A new political system in Armenia

Armenia held parliamentary elections on April 2, the first to be held after a series of substantial constitutional and electoral system changes largely implemented after a 2015 referendum. The changes, which were controversial owing to the disputed referendum, changed Armenia's system of government from a system of semi-presidentialism to a parliamentary system, and changed the electoral system from a mixed-member majoritarian system to an equally unique system of party-list proportional representation.

The electoral system

Armenia's experience of democracy before Soviet rule shortly after World War 1 was very much limited, and as a result it was in a similar place to much of post-Soviet Central Asia after the fall of the Soviet Union in 1990: left with the difficult business of building from scratch a system of democratic and constitutional government.

Many post-Soviet countries, along with various other democratising or reforming nations around that time, introduced mixed-member electoral systems. Armenia's 1995 election law provided for a 190-member legislature, with 150 members elected through a two-round system (though candidates only had to secure 25% of the votes to win in the first round). The remaining forty seats were elected through a closed-list proportional representation system, making a mixed-member majoritarian system with a remarkably low share of party-list seats.

For post-Soviet countries with new and weak political parties, independents were relatively successful in the district tier elections. In Russia's first democratic election (in 1993) independents won 48% of the district vote: similar results were, and still are, in the Ukraine.

In the district tier for Armenia at the 1995 election, independent candidates won 72 of the 150 seats, making them by far the largest party in this tier. The Republic Bloc, a party tied to incumbent President Ter-Petrosyan, won 68 district and 20 list seats, making them the largest party (an Organisation for Co-Operation and Security report stated that the President would have the support of two-thirds of the legislature, implying that many independents were actually allied to the President). No other political party won more than ten seats.

Independent candidacies, however, have waned over recent elections in the nation, as can be seen above. Part of this may be a result of the change in the share of seats allocated on the party list; the share increased at the 1999 and 2007 election. It can also be attributed to the relative dominance of the Republican Party, a party that has been the largest at every presidential and legislative election since 2003 (though they have been dogged by allegations of electoral fraud). This represents an increasing institutionalisation of the party system, as parties (a party, to be precise) becomes the key part of elections.

The new electoral system represents what will likely be a complete removal of independent candidacies from Armenian politics. The full document, passed last year, divides Armenia into thirteen electoral districts. Parties must nominate a list in each district, and a national list. When voters vote, they choose a party list, and may also cast a preference vote for a candidate on the district list.

Seats are initially allocated between using the Hare quota and largest remainders, with a threshold of 5% for parties and 7% for alliances of parties. However, after the Electoral Commission determines the seat allocation, if no party receives at least 53 seats (a majority of the 101-member Assembly; such a party would then receive a top-up to give them 54% of the total seats), and no 'stable majority' coalition (a group of parties which has been allocated at least 54% of the seats in this preliminary distribution agreeing on a Prime Minister) can be formed within three days, a second round is held three weeks later between the top two parties or coalitions. A further four seats are allocated to ethnic minorities, and there are quotas for women representation.

In the second round, new parties may join with the parties or coalitions in the top two, though seats won by parties outside the top two in the first round are apparently not altered by the second round results. The party that wins in the second round is allocated 54% of the total number of seats.

For allocation of seats to actual candidates within parties, for each party half of their seats are allocated to the candidates on the national list (which is closed). The remaining seats are allocated between the districts using the Hare quota again (based on the number of votes cast for the party in each district, so if the Republican Party were to get 20% of the vote in Yeravan District, 20% of the Republican Party's district seats would be allocated to candidates in the district). Seats are allocated to the highest polling candidates within districts. The system is similar to that passed in Italy in 2015 (see this article for details) but later ruled unconstitutional.

In this election, the Republican Party appears to have won a majority even without the special provisions. The party won 49% of the vote, equivalent to 54% of the vote amongst those parties that passed the threshold. The normal Hare distribution of the 101 seats would give them 55 seats (near-exact 54% of the Assembly).

The new Constitution

Up until a criticised 2015 referendum, the 'Yes' campaign in which was supported by the Republican Party, Armenia was a semi-presidential country. This means that it had a directly-elected fixed-term President as head of state, as well as a Prime Minister as head of government responsible to the majority of the National Assembly, who both share executive power.

The 2015 referendum, in which the proposal was approved by 66% of the vote, changed the system to one that appears to be parliamentary; where executive power is in the hands of a Prime Minister responsible to the legislature. The President is elected by the majority of the National Assembly, but it is explicitly stated that "The Government (the Prime Minister and Cabinet) shall be the highest body of the executive power".

Few discretionary powers are granted to the President, who is not even vested with the power to appoint the Prime Minister; instead, he is expected to appoint the candidate who has the support of the aforementioned guaranteed parliamentary majority. He cannot veto legislation, and the determination of policy is reserved to the Prime Minister and Cabinet.

The question of whether this will increase the power of the Republican Party, and its leader (incumbent president Serzh Sargsyan) is a most interesting one. For Mr Sargysyan, at least, the change will allow him to remain in control of executive power beyond the two-term limit proscribed for the presidency under the previous semi-presidential system. 

In a more general sense, if the party system of a country is fragmented, parliamentary governments can be dependent upon shifting coalitions (for example, the Presidency of Nauru) and the parties supporting them can hold only a minority of the legislature, reducing their ability to pass legislation. When a great deal of Armenia's parliament was comprised of independents, a parliamentary government would have been weak, and the fixed-term and non-removable status of the Presidency can give the executive strength through stability.

On the other hand, under a presidential system, the possibility exists that the Presidency and legislature can be in different partisan hands, thus depriving the President of the power to pass legislation. A Prime Minister must at least have the tolerance of the legislature in order to stay in office, and the election law in Armenia actually guarantees a party a fairly comfortable parliamentary majority (this is underlined by a constitutional requirement that one party or coalition must end with 54% of the Assembly seats).

A Prime Minister with disciplined control of his majority political party can pass whatever legislation he supports, and also has control of the executive branch. If the Republican Party are able to maintain control over their members, the new electoral system and system of government will substantially increase their power.

France Presidency 2017

France is scheduled to hold the first round of elections to the Presidency on the 23rd of April; if no candidate receives a majority of votes in this round, a second round will be held, between the top two candidates in the first round, on the 7th of May. Elections to the National Assembly, the popularly elected and most powerful house of the bicameral legislature, are also scheduled to take place in June, roughly one month after the likely second round of the presidential election.

I've written before about France's electoral system, but it is worth summarising the nation's constitutional arrangements at present. France has a semi-presidential system of government, with both a directly-elected President for a five-year term and a Prime Minister responsible to the lower house of the bicameral legislature (the National Assembly). The system is of the premier-presidential sub-type, meaning that the Prime Minister cannot be removed by the President, though they may appoint a Prime Minister.

This election follows five years of the presidency of Francois Hollande, a Socialist. Mr Hollande was elected to the presidency, defeating the leader of the centre-right UMP (Union for a Popular Movement) after seventeen years of centre-right control of the office. Mr Hollande, however, has struggled with a stagnant economy and high unemployment, and did not choose to seek re-election. He leaves office with low approval ratings, and with a Socialist Party that lost substantial support in local and European elections during his tenure.

Candidates

Benoit Hamon-Socialist Party

The governing Socialist Party held an open primary to determine their presidential candidate. Voters were required to be registered to vote in normal French elections, to donate one euro to the organisation conducting the primary (while only Socialist candidates were likely to win, candidates from minor parties closely affiliated to the Socialists also competed, hence the primary was branded as the "Citizens' Primary"), and to generally accept the values of the left. 1.6 million votes were cast in the first round, a figure which increased to 2 million in the second.

The leading candidates for this primary were Manuel Valls, a former Prime Minister, and Arnaud Montebourg and Benoit Hamon, both former cabinet ministers. Valls, considered a more right-wing candidate than the other two, led in early polls, but the first round of the primary resulted in an unexpected first place for Mr. Hamon, who won 36% to 31% for Mr. Valls and 17% for Mr. Montebourg. No other candidate won more than 7%. Montebourg endorsed Hamon for the second round, who won 58% to 42% for Valls.

Hamon is considered to be on the left of the Socialists, supporting a policy of providing a basic income to all citizens and the legalisation of cannabis.

Francois Fillon-The Republicans

Like the Socialists, the Republicans (a re-brand of the UMP) held an open primary to determine their nominee, in which the general public could vote. The unpopularity of the incumbent Socialist government made it likely that the Republican nominee would have a good chance of victory; hence, there was more interest in the Republican primary. 4.3 million voters turned out in the second round, 4.4 in the second.

Also similar to the Socialists, there were three main candidates in this primary. Former President Nicolas Sarkozy and former Prime Ministers Alain Juppe and Francois Fillon. Mr Juppe was the front-runner, with most expecting the runoff to between him and Mr Sarkozy. However, after a strong debate performance, Fillon surged to 44% in the first round, with Juppe on 29%, Sarkozy on 21% and no other candidate above 3%. With Sarkozy endorsing Fillon, he won an easy victory in the second round with 66% of the vote.

The victory gave Fillon frontrunner status; given the divided nature of the left, it was considered likely that he would face National Front candidate Marine Le Pen in the second round. Ms Le Pen's radical views mean that Fillon would likely win such a runoff comfortably with leftist votes. However, in recent days, he has been beset by a scandal involving his wife being paid for an apparently 'fake job', and his polling has dropped accordingly. It remains to be seen whether he will remain in the race.

Emmanuel Macron-Independent/En Marche!

Emmanuel Macron served as economy minister for two years as a Socialist, but resigned from the position last year, after conflicts with party positions on various matters within his portfolio. He then launched a new political party, En Marche!, and ran for the presidency. He has also signalled his intention to run a slate of candidates for the National Assembly election. 

Initial polls had Macron in third place, behind Le Pen and Fillon. However, following the Fillon scandal, recent polls have shown him catching up to Fillon, and advancing to the second round, where he receives the support of the centre-right and beats Le Pen comfortably. He stands on a platform of economic liberalisation and general social liberalism, to the right of Hamon and perhaps Le Pen economically, but to the left of Fillon and Le Pen on issues like immigration. 

Marine Le Pen-National Front

The National Front are a long-term minor presence on the French political scene. The usage of the two-round system, where the centre-left and right generally team up against National Front candidates in the second round, has generally led to little representation for the party in the National Assembly. The party's most substantial result in the past was Le Pen's father, Jean Le Pen, reaching the second round in the 2002 presidential election, narrowly beating Socialist Lionel Jospin in a fragmented race. Mr Le Pen's opponent in this round, UMP incumbent Jacques Chirac, received the endorsement of Mr Jospin, and much of the left, propelling him to a landslide victory (82-18).

Mainstream opposition to the party comes from distaste of its opposition to immigration and Islam, however, with an increase in concern about terrorism and immigration after the Syrian refugee crisis, the party's stocks have risen. They won the highest number of votes at the 2014 European election, and have performed strongly at lower-level elections throughout Mr Hollande's term. It appears likely that Ms Le Pen will win the highest number of votes in the first round of the election, with roughly 24%; however, most polls have her losing a runoff by twenty points or more to Mr Macron or Fillon.

Other candidates in the race include leftist Jean-Luc Melanchon, running with the support of the Left Front (successor to the Communist Party), though his candidacy is under the name 'Unsubmissive France', Green candidate Yannick Jadot, Nicholas Dupont Aignan (who is attempting to fill the niche between Fillon and Le Pen), and various other irrelevancies. Melanchon is the strongest of this group, polling at around 10%. None of the others is higer than 3%. Centrist Francois Bayrou has not yet stated whether he will stand for the election; polls that include him show him at 5%.

Problems with the two-round system

The two-round system is one of those most commonly used for presidential elections around the world. Much of this is due to many presidential systems (such as those in Senegal and the Central African Republic) being in place due to French influence during colonial times, but the system is used in countries like the Ukraine and Poland because it ensures a candidate will be elected with majority support. 

Nonetheless, the system has a substantial disadvantage in fragmented elections, which we may see demonstrated in this upcoming vote. In a fragmented election, the possibility exists that two candidates can make it to the second round with little initial support. If an ideological group splits itself between too many candidates, the possibility exists that no candidate representing a substantial ideological group is able to enter the second round.

An example of this is shown in the 2002 presidential election. Red candidates represent leftists, blue conservatives, black far-right candidates and cyan centrists. As you can see, Chirac and Le Pen finished first and second, and all voters had to choose between them in the second round. However, 45% of voters, all up, voted for a leftist candidate, compared to 29% for the left and 19% for the far-right. Yet there was no candidate for the leftists in the second round, because of the increased fragmentation of this group.

The problem arises because the two-round system does not necessarily provide great incentives for voters to coalesce around two candidates. Left-inclined voters in 2002 may have felt comfortable knowing that they could cast a ballot for a minor leftist, to signify their support for that particular candidate, thinking that Jospin would certainly enter the second round. A first-past-the-post system would mean voters would coalesce between two candidates, at least in theory; often, this squashes diversity in the party system, or leads to candidates being elected with little support.

While Fillon's woes have made this possibility likely, it could potentially have been the case that the left, with the backing of roughly 40% of the electorate, would have had no representation in the runoff. This particular issue is partially circumvented for National Assembly elections, where candidates can enter the second round if they receive the support of 12.5% of the registered electorate (on average, this represented 21.8% of the vote cast at the last election). However, the Constitution of France specifically entrenches the top-two requirement for presidential elections.

Even so, one of the key advantages of preferential voting for single-member seats (as the Presidency of France is) is demonstrated by this particular alternative; the usage of several rounds of exclusions and transfers results in the candidates in later stages of the count having wider support than their equivalents under the two-round system.

The National Assembly

The President has the right, after 'consultation' with the Prime Minister and Speaker, to dissolve the National Assembly at any time of his choosing. However, the Assembly's maximum term is five years, meaning that an election must be held by the tenth of June this year. 

No doubt, such an election date would serve the victor of the election well. The popularity bump incumbent presidents receive has meant that the last three legislative elections, all held shortly after those for the Presidency, have resulted in majorities for the newly elected President's party, a useful tool given that failure to control the Assembly means the President loses control over the cabinet and becomes less able to pass their agenda.

This will become an especially important point in the case of a victory by Mr. Macron. His 'En Marche!' party, as a cursory examination of its website will show, spends much of its time discussing Macron's statements alone. He has said he will run candidates for all 477 seats, but the  gives the appearance of being a mainly personalistic vehicle, focusing on providing a brand to its lead candidate, far more than any other French party. The Socialist and Republican sites show statements from a variety of other figures, and both parties, despite their weaknesses at this election, do have large legislative caucuses and incumbent members with personal vote factors.

Normal behaviour has been for the centre-left and centre-right to form opposing alliances where they allocate seats to parties within said alliances, with the National Front generally not being able to make the second round in most seats due to this tactic (unlike the presidential elections); in 2012, they only entered the second round in sixty-five seats, and won two. If Macron wins, it may well be the case that he forms an agreement with the existing leftist alliance (Socialists+Greens) that would allow the Socialists to have some influence over the new government, while giving some experience and aforementioned personal vote factors to the President.

It is still largely unpredictable what will happen at these elections. Perhaps reflecting the irrelevance of such polling until the winner of the Presidency is determined, the most recent poll with seat numbers was taken in June 2016. It had the centre-right winning a majority, and the National Front winning around fifty seats (in normal two-round elections, they have never left single digits; this would be their best result for any National Assembly election). Such a result, which seems consistent with general increases in support for the FN at the local and European level (implying it's not just Ms Le Pen's personal support) would provide a clear reminder of that party's growing influence, even if Le Pen loses.

Do South Australian voters get a Rau deal from the 'Voter Choice' Bill?

On 16 November this year, South Australian Attorney General John Rau introduced a bill into the House of Assembly (the lower house of South Australia's bicameral Parliament) to change the electoral system used to elect members of the Legislative Council. At present, members of the 22-member Legislative Council are elected eleven at a time for eight year terms; half face election at each election for the House of Assembly, the members of which serve four-year terms.

These elections use the single transferable vote system in one statewide district. However, the system has an important modification. Voters can either vote for one party ticket, which accepts an ordering of all the candidates in the election determined by that party and lodged with the Electoral Commission ahead of the election, or number every candidate in order of their preference. I have written about the severe flaws of this system in the past when used at the federal level, and many of the same criticisms apply to the South Australian system.

What the proposal means

If the bill is passed, South Australian voters will be faced with the same ballot paper (reproduced below) that they have received at past elections. However, the law changes substantially the functions of the above-the-line box.

South Australian Legislative Council sample ballot paper (Source: Government of South Australia 2011)

Under the current system, a vote like the one on the sample paper above would have been considered an adoption of the ranking of all the candidates that was submitted to the Electoral Commission before the election. Group C might have asked that an ATL vote for them next go to the candidates of Group A, then Group D, then B and E.

The new system changes the meaning of this vote. Now it only goes to the candidates of Group C. If all the candidates of Group C are excluded, the vote then exhausts. More importantly, voters may only cast one first preference above the line. So even if the voter voted 1 for Group C and 2 for Group A, the vote would only go to the candidates of Group C, and then exhaust. If a voter wishes to express preferences across party lines, they must vote below the line; the law creates a savings provision so that a first preference for the first candidate within a party group counts as an above-the-line vote for that party.

How would this work in practice? Well, the STV system initially allocates seats to candidates who receive a Droop quota ((votes/seats+1)+1). Once no candidate has a Droop quota, the candidate with the lowest number of votes is excluded, and their preferences. However, given that most South Australians vote above-the-line (96% at the last election), and that all above-the-line votes will immediately exhaust when their party does, this will mean that the exclusions will have a very minor impact, and it is most likely that the candidates which have the highest vote share after the process of allocating seats to candidates with Droop quotas will fill those final seats.

In effect, this means that the electoral system will be very much similar to the 'largest-remainder' method of party-list proportional representation. Each elected candidate within a party will receive exactly a quota of that party's vote before being elected, and the last candidate will receive the rest of that party's vote (the remainder).

How would it work?

It's worth noting that the largest-remainder system is designed to produce a generally proportional outcome, so the Legislative Council will likely continue to have a more proportional composition than the House of Assembly, which is elected in single-member districts using the single transferable vote. This means that the chamber can still fulfil its role as a check upon the powers of the Assembly; it may reject legislation, but cannot remove the government.

Nonetheless, the system will switch emphasis from attracting preferences to entirely attracting first preference votes. It would also cause a small change in the composition of the current Legislative Council, as can be seen below.

Party	Elected in 2010	Elected in 2014	Total	Change from GTV
Labor	4	4	8	0
Liberal	5	4	9	+1
Nick Xenophon Team	0	2	2	+1
Greens	1	1	2	0
Family First	1	0	1	-1
Dignity for Disability	0	0	0	-1

The Dignity for Disability Party won their seat in 2010 off preferences from other small parties, their first preference vote being only 1.2%. The new system would have given that seat to the Liberal Party. Family First won a seat off 4.3% of the primary vote and preferences from other parties; the new system would make that 0.52 quotas, to 1.55 for the Xenophon Team. It is possible that the new system could increase the number of below-the-line votes and make preferences a factor, hence giving that seat to Family First.

Michael Gallagher's 1992 paper on the subject of different methods of party-list proportional representation discusses effective thresholds for winning seats under these methods. He concludes that the threshold of exclusion; that is to say, the minimum number of votes a party can receive without securing a seat (adding one to this total will guarantee that party a seat) for the Droop quota and largest remainder system is 1/(s+1), where s is the number of seats to be allocated (this is in percentage terms). For South Australian elections, that would be equal to 8.33% of the vote. 

Distinct from this is the threshold of representation; that is to say, the smallest number of votes a party can receive and still receive a seat. For this particular figure, the equation is 2/(p(s+1)), where s is seats, and p is the number of competing parties. At the last election, this would be equal to 0.64% of the vote. A more general threshold equation, 75%/(s+1), gives a figure of 6.25%. 

Wasted votes

One advantage of the current STV system is that nearly all votes do go to an elected candidate. Given that a candidate must receive one quota to be elected, and the quota is (votes/(seats+1)+1), only enough candidates to fill all the seats may receive quotas; hence, the maximum number of votes that do not end up with an elected candidate cannot be more than votes/(seats+1) (8.33%).

The new system, however, would be more likely to disregard a larger number of votes. If we consider a vote that is not part of a quota or a remainder rewarded with a seat 'wasted', for my analysis of the last state election, 16.4% of all votes would be wasted, compared to the 8.3% of the vote left with candidates not elected in the actual election. These figures are relatively consistent for recent elections.

Nonetheless, it is worth noting that, to some extent, the current system lowers this figure to an unrealistic amount if voter preferences are to be legitimately consulted. If group voting tickets are to be done away with, getting this figure of only a quota wasted would require voters to cast a preference for every candidate or party group. This would lead to a high informal rate; when voters were required to preference every candidate for the federal Senate, informal rates larger than 10% were not uncommon. Usage of the federal Senate system, which has optional above-the-line preferences and potentially allows votes to exhaust, would increase this figure.

Labor's hypocrisy on exhausted votes

The South Australian Labor government's willingness to tolerate high exhaustion rates contrasts interestingly with Federal Labor's conduct during the debate over introducing optional preferential above-the-line voting. Labor opposed the changes, which passed nonetheless with support from the Greens and Nick Xenophon, on several grounds. One of them was the claim, made by South Australian Senator Penny Wong, that "It (the reform) will mean the votes of up to three million voters effectively going in the bin" and "disenfranchises more than three million voters—people who, at the last election, chose to vote for someone other than the major parties or the Greens". 

Ignoring, of course, what a load of nonsense these predictions were proven to be, I find it quite remarkable that the party that found it so undemocratic that above-the-line votes could exhaust is now introducing a system that guarantees above-the-line votes will exhaust.

 Why the state Labor government is not simply copying the federal system is somewhat confusing, and introducing preferences would improve on this proposal substantially. Nonetheless, the proposal does give voters certainty that their votes will count for their explicit choices only, and the value of preferences under GTV are very much questionable if preferences do not flow the way a voter wishes.

As always, Kevin Bonham has an excellent take on the matter, if you wish to read further.

Hong Kong 2016-Electoral systems against political parties

The small city-state of Hong Kong held general elections for their Legislative Council on September 4. Hong Kong, though technically a part of China (PRC), was granted substantial autonomy upon its return to China in 1997 by the British (it had previously been a British colony). The citizens of Hong Kong enjoy civil liberties not held by other Chinese, and, to some extent, they are able to choose how they are governed.

It is this extent that has been one of the key areas of debate in Hong Kong politics ever since the handover, and explains why the state's politics have traditionally been between pro-democratic parties (which support rapid transition towards democratic governance) and pro-Beijing parties (which support either no change towards democratic governance, or more gradual change than the pro-democrats).

Executive government in the region is controlled by the 'Chief Executive', and a cabinet of Secretaries appointed by him. The exact method of selection of this Chief Executive is, at present, by a 1,200 member 'Election Committee', which is indirectly elected and comprised of representatives mostly chosen by business interests. This has led to Chief Executives coming from the pro-Beijing faction of Hong Kong politics, which is usually in an electoral minority.

The Basic Law states that "the ultimate aim is the selection of the Chief Executive by universal suffrage upon nomination by a broadly representative nominating committee in accordance with democratic procedures", though no specific timeline is laid down for this process. Last year, I wrote about the proposal for a new way to elect the Chief Executive; direct elections, but with candidates chosen by a somewhat unrepresentative nominating committee, and with the possibility of no candidates from the pro-democratic camp being permitted to contest the election. The change would have required amending Hong Kong's Basic Law, which needs support from two-thirds of the Legislative Council. As the pro-democrats have over a third of the seats, and as they refused to acquiesce to the proposals, the changes were not made.

The Legislative Council's composition is also a bone of contention. Out of the seventy members of the council, thirty are elected from what are known as 'functional constituencies'. These members are elected by people registered as having an interest in certain areas of business, like law, fisheries and banking. Five additional members are elected in a 'super' functional constituency, in which all electors ineligible to vote in one of the other functional constituencies are permitted to vote; only members of local councils may run as candidates in this functional constituency.

On average, each of the Functional Constituencies that went up for election this year had approx. 8,500 voters. This is compared to approx. 62,000 voters per seat elected in a 'geographic' constituency, in which anyone over 18 may vote and stand as a candidate (with the exception of people who refuse to acknowledge Chinese sovereignty over Hong Kong). There is huge variation between the seats, with the largest district (Education) having 482 times the number of voters as the smallest (Agriculture and Fisheries); both elect one member. 

This over-representation of business interests, which tend to support pro-Beijing parties, have ensured a majority for the pro-Beijing faction has prevailed since Hong Kong was returned to China, despite these parties never receiving a majority of the votes in the geographic constituencies. Pro-democratic parties forcefully argue against this, claiming that it is undemocratic, while pro-Beijing parties would argue that given that business makes a large financial contribution to Hong Kong, they should have a large say in governance.

The electoral system for universal suffrage elections

As stated above, however, Hong Kong does allow all voters to choose some members of the Legislative Council. Thirty-five members are chosen in the geographic constituencies; as the name implies, these members are elected from five specific geographic areas. Another five are chosen in the special functional constituency.

The first universal suffrage elections to the Legislative Council took place under British rule in 1991. This was for only eighteen seats, with twenty-one being appointed by the colonial Governor, and another twenty-one being chosen by functional constituencies. These elections took place in nine two-member districts, with voters having two votes for individual candidates. The two candidates with the highest votes would win. 

In general, this system would be expected to result in the party or faction with the most votes winning both seats, given that voters for a party would vote for both of that party's candidates. The results seemed to bear this out, with the pro-democracy parties winning sixteen seats (later increased to seventeen after a by-election) of the eighteen, despite only receiving 58.2% of the vote. This clearly had little impact on the government of the city, since the members were outnumbered by the appointed, generally pro-establishment members. 

At the next election, held in 1995, a number of changes were made to the composition of the Council. Twenty members would be directly elected, and they would be elected in single-member districts, though the electoral system would still be plurality (one vote, candidate with the most votes wins). Nine new functional constituencies were added.

These results were a landslide win for the pro-democratic parties in the directly elected seats; they won 17 with 63% of the vote. This landslide, along with relatively strong support in the functional seats, allowed the pro-democrats to win a narrow majority in the Council. This obviously displeased Beijing, which was scheduled to take over the city in 1997.

For the immediate time, Beijing destroyed the pro-democrat majority Legislative Council by appointing their own Elections Committee to choose a Provisional Legislative Council, which took over the role of the provisional Legislative Council.  However, upon the resumption of elections post-Beijing takeover, an important change was made to the electoral law; for the twenty directly elected members of the LegCo, the single-member plurality system was replaced by party-list proportional representation, in districts with an average magnitude of four members.

The results of the 1998 election, the first held after the handover, resulted in the three main pan-democratic parties securing 57% of the vote. This figure does not include independent candidates, some of whom may have been sympathetic to the pan-democrat cause. These three parties were able to secure thirteen out of twenty seats in the direct seats. However, once the results from the thirty seats elected by the functional constituencies and the ten elected by the Elections Committee came in, the narrow pro-democratic win in the directly elected seats were more than balanced out by the massive pro-Beijing majority on these other seats, allowing the pro-Beijing parties to win a majority.

For the most part, the statement made by the Hong Kong Electoral Commission that results with PR would "more accurately reflect the wishes of the electorate" was correct. At the same time, the Legislative Council was not representative as a whole of the electorate of Hong Kong. PR also had its clear advantages to the pro-Beijing political parties. But the advantages for Beijing do not stop with preventing pan-democrat landslides in the elected seats.

SNTVisation

The specific party-list electoral system that was used for the geographical constituency elections was the largest-remainder method with the Hare quota. This particular method is notable for, compared to other electoral systems, advantaging small parties. It sounds rather counterintuitive, but for largest-remainder proportional representation systems, higher quotas advantage small parties. The reason for this is that distributing seats by remainder is very advantageous to small parties, given that fewer votes are needed for a seat won by remainder than a seat won by quota. Higher quotas also reduce the remainders for parties that win seats with a quota, but do not do that for parties that reach a quota. If you're more interested in this, I would encourage reading Michael Gallagher's paper on the matter.

Under an electoral system where small parties are advantaged, the rational thing for a large party to do is to transform itself into several small parties. The advantages given to parties that win seats by remainder means that these small parties should aim to win seats by remainder only, thus they should aim for each of these lists to win one seat. If elections are between lists, each trying to elect one member, with the lists with the highest M votes being elected (where M is the number of seats to be elected), the electoral system becomes roughly equivalent to the single non-transferable vote.

This process did not happen immediately after PR was introduced, as can be seen below. However, it is in the last two elections that it has become completely pervasive; all lists elected only one member.

For small parties, with enough support to win one seat in a district, SNTV is an easy electoral system to manage. They run a single candidate, and concentrate all their votes on that candidate. However, for large parties with enough support to win more than one seat, there is substantial difficulty involved in maximising that potential. Run too many candidates, or spread your vote too thinly between those you run, and you run the risk of all these candidates receiving too few votes; run too few, or concentrate your votes on only one, and that candidate could win far more votes than other elected candidates, thus depriving your party of seats.

The advantages that the system gives small parties has led to a more fragmented legislature as the number of lists electing only one member has increased, as can be seen below (the 'effective number of political parties' figure measures, roughly, the number of equal-sized political parties equivalent to the actual makeup of the legislature).

The effect of the electoral system, therefore, appears to have been to stunt the creation of a large party on either side of the major political divide. It would not be unreasonable to say that the possibility of a large, unified anti-Beijing party could be concerning to Beijing's interests. This is why, even as the electoral system appears to hurt the pro-Beijing parties, they may be wary about changing it to reward party consolidation.

Did the electoral system hurt the pro-Beijing parties?

The issue of whether the SNTV system hurt the pro-Beijing political parties is somewhat important, given that these parties have authority to amend the electoral law if they so desire. At the 2012 election, there were a number of cases where the pro-democracy parties made nomination errors. This was especially substantial for the Civic Party, which decided to run one list in the New Territories West and Hong Kong Island seats with two incumbents, and encourage all their voters to cast a vote for this particular list.

The strategy backfired quite substantially. In New Territories West, the Civic list received 14.5% of the vote. The quota was 11.1% of the votes, as there were nine seats. As a result, the Civic Party was allocated one seat for their full quota, and then had 3.4% of the votes left as a remainder. This was not enough to beat the other parties; the last seat went to a pro-Beijing list with 6.8% of the vote. Had Civic successfully divided their vote into two, they could have beaten the bottom list and won two seats. Nomination errors along similar lines occurred in other Civic districts.

The usage of functional seats means that the contest in the geographic seats cannot be meaningfully considered important for overall control of the Council. However, given that a two-thirds majority is needed to amend the Basic Law (which entrenches many of the civil liberties given to Hong Kongers), the pro-democrats need to do relatively well in the elected seats in order to ensure that this law cannot be amended without consultation with them.

At this election, however, a substantial fragmenting factor appeared on the pro-democratic side. Localist candidates, supportive of increased autonomy and in some cases independence for Hong Kong, ran for election. These candidates appear to have taken most of their support from existing pan-democrats, which fragmented the anti-Beijing vote. Fragmentation, however, can be an advantage under this electoral system; as stated above, vote division that is a consequence of fragmentation can be useful to parties under SNTV. On the other hand, there were only three large pro-Beijing parties running, and they would have to make difficult internal tactical decisions about how to win the most seats.

So, did the SNTV system advantage the anti-Beijing parties? In order to calculate this, I compared the SNTV results to results using the D'Hondt system and party vote figures. The D'Hondt system with party vote figures is equivalent to what the SNTV system would look like if parties nominated the exact number of candidates as seats they can win, and then divided these votes perfectly between these candidates. This represents what the result would look like if vote distribution were not a factor.

The results of the analysis were that the pro-Beijing parties would gain two extra seats out of thirty-five elected seats. In both of these seats, the seats were lost due to an overly conservative nomination strategy; the party nominated too few lists to win the number of seats that they are entitled to. For example, in the Kowloon West seat, the pro-Beijing Democratic Alliance's one list received 18.8% of the vote, above the 16.7% quota. Under largest-remainder, this list's remainder of 2.1% was not nearly enough to win a seat. However, under D'Hondt, the party's vote was divided by two, meaning that the 9.4% left after the first seat was enough to beat the localist 'Youngspiration' candidate, with 7.4% to the last seat.

If the results of this election are anything to go by, then, it may be in the political interests of Hong Kong's pro-Beijing parties to introduce a system, potentially like D'Hondt, that rewards consolidated parties. However, as stated above, this could conflict with broader political goals in Beijing to encourage the pro-democratic parties to be fragmented and to have internal arguments.

A pattern? Macau's electoral system

Macau is another one of the territories returned to China by Portugal where China's political system does not fully operate. Like Hong Kong, Macau has a Legislative Council which is partially elected directly and partially elected through 'functional constituencies', though there are also seven members appointed by the Chief Executive. The Chief Executive, who performs a similar function to the identically named leader of Hong Kong, and is chosen by a similar, not directly elected, Elections Committee.

In Macau, only 14 of 33 members of the Legislative Council are directly elected, so there is a much smaller risk to the government of the pro-democratic parties winning a large number of seats. However, the electoral system used for those elected seats is uniquely designed to produce party fragmentation.

The electoral system for the elected seats is a variant of the highest averages method, like the D'Hondt method described above. However, when seats are calculated, the list of numbers used starts with one, and then are multiplied by the next number; the list goes 1, 2, 4, 8, 16.... A formula for a party's divisor would be 2^n, where n is the number of seats the party has already won. 

The effect of this is to very heavily penalise large parties, since their vote is divided into much smaller groups as they win more seats. The below chart shows how a party with 1000 votes would have their vote go down to 2 under the Macanese system after ten seats, compared to 100 under standard D'Hondt.

The effects of an electoral system that disadvantages large parties is, obviously, to encourage small parties, or to encourage large political factions to form small parties. This is certainly the case in Macau, where the largest party at the last election had merely 18% of the vote.

While there are only two regions to sample from, it would certainly not seem inconceivable that Beijing would have a political interest in keeping political organisations in the areas that are democratic divided. Electoral systems can have a substantial impact on political party systems, and the two chosen for these regions, by pro-Beijing political parties, encourage small, divided political parties.

Australian election, 2016-Xenophon, Hanson and Singh

Australia held a federal election on July 2 of this year for all members of the Federal Parliament. The Australian Federal Parliament consists of a 150-member House of Representatives and a 76-member Senate. The government is responsible to the House of Representatives, which is elected through preferential voting in single-member districts for a three year term (though it may be dissolved at any time by the Governor-General, acting on the advice of the Prime Minister).

However, all legislation must pass through the Senate, which is elected through the single transferable vote, though with substantial modifications described at the end of the article. Elections to the Senate are usually for 40 seats at a time (six Senators per state for six-year terms, plus four Territory senators elected for three-year terms), but if the Senate rejects a bill passed by the House of Representatives twice, the Prime Minister may advise the Governor-General to call an election for all members of both houses.

The result was the narrow return of the incumbent Liberal/National coalition government, led by Prime Minister Malcolm Turnbull. In the 150-member House of Representatives, the party will definitely have 76 seats, which is a majority of one. If the Speaker of the House is a Liberal, which seems likely, the government will have a majority of 75-74.

The seat of Herbert, in the north of Queensland, is the only seat that could still likely switch between the two parties. Labor candidate Cathy O'Toole narrowly edged out Liberal incumbent Ewen Jones by eight votes on initial counting; the margin increased to 35 following a recount. While a narrow margin of this sort could theoretically be upheld, any minor error in counting or voting that would be ignored in a seat with a wider margin could lead to the election heading to the courts.

Even if Herbert is won by the government, the 77 votes in the House will represent a knife-edge majority almost as close as that won by Robert Menzies in 1961 (62 Liberal/Country, 60 Labor with full voting rights). The Turnbull government will have the advantage, though, that the Labor Party do not have all the remaining MPs. The House of Representatives crossbench consists of one Green, one Katter's Australian Party (Bob himself), two Independents (Andrew Wilkie in Denison and Cathy McGowan in Indi) and one member of the Nick Xenophon Team.

Whether these members will support the government consistently is unclear. The AEC conducts preference counts between the two major nationwide parties in each seat for statistical purposes. At the last election, McGowan's division of Indi split 59-41 to the Liberals, and Katter's division of Kennedy went 67-33. The Xenophon Team's seat of Mayo split 63-37 to the Liberals, though the Xenophon Team's preferences are more of an unknown quantity. Consistent opposition to the government, or supporting the installation of a Labor government, would likely be harmful to the future electoral prospects of these MPs.

The Xenophon Team's result

Before this election, I wrote about the Xenophon Team's prospects. I said that the difficulty Xenophon had in transferring his support to his chosen candidates, demonstrated in the 2014 South Australian election, would make a Xenophon lower house seat unlikely. Nonetheless, the party appears to have won a seat. So, how big was the difference between Xenophon Team House candidates and the support for the man himself?

Measuring the dropoff between Xenophon's House and Senate support simply by comparing their share of the votes in both houses is the obvious way to do this; however, it is something of an unfair comparison, given that there were an average of 6.5 candidates per House seat compared to 23 groups in the Senate. Nonetheless, here it is, though this is based on somewhat incomplete vote totals (as counting and data entry still continues).

In only three seats (Mayo, Barker and Grey) did the Xenophon House candidate outperform the Senate ticket, even with increased choice on the Senate ballot paper. Incidentally, these three seats were the strongest for Xenophon Team House support. On average, the Xenophon Team performed 1.24% stronger in the Senate than the House. This suggests that the dropoff between Xenophon House and Senate support is smaller than the 2014 SA election would suggest, but still substantial.

Incidentally, if you calculate Xenophon Team support as a percentage of the total for the parties that contested all the House seats (that is; Labor, the Greens, NXT, the Liberals, and Family First) in both houses, you get a somewhat different result.

This result moves Grey into the seats where the NXT Senate ticket performed better than the House, and increases the average to 2.3%. In general, NXT did not make much of an impact in the other states, winning an average of 1.8%, and probably not enough to win a seat (though a very strong performance on preferences might give them a chance in Western Australia). However, they won 21.6% in SA, giving them 2.8 quotas and likely three seats.

One Nation, under Palmer?

The other substantial new minor party presence in this election was the One Nation party. This party was formed by Pauline Hanson, elected as an independent in the seat of Oxley in 1996 (with a nearly 20% swing towards her) after being disendorsed by the Liberal Party for making controversial comments about indigenous Australians. One year later, she formed a political party, called One Nation. This party espoused anti-immigration views, though, as is not uncommon with this sort of party, supported somewhat economically leftist policies, especially opposition to privatisation and free trade (a lot of her views are laid out in her maiden speech to the House).

This party first contested the 1998 Queensland election, winning eleven seats and 22.7% of the vote. However, the party soon split into two, with some MPs joining the City Country Alliance (warning: vile web design), and the party lost most of its seats at the 2001 election. 

At the federal election of 1998, the party won 8.4% of the House vote (14.3% in Queensland) and 9% of the Senate vote, though weak preference flows meant that this only translated into one seat, in Queensland. Hanson ran in the seat of Blair, and won 36% of the primary vote to 25.3% for Labor, 21.7% for the Liberals, and 10.2% for the Nationals; however, the Liberal candidate received enough preferences from the National to pull ahead of the Labor candidate, whose preferences elected the Liberal over Hanson 53-47.

This election represented a peak for One Nation, whose vote roughly halved at the next election, and declined to below 1% after that. Hanson continued to contest elections, though often not as a member of the One Nation party; she ran as a member of her own United Australia Party for the Senate in 2007, winning 4.2%. She came close to winning a seat in the New South Wales upper house in 2011, ran for the Senate in 2013 (and would have potentially won had voters not confused the Liberal Party with David Leyonhjelm's Liberal Democrats), and came within 0.2% of winning the Queensland state electorate of Lockyer in 2015).

But now, she appears to have certainly returned to the Senate, as One Nation has secured 9.1% of the Senate vote in Queensland, comfortably above the quota for election to one of the twelve seats. One Nation are also in contention to win a seat in New South Wales and Western Australia with about 4%. They also missed out on a Tasmanian Senate seat by 140 votes off 2.57% of the primary vote.

So, where does this One Nation vote come from? Well, the below chart shows how the One Nation vote correlates to the vote of the party whose vote dropped most dramatically at this election: the Palmer United Party. This party was formed by mining billionaire Clive Palmer leading up to the 2013 election, and won two Senate seats (with an extra member elected in the Western Australia re-election) and one House seat (Palmer himself won the seat of Fairfax). However, two of the party's Senators left, and Palmer did not recontest Fairfax. None of the party's Senate tickets secured as much as half a percent of the vote.

The below chart shows the correlation between the Senate vote for the Palmer United Party in 2013, and the Senate vote for One Nation (based off current counting) for this year.

The two variables have a correlation coefficient of 0.73, suggesting a relatively close correlation. However, this likely reflects the fact that in most electorates, both One Nation and the Palmer United Party are/were a relatively minor presence. In inner-city electorates, both One Nation and the Palmer United Party having roughly 1% of the vote is not an especially meaningful correlation. The below chart shows the correlation for the divisions where the Palmer United Party received more than 7% of the Senate vote (the vast majority of which are in Queensland).

Here, we see much greater variation, and a much weaker correlation coefficient of 0.22. While this is dragged down somewhat by the presence of Jacquie Lambie in Tasmania (presumably taking some of One Nation's constituency), there are only two Tasmanian electorates in that dataset. While both the Palmer United Party and One Nation have substantial support in Queensland, they do appear to have substantial differences in where they win support there.

Lisa Singh wins on BTL votes-could it happen elsewhere?

So far, only two jurisdictions have declared Senate results; Tasmania, and the Northern Territory. The Senate electoral system has changed this year. Amongst other changes, voters now only have to number six boxes in order to cast a formal vote below the line (for individual candidates), though the ballot paper says twelve.

When tickets for the Senate were drawn up for Tasmania, two controversial decisions were made. Labour incumbent Senator Lisa Singh was demoted to fifth on the ticket, a very difficult position to win, while Liberal Tourism Minister Richard Colbeck was moved to the same placing. 

As casting a vote for these candidates individually is much easier under the new system, both Colbeck and Singh either ran, or had campaigns run for them, to encourage people to vote for them below the line. In the end, Singh was returned to the Senate, with 6.12% of the below-the-line vote, while Colbeck was not returned, despite winning 4% of below-the-line votes. The result represents the first time since the 1950s, and the first time since any type of above-the-line voting existed, that a Senator has been elected out of party ordering.

So, could the new system allow this to happen in other parts of the country? My answer is probably not. As I wrote when I was discussing the initial version of Senate reform, that would have required voters to number every box below the line, the states of South Australia and New South Wales both fairly briefly used the single transferable vote for multiple seats to elect their upper houses, without any form of above-the-line voting. While New South Wales required voters to number seventeen boxes, while all were required in South Australia, the systems shared one common characteristic; it was no harder to vote against the party ticket than to fully accept it. In both of these cases, the vast majority of voters appear to have accepted the party ticket.

The fact is that Tasmania is a much smaller state than any on the mainland, and running a statewide campaign for below-the-line votes is therefore much less costly than in any of the mainland states. Given that political parties have expressed an unwillingness to encourage such campaigning, doing it on a larger scale would prove difficult. Colbeck and Singh had the wind to their backs in another way; this election is a double dissolution, for twelve Senators, while most Senate elections would be for six, making it even harder to win a seat.

Though the equal distribution of votes between a party's candidates is often advantageous (if too many votes are concentrated on one of a party's candidates, it can lead to the other candidates of that party being excluded early, thus costing that party seats), Australian political parties appear to remain opposed to individual campaigns. The difficulty a Senate candidate's campaign would face in getting attention in the midst of a House election, with the Prime Ministership at stake, would add to these difficulties. Outside of Tasmania, it will be unlikely for any Senate candidates to be elected outside their party's ranking in the near future.

Scotland and Wales-some simulations

For those that didn't notice, elections to Scotland, Northern Ireland and Wales's devolved Parliaments, as well as to various local authorities in England and the mayoralty and assembly of Greater London, took place on May 5.

In 1997, referendums took place in Scotland and Wales on whether country-wide Parliaments should be introduced to govern the two regions. In both cases, the proposal was successful. Further referendums were held in Northern Ireland (where the assembly was part of a comprehensive peace deal) and London in 1998, where devolved assemblies were introduced.

In order to gain cross-party support for these assemblies, the Blair Labour government decided against using a single-member plurality electoral system to elect members of the Scottish and Welsh assemblies. Instead, it was decided to use a mixed-member proportional representation system.

In London, there are fourteen members elected in single-member districts, and eleven members elected from closed party lists. Voters have two votes; one for their single-member district candidate, and one for a party list. In the districts, the candidate with the most votes is elected. Following this, all the list votes are tallied up, and the eleven party list seats are allocated using the D'Hondt method of party list proportional representation.

However, it is modified somewhat. The number that the party's vote is divided by is increased by the number of single-member districts the party has won. So, if a party wins five single-member districts, its vote will be divided by six at the beginning of the D'Hondt count. A party needs to win 5% of the vote to win any party-list seats.

A very similar electoral system is used for Scotland and Wales. Scotland is divided into eight districts. In each of these, eight to ten members are elected in single-member districts, and seven members are elected using party-lists. An identical system to the one used in London is used to allocate the party-list seats: however, there is no threshold. This is made up for by the substantially reduced number of seats to be elected in these districts. If we add all the seats in a district together, we get an effective threshold of about 4.4%; however, this is probably lower in practice, and may depend on the results of the single-member districts.

Wales is identical, except the districts are somewhat smaller. Each district elects between seven to nine members in single-member districts, and four members in the party-list system. This makes it very much less proportional

Scottish results

A couple of months ago, I wrote this blog post on decoy lists in Scotland. As it turns out, Nicola Sturgeon does not read my blog, and as a result no party in Scotland tried the decoy list strategy. While the Greens only ran district candidates in a small number of districts, this was more so that they could focus their efforts on winning list votes.

However, what if the parties had used decoy lists? The below chart shows what would have happened if only the SNP had used decoy lists; that is, their list candidates and district candidates were not affiliated to each other. 

Compared to the actual results, the SNP would gain thirty seats. The Conservatives would lose thirteen seats, Labour eleven, the Greens five, and the Liberal Democrats one. Rather than their current position of governing in minority, with support from one of the opposition parties needed to back legislation, the SNP would have a comfortable majority. 

But what if other parties had followed the SNP's strategy? This would make Scotland effectively mixed-member majoritarian, an electoral system where the aim is to add some proportionality onto a majoritarian system. The goal of mixed-member proportional representation is to make the entire result proportional.

The SNP would only gain twenty-four seats this time, with their list gains balanced out by the ability of the Conservative and Labour parties to make the same sort of gains. However, Labour would lose ten seats and the Conservatives would win nine; Labour's substantial weakness in the constituencies would be exaggerated. The Liberal Democrats would win the same number of seats, as most of their seats were won in constituencies. The Greens would be, proportionally, the biggest losers; they would lose all but one of their seats.

Following the election, and the SNP's failure to win a majority, Alex Salmond stated on his weekly radio show that the electoral system used in Scotland was responsible for the result. In an interview that appears fairly incoherent, Salmond claimed that the 'variations' that led to the SNP not winning a majority were the fault of the regional list system.

But is this the case? Well, we can test this. The below charts show the results of the election using a national list system; to be precise, such a system would allocate all the list seats in one district, covering the entirety of Scotland. As such a system would be very proportional, there are two simulations; one with a 5% threshold, and one without.

It's quite clear that Salmond is wrong, at least in that sense. The national list system would not have given the SNP a majority; in fact, in both simulations they would be in an even weaker position. They would have won only the 59 seats they won in the constituencies. As you can see, there are few other differences; the Liberal Democrats and Greens would both gain a couple of seats, as they were disadvantaged by having their vote spread out in the districts, while UKIP, which won only 2% of the nationwide constituency vote, would win two seats without a threshold, and none with one.

In the same article, Salmond also supports the introduction of a single-vote MMP system. Under such a system, voters would have one vote, for a constituency candidate. That vote, however, would count as a party vote for the party that constituency candidate was affiliated to.

Were such a system implemented in Scotland, it would have a number of effects. For a start, it would be bad news for the Green Party. The Greens only ran a few constituency candidates, and focused their efforts on the list. In most constituencies, the Greens have little chance of election, and Green voters would be pushed towards tactically voting for a more competitive contender. This would mean the Greens would win fewer party votes, and thus substantially fewer seats.

At the same time, tactical voting in the constituencies would go down somewhat. Despite the above, some people would still vote Green in the constituencies, but they would obviously vote for someone else if there was no Green candidate, which is the case in most places. Abolishing the list ballot would mean the Greens would be forced to run a candidate in every seat. The same would go for weak Liberal Democrats, Conservative and Labour candidates; partisans for these parties would be less likely to switch to more viable constituency candidates closer to their party affiliation if that meant that they could not vote in any way for the party of their first choice.

Wales

The results of the Welsh elections were, on the face of it, rather unusual. Labour's vote in the constituencies dropped by 7.6% and their regional vote dropped by about 5%, but they only lost one seat. So, how did this happen?

Well, there are a number of reasons for this. First of all, the big gainer in these Welsh elections was UKIP. This Eurosceptic party has gained substantial support in recent years, and while it failed to make much of a mark in Scotland, at the 2015 general election the party polled 13.6% in Wales. 

Rather than focusing their attention on the party-list seats, like the Scottish Greens, UKIP ran constituency candidates in all but two constituencies. This meant that the opposition vote became more split. Labour also had an efficient vote spread; only 16% of the vote for Labour was cast in the constituencies that they did not win (which constituted 26% of the electorate).

This on its own does not cause disproportionality. For example, in Scotland, the Scottish National Party received 80% of the district seats, off only 46.5% of the vote. Wales had a similar imbalance, with 67% of the seats for Labour for 35% of the vote. However, Wales was twice as disproportional as Scotland, using the Gallagher Index.

The key issue causing disproportionality in Wales is the very low number of party-list seats. In Wales, the percentage of list seats is very low for an MMP jurisdiction.

What if Wales had a similar amount of proportional seats to Scotland? I have simulated this by adding three seats to each region, thus making the percentage of list seats 46.67% (compared to 45.74% for Scotland).

Labour would be the main loser, falling from one seat short of a majority to just 40% of the Assembly. Plaid Cymru, the Conservatives and UKIP would be slightly better off. The Liberal Democrats would be the big gainer, winning four seats, up from just one. 

Overall, the Gallagher Index of disproportionality for Wales would decrease from 13.03 to 7.25, closer to Scotland's 5.6. In an area like Wales, where one party is dominant and the opposition is heavily split, increasing the number of party-list compensatory seats would be a sensible step to ensure an accountable regional government.