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Ke e p i n g t h i n g s i n p r o p o r t i o n : h o w c a n v o t i n g s y s t e m s b e f a i r e r ?
TV Interviewer: One voter, 16,472 votes – a slight anomaly…?
Edmund Blackadder: Not really… You see, Baldrick may look like a monkey who’s been put in a suit and then strategically shaved, but he is a brilliant politician. The number of votes I cast is simply a reflection of how firmly I believe in his policies.
The by-election in the rotten borough of Dunny-on-the-Wold, in which Blackadder has been the sole voter since Wednesday morning, is funny not only because it makes a mockery of an 18th-century electoral system that to our eyes is laughably unfair, but also because the mechanics of that election still have a ring of truth. Though acts of reform and representation have abolished rotten boroughs, instituted secret ballots, and extended the franchise in Britain from 3% to 100% of the adult population, the mechanics of the first-past-the-post (FPTP) system, by which 14 000 individuals have been elected to parlia-
ment since 1832, remain largely unchanged. The US House of Representatives also elects members using first-past-the-post.
The system has, as opponents point out, disadvantages. The most glaring one is that it does not represent voters’ wishes. In 2010, the Conservative party won 36% of the votes, but 47% of the seats. Sometimes this effect can be extreme: in 1951 the Conservatives polled more than a million fewer votes than Labour, but won more seats and formed the government; in Feb-ruary 1974 the reverse happened, with Labour brought to power on fewer votes than their main opponent. Tactical voting, where voters vote for a candidate who is not their favourite in the hope of keeping out someone still worse, is another undesirable and perhaps undemocratic consequence of FPTP; as is the so-called “wasted vote”, for a candidate who cannot possibly win.
The movement to reform FPTP is not a new one. Like the Electoral Reform Society today, John Stuart Mill back in 1861 championed the single transferable vote (STV)1. A referendum on the alternative vote (AV) now looks likely, having
been extracted as a concession by the Liberal Democrats as part of their coalition agreement with the Conservatives; yet exactly one hundred years ago, a Royal Commission on electoral sys-tems advocated that same system for elections to the House of Commons. Incumbent majority governments have obvious practical reasons to
resist moves to more proportional voting sys-tems; they are effectively signing a warrant, dated for the next election, to put an end to their overall control of the Commons. It is not surprising, then, that despite Labour’s 1997 manifesto commitment to hold a referendum on electoral reform, it has taken a hung parliament (the very thing opponents point to as the men-acing consequence of voting reform) for there to be serious movement on this issue.
The principle usually declared as critical to any voting system is that it should be “fair”. Alas, in 1951, the economist Kenneth Arrow reached the pessimistic conclusion that there was no non-dictatorial voting system that could satisfy even fairly innocuous conditions of fairness. A particular sticking point is the criterion known as independence of irrelevant alternatives, which requires that if we rank, say, red over blue in an
In the 2010 UK General election the Conservative party won 36% of the votes – but 47% of the seats. The Liberal
Democrats won 23% of the votes and just 9% of the seats. Does the first-past-the-post system really give results
that reflect voters’ wishes? Gavin Thompson looks at alternatives.
Rotten boroughs
Until 1832, the constituency of Old Sarum in Wiltshire contained three houses, seven voters – and elected two MPs to Parliament. The industrial city of Manchester, on the other hand, had a popu-lation of 164 000 and no MP of its own. Old Sarum was one of dozens of “rotten boroughs”, places which had once been populous but which had kept their parliamentary representation as their population declined. Dunwich on the Suffolk coast was another. Its few remaining households still elected their own MPs even after most of the town had fallen into the sea. The Reform Act of 1832 abolished some fifty rotten borough constituencies. The absurdities of rotten borough elections were parodied in an episode of the TV comedy series Blackadder.
Pressure for voting reform is not new. Exactly one hundred years ago a Royal Commission recommended proportional representation
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election, the voting system should ensure this remains true irrespective of whether the colour yellow is available as an option. The proof is far beyond our scope, but an illustration was given by the philosopher Sidney Morgenbesser. At a res-taurant the waitress tells him he has two choices: apple pie and blueberry pie. Sidney orders the apple pie. After a few minutes the waitress re-turns and says that they also have cherry pie, at which point Morgenbesser says “In that case I’ll have the blueberry”. This is obviously absurd; yet in very many systems of voting, including FPTP, the addition of a third party that cannot win can often change the result. Ralph Nader adding his candidacy in the 2000 Presidential election is often credited with having given the election to George Bush rather than to Al Gore.
At root the problem is one of information: mechanical procedures of political choice cannot accommodate enough of it to reflect the prefer-ences of the electorate without trade-offs.
Despite Arrow’s “impossibility theorem” there remains serious debate on how an electoral sys-tem might be engineered to satisfy some practi-cal criteria for fairness (such as proportionality) and contribute towards outcomes seen as desir-able for a well-functioning democracy (such as strong government and political engagement of the citizens). This article does not try to identify
a single best voting system; instead, using case studies of elections since the Second World War in “Western” democracies, it attempts to summa-rise some measurable effects of system choice, effects which I hope inform readers in deciding for themselves. Proportionality, churn, and the
distribution of power are all measurable, and are all affected by the choice of voting system.
Proportionality
In this context, proportionality refers to how closely the make-up of the elected chamber re-flects the balance of opinion among the elector-ate. A simple measure of this is the deviation from proportionality (DV) score. This is the dif-ference between the share of votes and the share of seats, summed across all parties. Calculating it is simple: just subtract each party’s vote share from its seat share and add up all of the absolute values (i.e. ignoring negative signs). Table 1 shows this sum for the 2010 UK election, while Figure 1 shows that it has risen steadily since 1945. (The DV score is often divided by two, so that it lies between 0 and 100, but we shall ig-nore that refinement. In our version, it can reach up to 200, with 200 implying all (100%) of the representation goes to a party with none (0%) of the votes.)
The classification of voting systems
Most national electoral systems fall into one of three families:
• Majoritarian. Candidates are elected to single-member districts (except in the case of block voting), with the highest-polling candidate filling the position. Both FPTP and alternative vote are majoritarian.
• Proportional representation. These are explicitly designed to align the share of vote with the share of parliamentary seats. Candidates are elected at a national level or “regionally” to multi-member constituencies to achieve proportionality. Party list systems and single transferable vote are classified as proportional.
• Mixed. Any approach which uses a combination of proportional and majoritarian systems; usu-ally the proportional element is used to counteract the disproportional outcome from single-member constituency elections
Majoritarian systems are more common in established democracies and in the 50 countries in the “other” category, which hold elections but cannot be described as democratic. New democracies favour proportional systems. The table below is for elections to national legislatures and lower houses only.
Majoritarian Proportional Mixed Other
All countries Number 91 72 30 6Population (million) 2 647.0 1 186.1 1 071.7 34.4
Established democracies Number 35 23 6 4Population (million) 1 545.8 199.4 329.1 0.2
New democracies Number 6 19 6 0Population (million) 14.9 168.5 122.7 0.0
Other Number 50 30 18 2Population (million) 1 086.3 818.1 619.8 34.1
Source: Electoral System Design: The New International IDEA Handbook
Table 1. Share of vote and share of seats won, UK General Election 2010
Party Share of seats Share of vote Difference
Conservative 47.08 36.10 10.97Labour 39.69 29.03 10.66Liberal Democrat 8.77 23.06 –14.29Scottish National 0.92 1.66 –0.73Green 0.15 0.96 –0.81Independents 0.15 0.77 –0.62Sinn Fein 0.77 0.58 0.19Democratic Unionists 1.23 0.57 0.66Plaid Cymru 0.46 0.56 –0.10SDLP 0.46 0.37 0.09Alliance 0.15 0.14 0.01Speaker 0.15 0.08 0.08Others 0.00 6.12 –6.12
DV score (sum of right-hand column, ignoring signs) 45.32
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Fig.1 UK DV score 1945-2010
Figure 1. UK DV score, 1945–2010
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The DV score can be interpreted as the extent to which votes are “wasted”, in the sense that they do not contribute to the electoral outcome. In constituencies where Labour and Conservatives are close frontrunners and Liberal Democrats are expected to come a poor third, the Labour and Conservative candidates commonly claim that a Lib Dem vote is wasted in that it cannot affect the result. (The claim is often intended to attract Lib Dem votes to themselves.)
The UK has a DV score that is comparatively high (as we shall see later), and that has been rising chiefly because of the increasing propor-tion of votes cast for the Liberal Democrats and other parties (Figure 2). The UK has a mean DV score since 1945 of 29.4. The score for the United States over the same period is 12.7.
Churn, migration, or “kicking the rascals out”
For many, elections to a chamber of representa-tives should have the capacity to generate flux, as unpopular members (and governments) are given their marching orders. On the other hand, constant movement in and out of the chamber might be a sign of instability. The extent of this “churn” can be measured by the change in the share of seats from one election to the next, again summed across all parties (Figure 3). In the UK, what is
commonly called the electoral cycle is in evidence from this measure, as periods of calm are punctu-ated by occasional mass migration. The UK has a mean post-war “churn” of 17.3 percentage points (standard deviation 12.8); the value for the US is 8.3 percentage points (standard deviation 7.6).
The distribution of power
Is power concentrated in the hands of one or two parties? Does one party have a majority of seats, or does it have to operate in coalition? These questions relate to the distribution of power. One way of graphically summarising this is through a cumulative percentage frequency chart (Figure 4). The first marker shows the percentage of seats held by the largest party, the second represents the two largest parties together and so on.
The fact that the line for the UK, showing the distribution of power following the 2010 general
election, is bowed towards the top left implies representation in the chamber is concentrated in the hands of a small number of parties (the Conservatives and Labour). The remaining 13% of seats are held by the Liberal Democrats and a comparatively large number of nationalist par-ties, shown by a long right-hand tail. The first marker lies below the 50% line, showing that the Conservatives have no overall majority. The line for the US shows that power there is even more concentrated in the two largest parties. It is not easy to imagine, in the near future at least, a hung House of Representatives in which a third party holds the balance of power.
Turnout and political engagement
It can be argued that proportionality, churn and the distribution of power are all closely related to the choice of voting system. In the case of turnout and voter engagement, the causal effect is at least one step removed, operating through a feeling of impotence at being unable to in-fluence the result. Alienation from the political process, moreover, has many other varied and complex causes. Though turnout is given as a statistic in the case studies that follow, it would for these reasons be unwise to attribute any dif-ferences to the particular electoral systems under examination.
Alternative vote
Under AV – also known as “instant runoff voting” and “preferential voting” – voters rank candi-
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Figure 2. Share of vote won by parties other than Conservatives and Labour, 1945–2010
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Figure 3. UK churn, 1950–2010
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Fig.4 Distribution, UK and US House of Representatives
Figure 4. Distribution of power, UK House of Commons and US House of Representatives
Alternative vote case study: Australian House of Representatives
Average turnout: 94.5% (voting is compulsory in Australia)Mean DV score: 27.3Average churn (standard deviation): 19 (14.33)
The Australian House of Representatives has been elected using AV since 1918. Electoral out-comes have proved only slightly more proportional than in the UK, with a mean post-1945 DV score of 27.3 as compared with 29.4 in the UK. As in the UK, there is cyclical churn, with seats swinging between the two main parties (the Australian Labour Party and the Liberal Party) every two or three elections, and an even greater concentration of power, with the two largest parties holding 92% of the 150 seats after the 2007 election. Overall majorities for single parties are fairly common, occurring in 12 of the past 25 elections.
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dates in order of preference. If no candidate re-ceives more than half the first-preference votes, the last-placed candidate is eliminated and their second-preference votes redistributed to the rest of the candidates and counted as if they were first choices. The process repeats itself, with trailing candidates being successively eliminated, until one candidate has more than 50%. The process is often said to “guarantee” that the candidate is chosen by at least half of the electorate, although this majority may be composed, to a greater or lesser extent, of second preference votes.
Party list proportional representation
Proportional representation (PR) covers a family of voting systems in which seats are allocated in proportion to the number of votes received. Under list-based systems, a set of candidates are put forward by each party, arranged in the order they will be elected. Under a closed-list proportional system, the electorate votes whole-sale for a list, whilst open-list systems allow voters to express their preferences for individual candidates, so that they can leapfrog the order dictated by the party. Countries using list PR commonly require parties to win some minimum threshold percentage of the vote before they receive any seats.
Until genetic engineering makes possible the new generation of hybrid MPs (say a member who
is 36% Conservative and 23% Liberal), multi-member constituencies are required to achieve proportionality. The more members per constitu-ency, the better the allocation of seats in propor-tion to votes, but the weaker the constituency link becomes. Opponents of list PR make much of
its potential to estrange the electorate from their representatives; closed-list systems do not allow voters to choose their representatives at all, and open-list systems require high levels of engage-ment if the voter is to make an informed choice. A four-member constituency with seven parties standing could have as many as 28 candidates to choose from.
Single transferable vote
STV is a form of proportional representation whereby voters rank candidates in order of pref-erence for election to a multi-member constitu-ency. The process involves redistribution of votes in a manner analogous to the alterative vote, although “surplus” votes for winning candidates as well as those for trailing candidates can be redistributed. STV is described as proportional (and AV is not) because more than one candidate is elected in each constituency.
STV is the system advocated by the UK Elec-toral Reform Society and many psephologists because the redistribution process reduces the waste associated with FPTP and other ma-joritarian systems, whilst the direct election of candidates ensures a link between voter and representative, something that the party list system is seen as undermining. The mechanics of allocating seats to votes under STV, however, is undeniably complicated. In particular, there are a variety of processes to decide which votes are surplus (and which are meant for the win-ner), and how they are distributed – should it be all at once, or in segments? It might be con-sidered reasonable for the voter to understand these; in practice, very few voters would try.
Open-list PR case study: The Dutch House of Representatives
Average turnout: 81.4% (since 1971, before which voting was compulsory)Mean DV score: 5.22Average churn (standard deviation): 21 (10.9)
Elections to the Dutch House of Representatives are held using open party-list proportional representation, with the 150 seats allocated on a national basis. Candidates are assigned to seats in the order that they appear on the list, although it is possible for candidates to leapfrog others in the order if they win enough preference votes. These elections are also notable for having the lowest possible democratically fair threshold for representation (1/150th).
The large size of the electoral “constituency” (effectively, the whole country) and the low vote threshold mean that the Netherlands has an exceptionally low DV score, with seats allocated in almost exact proportion to votes. Churn in post-war elections has averaged 18 percentage points, higher than in the UK, although the electoral cycle is not so pronounced. Although the Netherlands rarely sees large changes from one election to the next, in no election has there been a shift of less than 8 percentage points among the parties; such stasis has occurred in the UK six times over this period.
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Single Transferable Vote case study: the Irish House of Representatives
Average turnout: 72.3%Mean DV score: 12Average churn (standard deviation): 17.4 (8.4)
All elections in the Republic of Ireland, including those for the national parliament (analysed below), take place using STV. The system has produced a lower DV score than in the UK, though not as low as for the Netherlands’ list-based system. The distribution of power in the parliament is slightly more balanced than in the UK, though the largest two parties still hold 77% of the seats. Levels of churn are very similar, although Ireland does not see the “landslide” changes experienced periodically in the UK.
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The additional member system
The additional member system – also known as mixed member proportional representation – is a hybrid system in which voters cast two ballots. The first is for an MP in a traditional single-member constituency, elected through FPTP (or other majoritarian process); the second is for an MP in a larger multi-member constituency (usu-ally called the regional MP) from a party list. The list MPs are allocated to counteract deviations in proportionality arising through the constituency elections.
First-past-the-post
FPTP and other majoritarian systems are based on the simple principle that, after votes have been cast, the party with the most votes is declared the winner. The drawbacks of FPTP have already been outlined; an advantage is its simplicity.
Although more countries (71) use list PR, in terms of electorate size FPTP is the most widely used system in the world. Its popularity owes much to the colonial legacy of Britain: three quarters of its former colonies use FPTP; former Dutch colonies, by contrast, all use proportional systems.
The two-party dominance shown in the case study is not unique to the US; indeed, FPTP sys-tems tend to produce a two-major-party effect so commonly that the phenomenon has acquired a name of its own, “Duverger’s law”, after the French politician credited with identifying the correlation. It arises partly because parties with significant but thinly spread support struggle to gain representation in any one electoral constitu-ency, and partly because potential supporters are prepared to cast a “pragmatic” ballot for one of the two main parties to avoid wasting their vote on a hopeless case. This latter phenomenon can lead to rather low DV scores for FPTP systems and is a dimension of “unfairness” that is difficult to capture from electoral statistics.
The UK has become in the past forty years an obvious exception to Duverger’s law, with 12 par-ties represented in the House of Commons. This is to some extent a consequence of the Welsh and Scottish nationalist and Northern Irish par-ties, for which support is almost by definition not evenly spread.
Conclusion
Though electoral reform for the House of Com-mons has proved to be a slow process, there has been a proliferation of different voting systems at other levels of government in the UK. The Scottish parliament came into being in 1999 and uses the additional member system, as do the Welsh and London assemblies. The Northern Ireland Assembly uses STV. Elections to the Euro-
pean parliament since 1999 have been through closed-list PR, whilst most elected mayors are chosen using the supplementary vote (a form of alternative vote with only two preferences). Let no one say the British are wed to tradition.
Finally, it is worth remembering that the bal-loting process on its own is far from sufficient to ensure fair elections, let alone a well-functioning democracy. The 2009 North Korean elections saw, according to official results, a 99.9% turnout and a 100% vote share for the Workers’ Party; in Gabon, following the death of Africa’s longest-serving president after 42 years in power, his son
was duly elected to replace him. The Democratic Party of Turkmenistan, meanwhile, holds all 2507 seats on the country’s elected legislative coun-cil. The astounding victories enjoyed by these ruling tyrannies owe little to a “bad” choice of voting system and much to suppression of pub-lic reasoning and political liberties. Democracy is not really about whether you put an X or a numbered preference in the box. It is what goes with it that counts.
Gavin Thompson is a statistician at the House of Com-mons library, specialising in electoral statistics.
FPTP/Additional Member System case study: New Zealand Parliament
Average turnout: 1946–93–88.9%; 1996–2008–82.1%Mean DV Score: 1946–93–26.3; 1996–2008–4.97Average churn (standard deviation): 1946–93–19.9 (17.2); 1996–2008–31.9 (19.4)
In 1994, New Zealand voted in a referendum to replace its FPTP system with an additional member system. The result (shown below) was a dramatic increase in proportionality, a more even distribution of power, and representation of minority parties in the chamber.
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1 2 3 4 5 6 7 8 9 10 11 12Distribution of powerChurnDeviation from proportionality (or DV)
First-past-the-post case study: the US House of Representatives
Average turnout: 65.3% (since 1968); in the US, voters self-register, and turnout has averaged 47.3% of the voting age population since 1946Mean DV score: 12.7Average churn (standard deviation): 8.3 (7.6)
The US elects members to the House of Representatives from single-member districts by the FPTP system. Candidates for each party are nominated through primary elections, in which voting is usually restricted to party members. In common with the UK, the US exhibits cyclical churn, with periods of calm alternating with higher turnover. On average, however, there is more stability in the composition of the chamber from one election to the next; this may be because elections to the House take place every two years. The share of votes going to other parties is so small that deviation from proportionality is far lower than in the UK: the two-party system is almost as entrenched in the decision-making of the electorate as it is in the House, with 96% voting for one of the two main parties.
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