heart isn’t a proportional system, and especially if the number of seats per constituency is small, the larger parties will dominate.

Advice for pro-independence voters: Vote until you boak – i.e., rank all the candidates, starting with the pro-independence ones and ending with the Tories.

  • Simplicity: ✔✔✔ (both voting and counting the votes are a hassle, but the concept is easy enough to understand)
  • Proportionality: ✔✔✔ (the results aren’t proportional, but it’s much better than FPTP)
  • Voter engagement: ✔✔✔✔✔ (all candidates need to fight for every vote, and voters have a lot of influence)

D’Hondt (the European Parliament system)

Under d’Hondt, the voters simply vote for parties in big constituencies, and the parties create prioritised lists of their candidates. In this illustration, we’ve created two constituencies, Auchterclyde–Balclyde–Carclyde and Dunclyde–Ellanclyde.

Here is an example of a completed ballot paper:

Ballot Paper for the Auchterclyde–Balclyde–Carclyde Constituency


Here are the full results for the two constiuencies:

Constituency CON GRN LAB SNP
Auchterclyde-Balclyde-Carclyde 5919 2557 3968 11218
Dunclyde–Ellanclyde 4987 2367 3480 9887

To turn this into seats, we divide the votes by 1, 2, 3 and so on. The first seat then goes to the largest number (In the first constituency, that’s the SNP’s 11218 votes), the second seat to the second-largest one (the Tories’ 5919 votes), the third seat to the third-largest number (the SNP’s 11218 divided by 2), the fourth seat to the fourth-largest one (Labour’s 3968 votes), the fifth seat to the fifth-largest one (the SNP’s 11218 divided by 3), and so on. We continue until all the seats have been allocated.

We now look at the the parties’ lists of candidates to determine who has been elected.

Here is the full distribution of seats:

Constituency CON GRN LAB SNP
Auchterclyde-Balclyde-Carclyde (9) 2 (Caitlin, Caleb) 1 (Gabriel) 1 (Lachlan) 5 (Samantha, Samuel, Saoirse, Sarah, Scarlett)
Dunclyde–Ellanclyde (8) 2 (Charlotte, Chloe) 1 (Giovanni) 1 (Lily) 4 (Skye, Skylar, Sophie, Stanley)

The result is very proportional, and it’s easy to understand. The downside is that the existence of party lists makes it impossible to prioritise any specific candidate. For instance, if it seems likely that the Greens only will get one candidate elected where you stay, you have a problem if you cannot stand the person who is top of their list.

Advice for pro-independence voters: Vote for any party that seems likely to win a seat – SNP and Greens are probably fine, but the smaller parties might not be.

  • Simplicity: ✔✔✔✔✔ (it’s really simple)
  • Proportionality: ✔✔✔✔(✔) (it’s very proportional)
  • Voter engagement: ✔✔ (every vote counts, but individual candidates don’t have a direct incentive to talk to voters)

AV (the proposed new Westminster system that got rejected)

AV (the Alternative Vote system) is basically just STV in single-member constituencies. It’s a vast improvement on FPTP, but it’s really not a proportional system.

Here is an example of a completed ballot paper:

Ballot Paper for the Auchterclyde Constituency

Caitlin (CON) ④
Gabriel (GRN) ②
Lachlan (LAB) ③
Samantha (SNP) ①

The counting is done in the same way as under STV.

Here are the full results:

Constituency Seats Elected candidates
Auchterclyde North 1 Caitlin (CON)
Auchterclyde South 1 Samuel (SNP)
Auchterclyde West 1 Saoirse (SNP)
Balclyde North 1 Sarah (SNP)
Balclyde South 1 Scarlett (SNP)
Balclyde West 1 Scott (SNP)
Carclyde North 1 Sean (SNP)
Carclyde South 1 Sienna (SNP)
Carclyde West 1 Simon (SNP)
Dunclyde East 1 Skye (SNP)
Dunclyde North 1 Skylar (SNP)
Dunclyde South 1 Sophie (SNP)
Dunclyde West 1 Stanley (SNP)
Ellanclyde East 1 Stephen (SNP)
Ellanclyde North 1 Struan (SNP)
Ellanclyde South 1 Stuart (SNP)
Ellanclyde West 1 Szymon (SNP)

16 out of 17 seats go to the SNP, but in one seat the transfers from Labour managed to get the Tory elected.

It’s better than FPTP because tactical voting isn’t necessary – if you prefer the Greens, you can rank them first and the SNP second, instad of having to vote tactically for the SNP. However, it really isn’t a proportional system.

Advice for pro-independence voters: Same as for STV (vote until you boak).

  • Simplicity: ✔✔✔ (same as for STV)
  • Proportionality: ✔✔ (it’s not very proportional)
  • Voter engagement: ✔✔✔ (there are fewer safe seats than under FPTP, and more candidates have a chance)

The Danish system

The Danish electoral system (PDF) is really complex, and what follows is a simplification. For a more detailed illustration of how it could be applied to Holyrood elections, please see this blog post.

Under this system, you vote for one candidate and implicitly for the party they represent, inside a multi-member constituency. (This means that ballot papers can get quite long if there are many parties and many seats.)

Here is an example of a completed ballot paper:

Ballot Paper for the Auchterclyde Constituency

  Caitlin ☐
  Caleb ☐
  Callum ☐
  Gabriel ☐
  Gabriella ☒
  Gary ☐
  Lachlan ☐
  Lana ☐
  Lara ☐
  Samantha ☐
  Samuel ☐
  Saoirse ☐

In real life you now go through a phase of d’Hondt counting, but it doesn’t really matter very much because of the next step, so I’ll ignore this here. This is because we now calculate each party’s share of the total votes and allocate seats accordingly:


Party Share of vote Total seats
CON 25% 4
GRN 11% 2
LAB 17% 3
SNP 48% 8

We now distribute these seats amongst the towns. The way we do that is that we take each party’s votes in each town and divide the figure by 1, 3, 5, etc. For instance, the SNP in Ellanclyde got 5296 votes, so the figures are 5296, 1765, 1059, etc. We now put all these numbers for all parties and towns into own list and sort it. The largest number is the 5296 that Ellanclyde SNP got, and that means the first seat goes to the SNP there. The second-largest number is 4591, and that gives the second seat to the SNP in Dunclyde. We continue like this so long as the party and the town both need more seats. The first time it fails is when we reach 1806, which is the number of votes won by the Tories in Balclyde – Balclyde needs more seats, but the Conservatives don’t, so this doesn’t result in a seat. We continue like this until all 17 seats have been allocated. The last one goes to the Greens in Balclyde (809).

At this point, we know how many seats each party will get in each town. For instance, the SNP will get two seats in Ellanclyde. To pick the successful candidates, we don’t have a party list, but instead we look at the personal votes. In this town, Stephen got 1522 votes, Struan 1097, Stuart 1596 and Szymon 1081. The first seat therefore goes to Stuart and the second one to Stephen.

Here are the complete results:

Constituency CON GRN LAB SNP Total
Auchterclyde 1 (Caitlin) 0 1 (Lara) 1 (Samuel) 3
Balclyde 0 1 (Gemma) 0 2 (Scott, Scarlett) 3
Carclyde 1 (Catherine) 1 (Georgina) 0 1 (Simon) 3
Dunclyde 1 (Christian) 0 1 (Lola) 2 (Skylar, Stanley) 4
Ellanclyde 1 (Conor) 0 1 (Luke) 2 (Stuart, Stephen) 4
Total 4 2 3 8 17

The result is extremely proportional, and the most popular candidates within each party win. One potential downside is that it can lead to a very large number of parties; because of this, in Denmark you need to win at least 2% of the popular vote to be allocated any seats.

Apart from that, it’s a system that works well in practice. Everybody seems to be happy with it in Denmark, and nobody ever suggests changing to another one.

Advice for pro-independence voters: Vote for your favourite candidate from your preferred party.

  • Simplicity: ✔✔✔ (the ballot papers are long, and it is somewhat laborious to count; however, the basic principles are easy to understand)
  • Proportionality: ✔✔✔✔✔ (it doesn’t get any more proportional – it’s even better than d’Hondt)
  • Voter engagement: ✔✔✔✔ (every vote counts, and every candidate needs to campaign for votes)


As we have seen, the six systems are very different. It’s not possible to say which one is best – they all have they pros and cons. Some are very simple, some are very proportional, and some are great for voter engagement. I personally prefer the Danish system, but then I believe proportionality and voter engagement are more important than simplicity.

The results are different in all cases, even if we just look at the number of seats each party gets, as illustrated in the following figure:

From the perspective of individual politicians, they’re even more different. Some candidates get elected in all cases (Samuel, Skylar and Stanley), and others never do (e.g., Callum, Lennox and Greta), but even within one party there are huge differences. Struan only gets elected under FPTP and AV in spite of the SNP’s great performance, whereas Catherine gets in under AMS, STV and the Danish system, even though the Tories in general does much worse than the SNP.

Some people would perhaps look at the performance of their party and choose a system that would favour it. I would caution against that. Labour chose the AMS system for Holyrood for this sort of reason, and it backfired less than ten years later. It’s better to think hard about how to rate simplicity, proportionality and voter engagement.

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