Democracies around the world have very different voting systems. The electoral system one chooses will have profound effects on the composition of legislatures, voter behaviour and the dynamics of democracy. This article is my examination of various proportional and non-proportional voting systems, including my personal notes on them for future reference. I was always fascinated by voting systems mainly because I’ve noticed early on that they can result in radically different outcomes, even though the preferences of the group have not changed. In the last Slovenian parliamentary elections I voted for the Pirate Party, but since the party didn’t make the threshold I effectively wasted my vote. The parliament uses list-PR voting and while mostly proportional it is not perfect and many people strategically vote for larger parties (or those likely to clear the threshold). It is thus fun to theorise and examine the many different kinds of proportional voting systems around the world.
Cluster theory#
Voting isn’t just a collective choice mechanism, it is a method to select the best choice among many given very diverse preferences. A group’s preferences, where individual preferences are points, are multidimensional, where the dimensions are some metric like the position on some issue, candidate quality or general attiude (such as the authoritarian-libertarian axis in the famous political compass). A voting system is thus set to achieve a successful identification of preference clusters and their sizes.
Of course there is great variance with what to do with this information. Some voting systems select a single large cluster, whereas others try to select multiple clusters and grant them the number of seats proportional to the cluster size. It is possible to see elections as a machine learning-like classification problem, except that it is the voters themselves that do the identifying and that preferences may change over time.
The distance between a voter and a candidate determines the strength of preference. Down below are 100 voters and 5 candidates on the political compass, obviously the voters will back the candidates closest to them:
Criteria for evaluating proportional voting systems#
There are many criteria which can be used to evaluate voting systems. I won’t cover them all, there are plenty formal ones such as Monotonicity, the Pareto Condition and the Independence of irrelevant alternatives. But I will list the most important criteria here for proportional multi-winner systems because the formal single-winner criteria become very insignificant:
- Resistance to strategic voting
In many voting systems you have to vote strategically to improve the odds of a desired outcome. There are many possible reasons why this may happen. The spoiler effect means that voting for your favourite choice, can negatively affet your desired outcome. This effect is related to the clone effect where introducing a candidate similar to another one can lead to both losing. In voting systems that are susceptible to such effects, you have to fill out the ballot dishonestly and vote for the lesser evil. A voting system that is well designed should be as strategy-proof as possible and prevent favourite betrayal. You should be able to vote for whom you want to vote for independent of other’s preferences without compromising the outcome.
Note that no voting system is immune to strategic voting because of Gibbard’s theorem, but some are arguably better than others.
- Minimisation of vote wasting
A good voting system should prevent vote wasting. A wasted vote is a vote that didn’t contribute to any desireable outcome.
- Proportionality
A voting system is proportional if its result accurately represents the factional composition of the electorate. Only multi-member voting systems can be proportional. By becoming more representative, at least in theory, the policies passed will more closely reflect the will of the people. This is in my opinion one of the most important features. One of the best measures of proportionality is the Gallagher index, which measures the difference between the votes received by parties and the corresponding seats in a legislature.
- Prevent excessive fragmentation
Proportionality can, however, lead to an obscene amount of political parties gaining seats, making governing hard, so finding the optimal cluster resolution is hotly debated.
Map#
Below is a simple map showcasing the families of the various voting systems. There are way more than that, but I wanted to cover the most interesting and representative ones.
mindmap
root((Voting Systems))
Single-Winner
First-Past-The-Post
Ordinal
Ranked Choice
Condorcet
Ranked Pairs
Schulze
Cardinal
Approval
Score Voting
Multi-Winner
Nonproportional
Single Non-Transferable Vote
Parallel Voting
Proportional
MMP
List-PR
Open
Closed
Ranked
STV
Meek-STV
EAR
MES
Condorcet-STV
CPO-STV
Schulze-STV
Cardinal*
Commulative voting
Proportional Approval Voting
Reweighted Score Voting
Sortition
Single-winner voting systems#
Single winner elections are not the focus of this article, but they are still interesting to examine, since a lot of countries use them. In some places these are used for positions like presidents or mayors, but in others they may be used to elect representatives. All in all, single-winner systems will always produce suboptimal results. A great overview of single winner systems is here:
First past the post (FPTP)#
flowchart TD
A([Start]) --> B[Each voter selects one candidate]
B --> D[Pick the candidate with the most votes]
D --> F([End])
The UK and other former British colonies such as Canada, the US and India all use first-past-the-post. In this voting system each voter can only vote for one candidate and the candidate is selected which has the most votes. This is a terrible system and will inevitably result in a two-party reality. It’s not really democratic nor fair, because it is possible to win elections with minority support (say 30%) leading to extreme tactical voting, limiting voter control and maximising vote waste. In a FPTP-election, an honest voter is effectively handing the win to his opposite preference due to the spoiler effect. Such systems are extremely susceptible to gerrymandering, where constituencies are drawn in a way that increases the odds of a party winning, effectively deciding the outcome of the election before the election itself. The UK is notorious for having extremely unrepresentative elections. In the 2024 British parliamentary election Labour only won 33% of the vote, but a very large majority in the House of Commons and 100% of the control.
Here is a simple visualisation of the spoiler effect, leading to radically different outcomes if a candidate similar to A is introduced.
Some countries tried alleviating FPTP such as France which uses run-off elections for the top two candidates in each constituency, but it doesn’t fix elections at all, other than preventing a two party system. FPTP systems simply select the largest cluster cluster among the clusters (the plurality).
Ordinal voting systems#
Ordinal voting systems use ranked ballots to capture the voters’ preferences.
Instant runoff voting (IRV)#
flowchart TD
A([Start]) --> B[Each voter ranks candidates]
B --> C[Count each ballot for its highest-ranked continuing candidate]
C --> D{Does a candidate have a majority?}
D -- Yes --> E[Declare candidate elected]
D -- No --> F[Identify candidate with the fewest votes]
F --> G[Eliminate that candidate]
G --> H[Transfer each affected ballot to its next-ranked continuing candidate]
H --> C
E --> I([End])
Australia is notable for using IRV for its parliamentary elections. Voters rank the candidates in order of preference and then the candidate with the least first preferences is eliminated and their votes transfered to their voter’s second choices, this is repeated until a winner is found. It improves FPTP by introducing ranked ballots and it fixes the spoiler effect. Unfortunately, however, it doesn’t make the result proportional at all, tends to produce centre-squeeze (a phenomenon where centrist candidates have close to no chance of winning) and the election outcome can be radically different depending on the order of candidate elimination. Imagine a scenario where a person X is ranked 2nd by everyone, but even though everyone likes the person, they have no first votes and are immediately eliminated. If the voters have access to polls they can vote tactically to change their rankings and thus change the outcome (this is a part of the monotonicity paradox). It also doesn’t minimise vote waste, as slightly less than half of a constituency will be left with a representative they do not like. Australia has one of the worst Gallagher indexes in the world and it has effectively a two-ish party system between Labor and the Liberal-National coalition.
Here is the simulation of a close 4-candidate election where the order of elimination
Ranked choice voting terminates smaller clusters and adds them up until there are only two clusters and the biggest one wins. All ranked choice ballots suffer from Arrow’s theorem meaning that all have to sacrifice some desirable criterion, though since most elections are roughly on a left-right axis, there exists the median voter theorem lessens the problem of Arrow’s theorem.
Condorcet methods#
flowchart TD
A([Start]) --> B[Each voter ranks candidates]
B --> C[Compare every pair of candidates]
C --> D[Count the number of wins in each pairwise comparison]
D --> L[Pick the candidate with the most pairwise wins]
L --> M([End])
I personally find the Condorcet condition to be the most desireable feature among ranked choice systems.
A candidate is a condorcet winner if they would receive more support than their opponent in an one-on-one race against any one of their opponents. This idea can also be expanded to a multi-winner context, where the optimal combination of candidates is referred to as the Condorcet committee. The condorcet criterion is the gold standard of single-choice voting criteria, in terms of cluster theory, it ensures that the outcome is truly prefered by the majority of voters and not just a plurality. A condorcet winner does not always exist, asides from ties, it is possible that there are preference cycles. If A prefers B and B prefers C, while C prefers A, then no majority winner exists. This is called the condorcet paradox, but it is quite rare in real politics. When candidates are tied or in a Condorcet cycle they are said to be in the smith set.
The reason why I like Condorcet methods is that they’re more strategy-resistant. Some of the voting systems that achieve this are Ranked pairs and Schulze’s method. Just like in IRV candidates are ranked, however Condorcet avoids a major problem of IRV, where candidates are eliminated based on first-preference votes leading to a completely arbitrary order of eliminations: In the scenario where a person X is ranked 2nd by everyone, IRV would instantly eliminate them, but this would not happen under Condorcet. In fact in Condorcet the most liked consensus-seeking candidate is likely to win. The image below by Closed Limelike Curves shows the ideological distribution of winners on a simulated political compass in different electoral systems, showing that Condorcet does not lead to centre-squeeze:
Both Schulze and Ranked Pairs has been shown to be very resistant to strategy with Ranked Pairs taking the edge as shown by David C. Parkes and Lirong Xia’s paper Schulze is beautiful though much more complicated to understand and it does not satisfy local Independence of Irrelevant Alternatives:
Awesome, so we should just elect legislatives using Ranked Pairs in single-winner constituencies? Not so fast. If you think about it, such a system would produce a dictatorship of the centre. Condorcet winners would always be very lukewarm, appeal-to-all candidates which would be members of the political centre. I find this very unfair, because it would make a system very unrepresentative and somewhat unaccountable. Why should 10% of the population get 100% of the control? Centrism is not inherently more right, it is just a more median ideology. We do not need to give up proportionality to have good continuity either: Political coalitions in parliamentary systems ensure more moderate policies, while staying very representative and accountable.
Borda Count#
I’m not going to write much about Borda. It’s ranked voting but the rankings determine the score that each candidate gets. It sounds neat, but is extremely susceptible to the spoiler and clone effects. It’s really not a good system but more on the system for the curious ones in the video below:
Cardinal voting systems#
Cardinal voting systems obtain the most data from the voter. We get to evaluate our preference for each candidates on a scale (for example from 1 to 10 or just from 0 to 1). Cardinal voting systes are most notably not subject to Arrow’s theorem, making them very attractive
Approval voting (AV)#
flowchart TD
A([Start]) --> B[Each voter approves zero or more candidates]
B --> D[Pick the candidate with the most votes]
D --> F([End])
AV is an easy-to-count system that can produce very desireable results. People are allowed to vote for any candidate they approve of. This system is great for groups quickly deciding on what to do. It is very easy to count, very fair and it is bound to find a candidate that is approved by as many people as possible. AV effectively hands the victory to the candidate who sits at the greatest intersection of preferences, so electing assemblies with single-winner AV would produce a similar dictatorship of the centre without minority representation as Condorcet, though it does not guarantee a condorcet winner. In my opinion the biggest issue with AV is that it becomes a strategic nightmare as shown in the simulation below:
Approval voting does not suffer from favourite betrayal, but if too many people vote strategically it turns into FPTP.
Approval voting is used in the company I work at to decide what to eat during lunch and it is a very sensible choice! However, when you repeat the same decision many times with AV and people vote mostly honestly it results in a very low variety of outcomes. In our case pasta with vegetarian sauce is almost always chosen.
Score voting#
flowchart TD
A([Start]) --> B[Each voter gives each candidate a score]
B --> C[Add all scores received by each candidate]
C --> D[Calculate total score for each candidate]
D --> F[Pick the winner with the highest score]
F --> G([End])
Score voting or range voting is the more expressive version of approval voting and it gives the most power to the voter by requiring everyone to score every candidates on a range. I really like this idea because when we rank candidates like A>B>C>D we do not really express the strength of our preference, we may like A and B roughly equally, while we strongly dislike C and D. It will also produce the most liked candidate with even more accuracy than with approval voting thus maximising happiness if everyone votes honestly. Range voting has the nice property that Bayesian regret is minimised in a range-based election. Other than that it would still lead to a centrist dictatorship, if we used it in many single-member constituencies.
It is unfortunately even more susceptible to strategy than approval voting. Just like with approval voting, voters are incentivised to vote dishonestly to make their candidate win by giving similar candidates a lower score than their first preference. If this is the optimal strategy then you can’t really support your second choices well without betraying your desired outcome, thus from a stratigic point of view leading to vote waste. In fact in the video above score voting does not necessarily produce the highest happiness for society (a utilitarian winner). Here’s a scenario: Voters for the condorcet/majority winner (60%) vote honestly, while a radical minority (40%) votes dishonestly. This would sway the election producing minority rule. I’m certain that after one or two elections, everybody would be voting very strategically, because if only one actor votes strategically, you have to do it as well or risk an undesireable outcome. For this reason STAR voting is being promoted in the US. It takes score voting but then puts the top two candidates to a runoff, but this takes its elegance away and does not really change that much, if everyone votes maximally strategically you get the French run-off FPTP system. The mere fact that STAR voting is promoted over regular score voting shows that score voting is prone to some serious strategic voting.
How different are utilitarian winners from their Condorcet counterpart? Suppose three friends want to go out and eat a Pizza together. One of the three is a vegetarian and of course the group is going to order a vegetarian Pizza, otherwise you’d be bad friends. The condorcet choice may not necessarily reflect that and could lead to salami pizza being selected (afterall 2 prefer it), whereas with score voting, a vegetarian pizza would be selected. However, the reality is that most of the time they will be the same, suppose there are multiple pizzas, then the rankings could look like this:
Salami > Vegetable+Cheese > Chocolate Pizza for the two omnivores and
Vegetable+Cheese > Chocolate Pizza > Salami for the vegetarian
The Condorcet winner then would be Vegetable+Cheese because it wins 4 times, while salami only wins 2 times and chocolate pizza 1 time in head-on-head comparisons. In fact the paper by Marcus Pivato shows that under right conditions Condorcet will also maximize or at least approximate the utilitarian optimum.
For repeated and important single-winner elections, for example for the mayor, where we seek consensus winners, I would prefer ranked pairs over cardinal voting systems. The reason I prefer it over score voting is that you can truly vote honestly (because it is significantly more strategy-resistant), ranked pairs is less likely to lead to vote waste, satisfies more theoretical criteria and often results in the same outcomes as score voting, thus also maximising happiness.
Opinion on single winner systems#
In my opinion if a group of friends needs to make a one-time decision, for example where to eat, approval voting is the best.
But how should a mayor be chosen? To minimise strategic voting and produce the most consensual result, Ranked Pairs or any other Condorcet method is the most suitable, assuming the city council is elected using PR and is the main driver of policy.
No matter how we spin it, single-winner systems will never be truly representative nor maximise happiness as much as multi-winner systems. No matter how optimised the voting system may be, the basic notions of fairness such as variety and consensus, majority-rule and minority-voice, are fundamentally contradicting. Much theory and research has been done on the topic, but the reality is that there is no good single-winner system. The only way to bypass this problem is to have multiple winners and a proportional representation (PR) system. PR bypasses a lot of the issues that single winner elections have so whenever possible we should have multi-winner elections.
Multi-winner systems#
There are many kinds of multi-winner systems in use around the world.
Non-proportional#
Some multi-winner systems are not really proportional or only slightly.
The Single Non-Transferable Vote (SNTV)#
flowchart TD
A([Start]) --> B[Each voter casts one vote for one candidate]
B --> C[Count all votes for each candidate]
C --> D[Sort candidates by total votes]
D --> E[Pick the N candidates with the most votes]
E --> G([End])
SNTV is used in many Asian countries like Japan, Taiwan, Hong Kong and Indonesia. In SNTV you can still only vote for one candidate and those candidates are selected which get the most votes. SNTV is essentially a multi-winner version of FPTP and as you can imagine it is not a good system. Just like FPTP the system is susceptible to spoiler and clone effects, except that here you are even more encouraged to betray your favourite, because if your favourite has good chances of being elected, voting for them could worsen your favourite party’s chance of getting a second seat, because even though your party should get two seats, too many people voted for candidate A and too little for candidate B resulting in a completely unproportional result. This leads to vote management, where people are asked to coordinate with other voters to distribute their vote for example all males should vote for candidate A and all females for candidate B. That’s not good, you should be able to vote honestly.
Parallel voting systems#
Places like Russia, Kazakhstan, Japan, South Korea, the Philippines, Taiwan and Thailand use such electoral systems. In parallel voting a part of the legislature is elected with two completely indepedent voting systems, typically FPTP or SNTV and Party Lists. Some places have a lot of Party List seats such as Armenia, while others have very few such as Taiwan. I do not see what the purpose of these systems is, they are not proportional so why even have party list or SNTV components? They are unfair and not really democratic. I suppose the ruling parties wanted smaller parties to have some representation but no shot at ever governing. In fact, parallel voting of all the systems tends most towards a dominant-party system.
Proportional voting systems#
Finally we get to the best voting systems! These allow for the population to be represented proportionally
Mixed-member proportional (MMP)#
flowchart TD
A([Start: General Election]) --> B[Voters cast two votes: Party Vote + Constituency Vote]
B --> C[Count all Party Votes nationally]
B --> D[Count all Constituency Votes in local districts]
C --> E[Calculate % of Party Votes for each party]
D --> F[Determine winner in each constituency: Constituency MPs]
E --> G{Party meets threshold? e.g., 5% of Party Vote OR wins at least 1 Constituency Seat}
G -->|Yes| H[Party qualifies for List MPs]
G -->|No| I[Party votes are wasted]
H --> J[Calculate total seats each party should have based on % of Party Votes]
F --> J
J --> K[Subtract Constituency Seats won from total seats due]
K --> L{Remaining seats > 0?}
L -->|Yes| M[Allocate List MPs from party lists to fill remaining seats]
L -->|No| N[No List MPs allocated]
M --> O[Total MPs = Base Seats + any Overhang Seats]
N --> O
I --> O
O --> P([End: Legislature formed])
MMP is used in Germany, New Zealand, Bolivia, Lesotho and Scotland. It is a unique system because each voter gets two votes: one for the local candidate and one for a party. The country is split into local constituencies and each elects one representative using FPTP. Then once all the local representatives have been elected, the rest of the legislature is filled with positions from closed party lists so that the result is proportional. This system ensures local representation while also keeping elections national and proportional. Asides from the FPTP local part, MMP is actually very fair and interesting. Here’s an example New Zealand ballot by Electoral systems from LibreTexts
Asides from using FPTP for the local candidate, which could easily be replaced with a better system my main issue with MMP has to do with thresholds. In order to prevent excessive fragmentation among parties, countries like Germany and New Zealand have enacted a 5% threshold. This means that if you vote for a small party that does not make the threshold, your party vote (which is arguably the more important vote) will be wasted and since the local election already entails a lot of vote wasting, MMP is very prone to favourite betrayal, though its a massive improvement over all the methods we have seen thus far and it does produce stable governments as we’ve seen in Germany and New Zealand which are both very democratic, have coalition governments and a high level of prosperity.
Vote wasting is however a real problem. In the 2025 German elections the BSW missed the 5% threshold by a slight margin (4.98%) and the FDP got 4.3% of which all got zero seats and in the 2013 elections the FDP narrowly missed the threshold with 4.8%. Now I am not a fan of the BSW at all, but if the BSW voters had transferred their support to any of the other parties, the final composition of the German Bundestag would’ve looked different. It’s not hard to imagine a scenario where a party could gain the majority of seats, without actually getting a majority of the votes. In New Zealand vote wasting is pretty much proportional to the voter turnout and this is very frustating (source is Wikipedia and the wasted votes are just a sum of all the parties not represented in Parliament):
| Year | Voter Turnout (%) | Wasted votes (%) |
|---|---|---|
| 2023 | 78,20% | 5,58% |
| 2020 | 82,24% | 7,71% |
| 2017 | 79,75% | 4,62% |
| 2014 | 77,90% | 6,14% |
Party Lists (List-PR)#
flowchart TD
A([Start: General Election]) --> B[Voters cast single vote for a party]
B --> C[Count all Party Votes]
C --> E{Party meets threshold? e.g., 5%}
E -->|Yes| F[Calculate total seats each party should have]
E -->|No| G[Party votes are wasted]
F --> H[Allocate seats to parties proportionally]
H --> I[Fill seats from party lists in order]
I --> J([End: Legislature formed])
G --> J
List-PR voting systems are widespread in Europe from Scandinavia to Greece. They are also widely used in South America like Columbia and Brazil. It is also used in Indonesia, South Africa, Nigeria, Tukrey and Israel. In a List-PR system the voter casts a vote for their favourite party list.
Voting is done in large (oftentimes national) constituencies and the number of seats won by each party corresponds to the ratio of votes given to that party and the seats are filled as specified on the list. Such systems often employ thresholds to prevent excessive fragmentation though the thresholds vary by country. It is generally smaller than in MMP, amounting to 4% in Slovenia, Austria, Indonesia and Sweden, 3% in Israel, Italy and Spain, but in Turkey it was 10% and in Kazakhstan and in Turkey today it is 7%. The most special party list system is in the Netherlands where there is no threshold. Any party which gets enough votes for a single seat, gets one.
There are two kinds of party list systems, open and closed. Open party list systems allow voters to influence which politicians from a party list get to represent their party, whereas with a closed list the order is predetermined by the party. In Lithuania voters use approval and disapproval voting to determine the order of selection within the party list they’ve backed.
Assuming a sufficiently small threshold, List-PR is the most proportional system of them all and one of the most resistant ones towards strategic voting, allowing voters to express their favourite choice. Not only that compared to all systems low-threshold List-PR allows for a very high resolution of representation allowing nieche groups to have seats in a legislature. This has a drawback as List-PR does tend to lead to fragmentation. Additionally List-PR does not guarantee local or regional representation, so while the result may be perfectly proportional, all the representatives could come from the capital city, which does not feel too representative. Some countries like Poland have thus split into many constituencies of 8 to 16 seats, while Slovenia ensures proportionality on the national level and then fills the seats from the party lists from its 8 regions to ensure regional representation.
The way the seats are distributed also impacts the composition of the legislature. D’Hondt is the most widespread, but favours large parties, Sainte-Laguë is very proportional, Droop is slightly biased towards big parties while Hare is similar and simple but slightly biased towards smaller parties.
List-PR systems suffer from the same problem as MMP. If a party that you’ve voted for misses the threshold, you’ve wasted your vote. This can be a huge problem and the share of wasted votes can be actually quite big and as the threshold get smaller and as people vote less tactically, there will be more parties that will miss the quota. Even in the Netherlands which has a threshold equal to one seat there are wasted votes, though only a few percent at most. List-PR also doesn’t give independents any chance at winning a seat.
There was the proposal in Germany to introduce the spare vote, where your vote could be transfered to a party that made the threshold, but it never got anywhere, which is a shame because if we could rank lists, one would eliminate the single biggest issue with List-PR and it would still be quite easy to count. This is shown in the simulation below, where voters can rank lists and those below 10% are round-wise eliminated:
Let’s compare the results of the two elections where 10 seats are up for grabs, in which we use regular List-PR and ranked-List-PR (where voters can rank parties)
| Parties | D’Hondt without transfers | D’Hondt with vote transfer |
|---|---|---|
| A | 3 | 2 |
| B | 3 | 2 |
| C | 3 | 2 |
| S | 1 | 3 |
| F | 0 | 0 |
| G | 0 | 0 |
| H | 0 | 0 |
| R | 0 | 1 |
| T | 0 | 0 |
| U | 0 | 0 |
This is a dramatic difference, note how S got 3 instead of just 1 seat and how R, a party initially not making the threshold now made it just because we allowed people to rank parties. This is a radical example, where many did not vote strategically and where vote wasting was not roughly equally distributed across the political spectrum. Most of the time List-PR leads to very proportional results, but it’s not fair to small parties.
Single Transferable Vote (STV)#
flowchart TD
A[Start] --> B[Voters rank candidates]
B --> C[Count first preferences]
C --> D{Any candidate ≥ quota?}
D -->|Yes| E[Elect candidate]
D -->|No| F[Eliminate lowest candidate]
F --> C
E --> G[Redistribute surplus votes]
G --> C
STV is used in Ireland, Malta, for Australian senatorial elections, local elections in Scotland, New Zealand and several cities in the Canada and the US. Formerly it was also used in Estonia. Unlike List-PR and MMP it is based on ranked ballots of candidates. The winning candidates are those which get enough votes to pass the quota. In STV voters rank candidates just like in IRV and the losers’ votes are transfered, unlike in IRV, STV selects several candidates, which get enough votes.
STV essentially works by testing the size of each cluster and merging smaller ones into sufficienly big ones to represent each major one. One of STV’s defining features is the minimisation of vote wasting, since votes are transfered from first choices to the next ones if not elected. How proportional STV is depends on the constituency size. Additionally, the bigger the constituency size the more parties can be represented. In a way STV introduces a very organic threshold that is determined by constituency size. This is where the local vs regional representation debate begins and I would like to argue that regional representation is better than local, because it allows for more proportionality, better representation of minorities and makes the elections more national. Elections are a national and not local affair. While I do think it’s important that not all MPs come from the capital city, I don’t think every locality needs their own MP. Ireland uses constituency sizes of 3 to 5, Malta 5 and the Australian Senate of 12 seats (though unfortunately only 6 are elected at a time). According to Wikipedia an Irish parliamentary committee in 2010 found that “a larger district magnitude is shown to have positive effects in relation to the representation of women and minorities, as well as allowing for a plurality of ideas in terms of policy” which is the whole point of PR and recommended a minimum constituency size of 4, while Northern Ireland determined that 6 is the minimum constituency size (and then went on ignoring its own recommendation by sticking to a uniform size of 5). Thomas Hare’s original proposal was for a single, nationwide district. The largest constituency size in use is in New South Wales, where 21 MPs are elected in a state-wide election. I think about 20 seats per constituency is actually the most fair size because it results in quotas around 4.76%, which are commonly found in other PR systems. There is a thing to be said about the complexity of voting, but I disagree. When STV is used with large constituency sizes it becomes effectively open list-PR but without vote wasting and giving independents a chance. In Australia you can even directly rank parties (assuming you, like 95% of the voters, accept the proposed ranking by the party):
On the topic of independents. The first US president, George Washington, in the 18th century has notably advocated for a non-partisan legislature, but that is unrealistic, because people naturally cooperate in politics and clusters organise. I suppose he feared division and highly valued independents to make decisions based on their conscience rather than by party lines, but this is made obsolete in a multi-party proportional representation system because independent opinions are really what small parties are all about. In fact political parties increase accountability, improve activism through organised action and make governing much more reliable. Political parties can cooperate in coalitions as is the case in parliamentary systems and these actually have a moderating, stabilising effect on society rather than making it fall apart. But does that mean we have to go the Brazil route and ban independents, those few politicians who aren’t members of a political party and don’t want to form their own? I don’t think so, I think voters should have the choice, even though independents are made obsolete with PR and I would unlikely vote for one. In fact there are always a few independents in the Irish parliament.
A neat feature of STV is also that it fosters cooperation between parties, especially smaller ones, since you want to be ranked as highly as possible. At the very least it provides a strong disincentive towards negative campaigning. Imagine that your party gets enough votes for 2.8 candidates. To get the third one you need transfer votes, but if your party is constantly hostile to others, you will not necessarily get the third seat.
There are drawbacks to STV starting with the arbitrary elimination order. Imagine a candidate X who is ranked 2nd by everyone, that candidate will be the first one to be eliminated, even though he actually should be elected. Unlike with IRV such a scenario is unlikely to happen though, as surplus votes from the first winners would be transferred to X. In small Irish constituencies of 3 seats, there is also vote management just like in SNTV. Both problems diminish with constituency size.
Additionally we need to talk about the counting system. If a candidate gets enough votes to be elected and received more votes than the quota, how should the excess votes be distributed to other candidates? This is always the thought I had after watching CGP Grey’s video. Little did I know he left it out for a good reason, because it’s a very complicated topic and would ruin the video, because there are many ways and they have huge consequences:
- Hare method
This is the original method proposed by Thomas Hare and it essentially randomly reshuffles the ballots cast to the winner and then randomly picks the excess votes which are transfered to their second preferences. Randomised transfers are actually quite accurate assuming large numbers, but terrible for auditing and not deterministic. Brian Wichmann also notes in his paper that the results of the Irish elections are are off by 1.8% just because of the counting method. There’s also something genuienly unstatisfying about randomness determining if your ballot will continue contributing to the election outcome.
- Gregory method
The Gregory method is used for the Irish Senate elections and is fully deterministic. Instead of randomisation, when a candidate’s excess ballots are to be transferred, all of the ballots second choices get a fractional transfer. So if a candidate got 30% but the quota was 15%, then they will support their second choice with 50% weight. There is also a unweighted version of the Gregory method used in Australia, but it is distorting the result.
The weighted Gregory method is in my opinion far more fair, deterministic and auditable, albeit a bit harder to count by hand.
Awesome all problems solved, right? No not quite sadly! It is possible that somebody’s later preferences are already elected candidates, meaning that some voters’ ballots will be exhausted quite soon and the remaining fewer active ballots will still have to hit the same quota which has not been adapted for the smaller number of active ballots leading to distortions and potentially too early eliminations.
Both Hare and the Gregory lead to Woodall free riding, where there is an advantage to first choosing a candidate who is unlikely to win rather than supporting a popular candidate. However, there is a counting method that fixes this issue:
- Meek
The Meek’s counting method is used in some New Zealand local elections. Meek’s tabulation can realistically only be done with computers (though note that the ballots should be physical and the counting should be done by humans as pointed out by Tom Scott). Meek recalculates the quota each round depending on the active number of votes, preventing unfair eliminations. Meek is based on weighted Gregory, but it introduces keep factors. Whenever a candidate is elected their keep ratio is reduced depending on the amout of excess votes they receive and their votes are always transferred, the keep factor is dynamic unlike in Gregory’s method.
There is a problem though, here’s an example from Wikipedia: A prior winner X could receive 20 transfers from second round winner Y. Then transfer the fraction from X. However, some of these fractional ballots may then transfer back from X to Y, creating recursion. The recursion is infinite with decreasing fractions. Meek iteratively adjusts keep factors until the tallies of all candidates are within a tiny tolerance (for example 10⁻⁶ or the 32-bit float resolution) of the quota, when they can’t realistically change the outcome anymore.
In Meek, even already elected candidates can continue to receive and transfer votes, ensuring all votes remain active in the count and you as the voter have maximum influence till the very end.
Here is the pseudocode by prfound.org: Initialize Election
Set each candidate’s state to hopeful or withdrawn. Set each hopeful candidate’s keep factor kf to 1, and each withdrawn candidate’s keep factor to 0. Set omega to 0.000001 (1/106). Rounds 2.1 Test count complete. Proceed to step C if all seats are filled, or if the number of elected plus hopeful candidates is less than or equal to the number of seats.
2.2 Iterate.
a. Distribute votes. For each ballot: set ballot weight w to 1, and then for each candidate, in order of rank on that ballot: add w multiplied by the keep factor kf of the candidate (to 9 decimal places, rounded up) to that candidate’s vote v, and reduce w by the same amount, until no further candidate remains on the ballot or until the ballot’s weight w is 0.
b. Update quota. Set quota q to the sum of the vote v for all candidates (step B.2.a), divided by one more than the number of seats to be filled, truncated to 9 decimal places, plus 0.000000001 (1/109).
c. Find winners. Elect each hopeful candidate with a vote v greater than or equal to the quota (v ≥ q).
d. Calculate the total surplus s, as the sum of the individual surpluses (v – q) of the elected candidates, but not less than 0.
e. Test for iteration finished. If step B.2.c elected a candidate, continue at B.1. Otherwise, if the total surplus s is less than omega, or (except for the first iteration) if the total surplus s is greater than or equal to the surplus s in the previous iteration, continue at B.3.
f. Update keep factors. Set the keep factor kf of each elected candidate to the candidate’s current keep factor kf, multiplied by the current quota q (to 9 decimal places, rounded up), and then divided by the candidate’s current vote v (to 9 decimal places, rounded up). Continue iteration at step B.2.a.
2.3. Defeat low candidate. Defeat the hopeful candidate c with the lowest vote v, breaking any tie per procedure T, where each candidate c’ is tied with c if vote v’ for c’ is less than or equal to v plus total surplus s. Set the keep factor kf of c to 0.
2.4. Continue. Proceed to the next round at step B.1. Count Complete Elect remaining. If any seats are unfilled, elect remaining hopeful candidates.
Defeat remaining. Otherwise defeat remaining hopeful candidates. Election count is complete.
4. Breaking ties
Ties can arise in B.3, when selecting a candidate for defeat. Use the defined tiebreaking procedure (I would recommend picking the candidate which beats the other one in more one-on-one matchups)Meek’s Pseudocode
You can try M-STV tabulation here.
Theoretical alternatives#
Expanding approvals rule (EAR)#
flowchart TD
A[Start: n voters, k seats] --> B[Initialize: Give each voter 1 unit of virtual money]
B --> C[Set rank r = 1]
C --> D[Check if any candidate is ranked r or better by a group of voters]
D -->|Yes| E[Select candidate c who can be afforded by the group]
E --> F[Add candidate c to the committee]
F --> G[Deduct price n/k from the balance of voters who rank c r-th or better]
G --> H[Increment rank r by 1]
H --> D
D -->|No| I[All seats filled?]
I -->|No| H
I -->|Yes| J[End: Return the committee]
EAR is not used anywhere but it works as a positive version of STV. Voters still rank candidates. Instead of eliminating them, candidates are added in each new round of voting, checking if a candidate passes the threshold and if so the ballot is deweighted. The ballots require only weak rankings, so it is possible to select multiple candidates as your second choice, thus combining ranked and approval voting. It has the benefit of not eliminating popular but not first ranked candidates first like STV. In the original paper, Haris Aziz and Barton E. Lee prove its proportionality (in fact it satisfies even more extensive axioms of proportionality) and it even satisfied weak monotonicity something which STV does not. It’s also easy to count. EAR has one central strategy, always rank your favourite party’s candidates over any second choice or compromise party’s candidates to prevent ballot exhaustion, so something like this: Favourite 1 > Favourite 2 > ... > Favourite n > Second-choice 1 = Second-choice 2 = ... > others. Though now that I think about it including a whole equivalence class like Second-choice 1 = Second-choice 2 = ... will be added in the same round, increasing the odds your ballot will be used on a second-choice candidate rather than your first choice, leading to a centre-bias, so voters are encouraged to rank as much as possible. Many ties are also possible.
I’ve created a python implementation with Mistral that works with the same input as the Meek’s STV tabulator provided above. Here are the comparisons using an example of 5 parties (left, centre-left, centre, centre-right, right) normally distributed with the centre at 10% and people ranking their party the highest followed by the more centre neighbour and then their other neighbour, so we observe the following patterns: L > CL > C for left voters (25, 12.5%) CL > C > L for centre-left (65, 32.5%) C>CL>CR for 50% of the centre (10, 5%) C>CR>CL for 50% of the centre (10, 5%) CR>C>R for the right (65, 32.5%) R>CR>C for the right (25, 12.5%)
| Voting System | Seats | Left | Centre-Left | Centre | Centre-Right | Right |
|---|---|---|---|---|---|---|
| EAR | 5 | 0% | 40% | 20% | 40% | 0% |
| EAR | 10 | 10% | 30% | 20% | 30% | 10% |
| EAR | 20 | 10% | 35% | 20% | 35% | 10% |
| STV | 5 | 0% | 40% | 20% | 40% | 0% |
| STV | 10 | 0% | 40% | 10% | 40% | 10% |
| STV | 20 | 10% | 35% | 10% | 35% | 10% |
What this simulation shows is that STV is more traditionally proportional. This is also noted in the paper by Bardal, Brill, McCune and Peters called Proportional Representation in Practice where the researches note that EAR performs slightly worse empirically than STV in terms of party proportionality even though it has better mathematical properties.
The graph compares STV to IRV and EAR in terms of proportionality (lower is better) with the data from the Scottish elections. S-STV corresponds to the inclusive Gregory method.
Method of equal shares (MES)#
MES unlike EAR is actually used in many European cities for participatory and proportional municipal budgeting. It is usually implemented with approval voting (though score and ranked variants also exist) and belongs to the EAR family of voting systems. It is a great method for budgeting, but for voting it is very similar to EAR and thus likely has the same centrist bias.
Schulze STV#
STV does not fix the problem with the random order of elimination. Additionally, even if we use Meek, there is still a form of strategic voting which is possible (especially if the constituency is small like 3 or 4 seats and the polls are very accurate) called Hylland free riding, where the voter omits their preferred candidate from their rankings to help them win (as counterintuitive as this sounds).
Schulze and CPO STV utilise the same ranked ballots and ensure the same proportionality, however they will produce a condorcet committee that is the most widely liked combination of candidates such that the result is still proportional. Both methods require the use of a computer because they involve an enormous amount of calculations. In fact finding the optimal solution is a NP-hard problem and does not scale well.
Schulze and CPO STV both first compute all possible combinations of winners and then treat them like candidates in single-winner ranked pairs (CPO) or Schulze elections, ultimately picking the best one. That’s a lot of possible combinations, in fact Schulze needs O(m^(3k)) operations with k winners out of m candidates. Schulze is faster to compute than CPO-STV, because we only compare the groups differing by one candidate. Schulze and CPO STV are the optimal variants of STV. There is no elimination order, the result is proportional and strategic voting is minimised as much as possible. However, it’s completely unrealistic for elections. For a 5-seat constituency and 32 candidates a single CPU would need an unrealistic number of operations. What would stop some joke party or a hostile foreign power to game the system and apply dozens of no-chance candidates to prevent the result from being determinable in realistic time? We would thus need extreme computing power, which reduces auditability. If you’re a journalist checking if the result is right with your own implementation of the algorithm, you will not be able to do it without expensive hardware. Maybe quantum computers could make Schulze STV viable one day though it’s possible there is no fast enough quantum speedup available, but until them Schulze STV is unrealistic and since electronic voting in general is quite problematic, I would not recommend it.
I think that overly fixating on the Condorcet criterium for multi-winner systems isn’t the most productive goal. Suppose everyone in a fictional country would vote the following way:
A>B>C>D>E>F
If we had two constituencies with Schulze STV each electing two candidates (constituency one would have A,B,C and two D,E,F) then we would elect A,B and D,E, both Condorcet committee but the final assembly would not be a Condorcet committee, so the Condorcet criterion isn’t the most important one in constituency based proportional representation. To be fair the main goal of Schule STV is resistance to strategy and for that purpose it is great.
There are many methods available to increase the odds of an approximately condorcet committee. Sequential STV is quite cool, you run a regular STV election and then check for every eliminated candidate if you were to rerun an election with them and the winning combination if the winning combination would still not contain the eliminee. There’s also the idea that one could replace the elimination with Ranked Pairs for every last pair of candidates. But while these are neatly computable, they are not worth the extra complexity when they cannot guarantee a Condorcet committee nor provide formal guarantees for Condorcet compliance. I think it’s a much better idea to just increase the size of STV constituencies. Most of the time Schulze and regular STV will produce the same or similar results, so is Schulze STV worth it?
Cardinal proprotional voting systems#
By this point one might ask themselves, if we can turn single-winner ordinal systems into STV, couldn’t we perhaps design a PR system with cardinal voting? The answer is yes!
Proportional approval voting (PAV)#
flowchart TD
A[Start] --> B[Initialize all ballots with weight = 1]
B --> C{Desired number of winners reached?}
C -->|Yes| D[End]
C -->|No| E[For each candidate, calculate score = sum of weights of ballots approving them]
E --> F[Select candidate with highest score]
F --> G["For each ballot approving the winner, update weight: w = w * (k / (k + 1)) where k = number of winners so far"]
G --> H[Increment winner count]
H --> C
PAV was used in Sweden in the early 1900s for distributing seats within parties and in local elections but was discontinued because it was rather hard to count. You pick all the candidates or parties you approve of and the candidates are elected round by round. The candidate with the highest score is elected and everyone who voted for the candidate has their ballot deweighted. This allows the other side’s candidates to keep a higher score and thus have their candidate elected. Let’s do a quick simulation to see how proportional PAV is.
We take the same 5 party distribution as above but introduce the rule, voters of one party approve of their party and their neighbours. Someone in the centre-right will thus vote for themselves but also for the centre and the right.
| Seats | Left | Centre-Left | Centre | Centre-Right | Right |
|---|---|---|---|---|---|
| 10 | 0% | 30% | 50% | 20% | 0% |
| 20 | 0% | 25% | 50% | 25% | 0% |
This is a very strong centre-bias and is likely caused by the votes being exhausted by centre candidates. Whenever a centre candidate is elected both sides lose weight, thus favouring the centre a lot.
Reweighted Range Voting (RRV)#
flowchart TD
A[Start] --> B[Initialize all ballots with weight = 1]
B --> C{Desired number of winners reached?}
C -->|Yes| D[End]
C -->|No| E["For each candidate, calculate score = sum of (ballot_weight * score) for all ballots"]
E --> F[Select candidate with highest score]
F --> G[For each ballot, calculate SUM = sum of scores given to winners-so-far]
G --> H["Update ballot weight: w = 1 / (1 + SUM / MAX)"]
H --> I[Increment winner count]
I --> C
Now we get to one of the most interesting voting systems in this whole article: RRV. It was used by the OSCARS for best visual effects and in the German Pirate Party. It is a very elegant and simple voting system that gives voters maximum control. It’s just like PAV but with score voting. Each voter assigns a score to every candidate depending on how much they like them for example 0 to 10. No other voting system gets more information from the voter. RRV also does not suffer from arbitrary elimination like STV and it just has really good properties, well, all except for one. The benefit of RRV over PAV is that it gives voters way more control over the reweighting process, allowing their ballot to remain important while also supporting their second choices a bit.
For the RRV simulation we take the same 5 party distribution as above but the voters of a party give a 10 to their first choice, 5 to their neighbours, 2 to the next neighbours and then 1 then 0. Such an arrangement results in:
| Seats | Left | Centre-Left | Centre | Centre-Right | Right |
|---|---|---|---|---|---|
| 10 | 0% | 0% | 0% | 50% | 50% |
| 20 | 0% | 0% | 0% | 50% | 50% |
Keep this result in mind. Now let’s assume every Right voter votes strategically giving everyone a 0, except themselves
| Seats | Left | Centre-Left | Centre | Centre-Right | Right |
|---|---|---|---|---|---|
| 10 | 0% | 60% | 0% | 20% | 20% |
| 20 | 0% | 55% | 0% | 25% | 20% |
Not optimal, what if they vote 10 for their party and 2 for the centre-right?
| Seats | Left | Centre-Left | Centre | Centre-Right | Right |
|---|---|---|---|---|---|
| 10 | 0% | 50% | 0% | 40% | 10% |
| 20 | 0% | 50% | 0% | 35% | 15% |
I tried a version with Sainte-Laguë, which is fairer to smaller parties and a electorate that votes with the following strategy: voting 10 for their party, 2 for neighbours and 0 for all else:
| Seats | Left | Centre-Left | Centre | Centre-Right | Right |
|---|---|---|---|---|---|
| 10 | 10% | 40% | 0% | 40% | 10% |
| 20 | 15% | 30% | 10% | 35% | 10% |
Hey this looks quite proportional! Let’s try Sainte-Laguë, but voters voting 10 for their party, 5 for neighbours and 0 for all else:
| Left | Centre-Left | Centre | Centre-Right | Right |
|---|---|---|---|---|
| 0% | 0% | 0% | 50% | 50% |
| 0% | 0% | 0% | 50% | 50% |
Well that’s a bit disappointing. The main problem with RRV is that it isn’t truly proportional. It satisfies some proportionality axioms, so it will satisfy coalition sizes (notice how the right and centre right together get roughly the amount of seats belonging to them) but it’s terrible for party proportionality, which it doesn’t respect at all unless you vote strategically. In fact rangevoting.org puts it nicely:
“If some voter faction (call them the “Reds”), consisting of a fraction F (where 0≤F<1) of the voters, wants to, it is capable (regardless of what the other voters do) of electing at least ⌊(1+N)F-⌋ red winners (assuming, of course, that at least this many red candidates run, and the total number of winners is to be N).
Specifically, it can accomplish that by voting MAX for all Reds and MIN for everybody else.”
But this means that to achieve proportional representation with RRV you have to vote dishonestly and strategically. Even in the example RRV election by rangevoting.org the authors note that there are candidates with strong support by a minority but no support from anyone else that get elected by Meek’s and Schulze STV, but not by RRV (it’s also noteworthy that Meek and Schulze STV differ only by one candidate). RRV has both a strong centre-bias (not so evident from my example because I made the centre purpusefully small, but if the centre is bigger it will become absorbing) and a strong majoritarian bias (absorbing small parties into bigger ones). Even with Saint Laguë reweighting RRV feels very discouraging when you realise that if you vote for a small party, you can only give a small part of your vote to a bigger second choice if you don’t want to make your vote worthless, but then only 10-20% of your vote will not be wasted, meaning that 80% are just gone and because of that RRV does not minimise vote wasting when your goal is to support your favourite to the best of your ability.
Now a lot of people will point out that unlike classical proportional representation, RRV will achieve a far higher average utility. If we assume the scores the people submitted are equal to the utility a person gets and that the voters voted honestly, then RRV will always achieve a higer score than regular PR methods, but this has a very uncomfortale effect. Assume we have an odd number of clusters of equal size, arranged on a political axis like left–right. Each voter gives their own cluster a score of 1, their direct neighbours a score of one half, the next neighbours one quarter, and so on, halving the score with each step. The median cluster, sitting in the middle, collects contributions from both sides, so it will always have the highest total score:
$$ S_\text{median} = 1 + 2\sum_{n=1}^k \frac{1}{2n} $$where the sum runs over the steps out to the edge clusters. The further the axis extends, the larger this becomes. And this leads to an uncomfortable conclusion: to maximise utility, all the seats should go to the median cluster, because that maximises the total score. Here’s a nice example to visualise this. Let’s assume three equal clusters: Left, Centre, Right and try out different compositions of a 99-seat constituency, with utilities ranging from 0 to 1 as above:
| Left seats | Centre seats | Right seats | Total utility score | Conclusion |
|---|---|---|---|---|
| 33 | 33 | 33 | 181.5 | Classical PR case, all looks good |
| 50 | 33 | 16 | 181.5 | Unfair advantage for the left, but the score is the same? This system is clearly rigged but the score does not reflect that! |
| 50 | 16 | 33 | 177.25 | Unfair advantage for the left, but this time the centre loses. The score is finally a bit lower |
| 20 | 60 | 20 | 190 | Unfair advantage for the centre, but this time… the utility is higher? |
| 10 | 80 | 10 | 195 | I don’t like the direction of this… |
| 0 | 100 | 0 | 200 | Wait, so to maximise utility the median cluster should always rule absolutely…? |
It can’t be that everyone will be happier if they are not represented at all, except for the minority whose cluster happens to be the most median one. I would argue that this is wrong. RRV does not measure utility. It only measures the points that individual candidates get, and intersections will always get the most. While STV combines small clusters into sufficiently big ones until they’re represented, RRV always starts at the intersections and then weakens each cluster of the intersection, but this makes smaller non-median clusters too insignificant. We all want to ensure our faction gets represented as well as possible to defend our interests, but RRV is not suitable for this.
Cumulative voting#
Cumulative voting is a used within List-PR systems in Switzerland and Luxemburg for parliamentary elections. Voters get a set number of votes and can give them to any candidate they like. Each lists’ score is then summed up and used to determine the number of seats received and the candidates are chosen depending on the score they’ve got. In Switzerland more than half of all people end up voting for a single party list, but if someone does decide to split their vote between several parties this is called panchage. I find cumulative voting to be one of the most elegant implementations of cardinal voting and it manages to produce a surprisingly good result in both Switzerland and Luxemburg, however, it suffers from the same problem as other cardinal systems in strengthening big parties. Suppose a 10 seat cantonal election and the two big parties each have 40% of the vote, while two smaller parties are projected to win 10 %. Voters of the smaller parties do not want to waste their vote, so they decide to split it up 5 for their party and 5 for the neighbouring party, but while they have to vote like that, members of the big parties do not split their vote, instead giving their 10 votes to their list only. This inherently means that the bigger parties will now together get 5% of votes more than if everyone voted for their favourite party only, leading to them getting all 10 seats. This is unfair and means that if you vote for your favourite, just to be on the safe side you have to give your second choice some of your votes, worsening the position for your favourite, but voting fully for your favourite puts you at a risk of fully wasting your vote. Unlike RRV, cumulative voting has less of a centre-bias effect and more of a majoritarian effect, leading to the bigger parties gaining more seats.
Sequential Phragmen’s rule#
Sequential Phragmen’s rule is a form of proportional approval voting where the voters simply tick all candidates they approve of and then the candidate with the smallest average cost is chosen and 1/N in cost is added to each ballot that approved the candidate.
Phragmen is similar to RRV and MES but is said to be more proportional. Let’s see how it performs with our multiparty simulation where people always approve their party and 50% approve of one of their neighbours.
FOr 10 seats:
| Seats | L | CL | C | CR | R |
|---|---|---|---|---|---|
| 10 | 2 | 2 | 2 | 2 | 2 |
This is a strange result and definitely not proportional that occured because of symmetry, but now let’s assume centre-left and centre-right do not approve of anyone but themselves, which is more realistic.
| Seats | L | CL | C | CR | R |
|---|---|---|---|---|---|
| 10 | 1 | 3 | 1 | 3 | 2 |
| 20 | 3 | 6 | 2 | 6 | 3 |
Hey this is surprisingly proportional! But what if every party’s voter approves of their party and the neighbouring party?
| Seats | L | CL | C | CR | R |
|---|---|---|---|---|---|
| 10 | 0 | 2 | 6 | 2 | 0 |
| 20 | 0 | 5 | 10 | 5 | 0 |
Hmm that’s very reminiscent of RRV. You can play yourself with Phragmen and a few related voting systems here. At least from my simulations it seems to be comparable to PAV and RRV and only delivers a proportional result if people vote strategically.
Sortition#
Finally we arrive at a very unique voting system: Sortition. Sortition is the selection of a legislature by choosing random people from the population. It was used in ancient Athens and for a long time I was a big fan of it especially because of David van Reybrouck’s book Against elections: The case for democracy, which I can really recommend! Assuming a sufficiently large assembly, sortition is the most proportional system of representation. Especially because people running for office have certain personality traits and backgrounds that not everyone in society does. Sortition adds proportionality also in terms of background: society’s losers also gain representation. Citizen’s assemblies in the past have proven to be incredibly effective for deliberation. They are also not corruptible, especially if frequently rotated.
The biggest issues with sortition are the complete lack of accountability. It is not possible to hold the representatives accountable for bad decisions. There’s also ample room for manipulation: who determines the topics the assembly will talk about? What about the appointments the assembly makes, who will recommend the personel to the assembly? The second and much more important issue is the lack of motivation. Politicians are very passionate about issues and this is important when society makes decisions. Very often we have to make decisions which will benefit some people at the cost of others and do we really want people who have no stake or passion to make such decisions? Imagine a road needs eminent domain to be built, it would massively benefit society, but at the severe cost of a dozen people who would lose their homes. Whom should the people whose homes could be bulldozed turn to? How is such a democracy to correct governing ideas? And would the alloted really be as motivated to look into the issue as politicians who were elected exactly because they were very interested in the issues and connect with activists and trying to defend the interests of their section of society? Given the track record of juries in the US, imagine an alloted assembly restricting civil rights and forcing christianity in a very conservative environment. I think the dynamic between a government and an opposition is very important for a healthy democracy. Sortition faces the problem that often no consensus, so a solution that might be chosen is not axiomatically correct and now lacks a proper opposition mechanism.
In my opinion sortition would be perfect for the judicial branch to help ensure its independence (judges of constitutional courts could be randomly determined from lower courts), for auditing and potentially for an oversight body, but I wouldn’t want the main chamber of parliament to be alloted.
Conclusion#
With this my inspection of the various kinds of voting systems concludes. There’s a whole lot more, but I believe I’ve included most of the relevant ones.
I am most notably quite sceptical of cardinal voting systems, even though I was initially very fond of them. They’re great on paper but quite bad in practice. The creme de la creme of voting systems remain List-PR, MMP and STV.
So which one is the best? Well it’s a though question, but for me the top choice would be:
Meek’s STV with regional constituencies
I would also be open to ranked List-PR with ensured regional representation or ranked MMP. Both essentially converge to the same system, one which mostly centres around party proportionality but where we can safely vote for our favourite party while not throwing away our vote. An open party list system with a spare vote has the clear benefit of being easier to count, but Meek’s STV has the advantage of giving more control to the voter while requiring electronic tabulation. Both would also ensure that every region has at least some representation.
Sources:#
- Wikipedia
- Elektopedia
- Edouard Heitzmann: Explaining STV from Scratch
- Edouard Heitzmann: Meek STV Explainer
- Jan Kok / Warren D. Smith: Reweighted Range Voting
- Warren D. Smith: Phragmén’s proportional representation multiwinner voting method
- Hshook: Australian Senate ballot paper for Victoria