This page brings together various blog entries on electoral systems, mainly on the UK but also on Austrlia and California. The dates are the original date, the oldest entries written in January 2010 (before the last UK election) come first. I hope the material helps voters making an informed decision in the referendum on May 5, 2011.

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Electoral Systems: UK

January 5, 2010


The Economist opens the year with an article on the de facto opening of the electoral campaign in the UK. The illustrations are revealing in what they say about the electoral system. A cartoon shows David Cameron (big) and Gordon Brown (small) at the starting line, with an audience asleep. What I found most interesting about the cartoon is what is not there: the about 30% of voters who vote for others than the two establishment parties, and the 40% of the electorate who didn't vote last time, and who are likely not to vote this time either. This is typical of the discussions in the British media, which give rather little voice to those 30% other parties, and those 40% non-voters (though noone can really speak for them).


The second illustration shows polling of voting intentions: most recently, roughly 40% Conservative, 30% Labour and 20% Liberal Democrats. In the British winner-takes-all constituency based system, this would translate into a solid Conservative majority in parliament. Thus, we can expect a Conservative government even though the majority of voters voted for policies of the centre left - the Liberal Democrats are nowadays on many issues to the left of Labour (as positioned by Tony Blair). For a non-British observer it is hard to see such a result reflecting the idea of democracy, even if it was reached by democratic rules.


In 2005 the result was Labour 35.3%, Conservative 32.3% and Liberal Democrats 22.1% and Others 10.3%. Most observers not familiar with the electoral system would probably expect either a coalition government, or run-off election as for example in France. Yet, Tony Blair was hailed as the big winner, as his party obtained 356 seats in parliament, compared to 198 for the Conservatives and 62 for the Liberal Democrats and 30 Others. A lead of three percentage points gave five year of almost unrestricted power to Labour. Not really satisfactory.


The first-past-the-post system of course influences how people vote. For example, everyone knows that the Labour party won't get a feet on the ground in the constituency where I live, and hence they would vote for one of the bigger parties (locally, that's the Conservatives and the Liberal Democrats). How would the results look like if there was no such tactical voting? The only indication we have comes from the European election (though many voters stayed at home). The result was: Conservatives 27.7%, UKIP 16.5%, Labour 15.7%, Liberal Democrats 13.7%, Green Party 8.6%, BNP 6.2%, Scottish Nationalists 2.1%, English Democrats 1.8%, Christian Party 1.6%, Socialist Labour Party 1.1%, No2EU 1.0%, Plaid Cymru (Welsh Nationalist) 0.8%, Others 2.7%.


What kind of government should Britain be getting based on that sort of results? For purpose of analysis let's assume that a) somewhat fewer voters desert the mainstream parties in favor of fringe parties and b) Labour gets not quite as big a drumming. With a French system we would see a run-off election between the Conservatives and probably Labour (or, possibly, UKIP or Lib-Dem). With an Australian single-transferable-vote system, the result would be similar as in the French system. With a German-style system with proportional representation and a 5% hurdle we would see four to five parties in parliament (Conservatives, Labour, Lib-Dem, UKIP and Greens), which means either Conservative-UKIP coalition, or a Labour-Lib-Dem coalition (with or without Greens). [under the specific rules of Germany the nationalists would get a few seats]. Under pure proportional representation without hurdle, as in Italy, we would have loads of parties in parliament - and very lively debates.


Of course all this is not going to happen. It is fair prediction that sometime between now and May, about 60% of the British electorate are going to vote, of which 40% vote Conservative (that's 24% of those eligible), and for the next five years we get a Conservative government. Thus, The Economist's cartoon gets right to the essence.


The question that the media really ought to discuss is whether 24% gives a government the democratic legitimacy to make huge budget cuts, or decide on war and peace in the land. For ordinary citizens, the best advice is to advice is to participate in the process - even if the result in your constituency, like in mine, appears a foregone conclusion with the reelection of the same bloke who did the job the last 30 years. At least, you may be able to set a signal for the next election.

The hidden costs of first-past-the-post

April 29


British media has in recent week seen something of a revolution on how they discuss their election. Rather than discussing the likely "swing" between Labour and Conservatives, the debate is focusing on the actual percentages of votes that parties are likely to get. And with this Pandora box being opened, it becomes obvious to all but some stubborn politicians that the current system does a poor job in translating the voters will into power in the parliament. Thus, the debate on electoral reform is gaining pace (also see January 5). To the arguments raised in the media, I would like to add four points. These concerns the question who represents the respective parties in parliament:

  1. First-past-the-post systems lead to local parties putting up candidates representing the relatively strongest group - which in practice (in the UK) are male, white, secular Christians living in a traditional family ... etc. Thus, the British parliament has been slow to increase the share of women and ethnic minorities. In fact, parties had to resort to special tricks such as 'all women shortlist' to force some constituencies to adopt a person not from this majority as their candidate.

  2. First-past-the-post systems lead to incumbents sitting in their seat for a long time, leading to an overall 'older' parliament. I some cases, MPs stay beyond the age when they are still effective (which of course varies - some may retire at 65, others are fit well into their 80s). This is because the personal name recognition is such a strong factor constituency votes, and replacing an experienced and well-known MP by a young candidate carries a risk for the constituency party. As an extreme example, consider Storm Thurmond in the US who served to the age of 100.

  3. First-past-the-post systems encourage individuals affected by a personal scandal to stay in their seat until the next election. In fact the parties would pressure individuals not to step down but rather become an absentee MP because they fear the by-election would lead to the loss of the seat. In a list based system (i.e. proportional representation) resignation of an individual would lead to the next person on the list taking up the seat, thus retaining proportions in parliament as they had been decided by the voters. Consequently, an MP affected by a personal scandal would be under pressure to resign his/her seat immediately (though, for good reason, no-one can force an elected MP to resign).

  4. First-past-the-post systems have no satisfactory mechanisms to allow MPs wishing to resign for personal reasons, notably illness, to step down. Resignation or death of an MP triggers a by-election, which creates opportunities for voters in one constituency to have a disproportionate influence on national politics. In the meantime, the seat remains vacant, which can shift the majorities in parliament -  the death of US Senator Ted Kennedy is a striking recent example. List systems allow a smooth transition to a new person consistent with the original election. In Denmark such a substitution is even further developed in that MPs can temporarily step down and be replaced by the next person on the list in case of for example illness or maternity. I don't know what women MPs in the UK do when they get pregnant - but then this is such a rare case anyway because of point 1 and 2 above.  



What If? Proportional Representation

May 8

How would the UK Parliament look like under proportional representation? Using the numbers of actual votes on May 6 provided by the BBC for each region, I calculated the seats for each party.

Figure 1 shows the total number of seats for each of the main parties. For ease of presentation I did not separate out the Northern Ireland seats, and I aggregated Scottish National Party (SNP) and Plaid Cymru (PC).


Figure 2 shows the pattern of seats across the regions of the UK using PR.

Figure 3 shows, for comparison, the pattern of actual seats.

 How I calculated these numbers:

  • Seats are allocated within each region of Britain using proportional representation (Hare Niemeyer procedure).
  • Within each region, a 5% hurdle applies. This seems reasonable in the UK given the special situation of Scotland, Wales and Northern Ireland in particular.
  • I have taken the number of seats in each region as given (see below for a variation).
  • I excluded the constituency of Thirsk & Malton, where no election has taken place due to the death of a candidate. Thus, there are only 649 seats in my data (This is a safe Conservative seat, and in the PR calculation this would probably also add one seat to the Conservatives).
  • I assume that no tactical voting has taken place in the elections. This is obviously not correct, but there is no way of knowing in which ways voters have voted tactically. Under PR some people would vote differently, and some people who never voted before may actually show up.


  1. The main observation, unsurprisingly, is that the LibDems more than double their number of seats. These seats come roughly equally from the Conservatives and Labour.
  2. Another major shift is in the regional representation of Conservatives and Labour. Conservatives gain 23 seats in Scotland, Wales and the North of England, while Labour gains 22 seats in the South of England. Thus, both parliamentary fractions would be more regionally balanced (and avoid a situation where the Conservatives’ sole MP from Scotland is the only way Scots might influence a Conservative UK government).
  3. Scottish and Welch Nationalists almost double their seat count. Note that this result emerges only if the 5% hurdle is applied separately for each region; with a nation-wide hurdle they would get no seat at all.
  4. In Northern Ireland, the DUP looses three of their eight seats to the UCU.
  5. No party other than Conservatives, Labour and LibDems makes it over 5% in any region of England.


Resizing Regions

In a follow-up investigation, I looked at the claim by the Conservatives that they need more votes on average per seat. It turns out this is true, but not by a huge margin. Two issues are at play:

  • Constituencies vary in size across regions: In Wales, 56,500 registered voters elect one MP, whereas in the Southeast it is over 75,000. 

  • Voter turnout at this election has been stronger in "Conservative areas" than in "Labour areas". Specifically, in the Southeast, 68.0% of registered voters actually voted, in the Northeast only 60.9%.

I made some further adjustment by allocating seats to region proportionately (again using Hare-Niemeyer). Thus, Scotland (-4), Wales (-8), West Midlands (-2), Northern Ireland (-1) and Northeast (-1) loose seats, while seats are gained by Southeast (+6), East Midlands (+3), Eastern (+3), Southwest (+2) and London (+2).  It results in a small change in the overall result for the main parties as the Conservatives gain 4 seats:







The Minimum Threshold in PR

May 10


Following up on my blog on May 8, questions arose with respect to the minimum threshold. In my simulations, I assumed a 5% "hurdle" that parties have to clear to be represented in parliament. The reason for this hurdle is that otherwise a parliament would become fragmented and unworkable - past experiences in Italy and Israel are indicative (or think of Germany in the 1930s).


In practice this hurdle varies across countries. Turkey has a 10% hurdle, which keeps out quite a lot of voters - most notably the party of the Kurdish minority. Few outside Turkey would consider a 10% hurdle as fair. On the other extreme, Denmark has a hurdle of 2%, which results in eight parties in parliament. This works fine in Denmark: governments typically are minority coalition governments which agreements with other 'support parties'. Yet, I don't think this experience is transferable to other countries because Denmark has a rare cooperative political culture. Thus, most countries use 5%, while Sweden uses 4% - and this usually works well with three to five parties in parliament.


I had assumed in my simulation that a 5% hurdle be used in the UK, and it be applied separately for each region because of the peculiarities of Scotland, Wales and Northern Ireland. To prevent fragmentation of the parliament, it may be appropriate that the 5% hurdle applies to England as a whole. In the May 6th election, UKIP came closest to this hurdle with 3.1% across the UK.


If a 5% hurdle was applied for each of the eight regions within England separately, nothing would change. If the hurdle was lowered to 4% and applied separately for each region within England, then UKIP would jump

over the hurdle in four regions and attain 10 seats, whereas the BNP jumps the hurdle in two regions and gets 4 seats. Obviously, an increase in small groups in parliament would make stable government more difficult, and an appropriate hurdle is necessary, preferably applied to the country as a whole.


In practice, voters are likely to vote differently under PR. The results from the European elections last June suggest that UKIP may well get more votes and pass the 5% hurdle, mainly at the expense of the Conservatives - and if they do they should also be in parliament. Also, the Greens are likely to gain more votes, mainly at the expense of the LibDems, though they would struggle to get over 5%. The BNP with their tiny but highly concentrated pockets of support are actually less likely get anywhere near parliament.



What IF? Alternative Preference Voting System

May 11


An alternative to the current first-past-the-post and proportional representation is an 'alternative preference system', as it is applied currently in Australia and for the election for the Mayor of London. The idea is similar to a run-off election as used in France, but rolled in with the original election. Hence, each voter has to rank the candidates, and the votes then are counted as if there are multiple run-off elections until one candidate gets more than 50% of the votes cast.


I tried to do a simulation for this one, but it is really a lot of work, and it requires a lot of assumptions. So, I assumed for example, 3/4 of Labour voters go LibDem in the run-off, 2/3 of LibDem voters vote Labour in the run-off, and so on. I choose the London region for this simulation because it has a wide variety of election results. Of 73 constituencies in London, in 32 the winning candidate had over 50% of the votes (14 Cons, 17 Labour, and 1 LibDem). Of the hypothetical run-off elections, 25 are between Cons and Labour, 5 between Cons and LibDem, and 11 between Labour and LibDem. Simulating the likely outcomes of these run-offs, I obtained only 4 differences to the actual results: 3 turned from Cons to Labour, while 1 went the opposite way. No changes affected the LibDems. I had expected more changes, but alas there were not.


The problem with this simulation, is that the actual votes may already reflect voters second preferences - so in practice we may see a wider spread of first preferences in the alternative preferences system. Another consequence is likely to be that even in 'safe' seats parties would be reluctant to put up a candidate holding polarizing views, because that would allow a centrist candidate from any of the other parties to make it in the run off, and win on second preferences. Thus, within the parties, more central candidates may gain influence vis-ŕ-vis the 'hawks'. But more importantly, a candidate with over 50% of votes could claim greater legitimacy than a candidate who is elected with 30-something percent, as is not uncommon in the UK at present.  (In London, last week, 5 of the new MPs  went through on less than 40%, the lowest being 32.8% for the Labour MP in Hampstead).


After writing this blog, I found some numbers in the FT (May 11, p. 2). The data are not reproduced in the online edition of the FT but available on the website of the "Electoral Reform Society".

For 'Alternative vote' they infer that LibDems would gain about 20 seats while Cons loose a similar number. The difference to my numbers is presumably in different assumptions about what voters second preferences are. If all Labour voters indeed have LibDem as second preference (and vice versa) then indeed LibDems would gain a lot, but I doubt that is the case.

For 'single transferable vote' in 'large multi-member constituencies' they obtain results that look conspicuously like my results for proportional representation. May be they assumed one region to be one constituency. Essentially, with multi-member constituencies, the larger they are the closer the results are to PR.



Electoral Reform in California?

June 6


Not only the British discuss the flaws of the first-past-the-post electoral system, so do Californians. In fact, they get to vote this Tuesday on "Proposition 14", which suggests that primary elections (when the parties select their candidates) be substituted by an open election where everyone can vote for all candidates. The first two candidates would then go forward to the actual election.


The primary elections are a critical difference between the US and British electoral systems: It gives voters associated with either of the main parties the chance to select whom the want to send into the actual election. Thus, voters have power than in the UK where the candidates are selected from a shortlist vetted by the national party leadership.


Californian politics has become highly "partisan". Most constituencies are 'safe seats' where either party can be practically sure to win. This is because the socio-demographic structure is so different between the coastal areas and the farming areas inland. In consequence, for many state senators winning the primary in the own party is more challenging than winning the actual election. Hence, most of them are more concerned with pleasing their own local party than working with others to make compromises that the state needs. Hence, paralysis is normal in Californian politics.


Supporters of Proposition 14 expect that "open primaries" with the first two candidates going through - even if they belong to the same party - will strengthen moderate candidates relative to hardliners, and hence create a parliament that actually works. The system would resemble a little the French system of run-off elections between the leading candidates, and have similar effects as the 'alternative preference' system currently being discussed in the UK (see May 11). If Californians pull through with this reform, it could have dramatic effects on the political culture not only in California, but throughout the USA. The adversarial nature of US politics could be - just a bit - mellowed. 

Postscript: On June 8, Voters indeed voted with a substantial majority for Proposition 14. The consequences are yet to be seen, but they may go well beyond California.




Elections Australian Style

August 22


Given my interest in election systems, it is fortuitous to observe the Australian elections first hand. For the election of the lower house of parliament, Australians use an 'alternative preference' voting system in which voters rank the candidates; the votes are then counted like in multiple run-off elections. Hence, to be elected, a candidate needs to obtain more than 50% of the votes including secondary preferences of candidates that did not make it into the top-2. Does this make any difference in practice?


Following the news in the run-off to the election, it is hard to notice much difference to the UK: Most of the media coverage was focused on just two candidates representing the two major parties: Labour and the 'Coalition', which consists of two parties (Liberals and Nationals) that do not actually compete against each other in the constituencies. Only paying careful attention, news-listeners or readers will actually note that, firstly, the Green party regularly gets double-digit shares of the (first-preference) votes, and that independents are important in a number of rural constituencies. The media give the impression that neither of the top candidates are very popular (not to mention charismatic) and the parties are very close to each other on many key issues. The media just love battles between two heroic individuals rather than deep discussions on issues - no election system will be able to change that.


The AP system, however, induces candidates to court voters whose first love is one of the smaller parties. In the UK, the message might be 'don't waste your vote on the Greens', in Australia the message is, 'if you want to vote Green give me your second preference vote'. Moreover, it avoids outcomes where MPs are legitimized only by a third of the electorate because the vote is split between several candidates. The political dynamics within each constituency thus are somewhat different, reducing the chance of a candidate with polar views being elected due to split opposition - which is good.


The election outcome suggests that the media may have paid too much attention to the big two parties: Out of 150 MPs, 5 are independent or Green (with 3 constituencies still not declared), and they hold the balance of power as the big parties have almost equal numbers of votes. In fact - like the UK - in 2010 Australia has the first parliament without overall control, and the first Green MP elected in a southern coastal city. Thus, voters around the world seem to be fed-up with two party systems, where two elites essentially shuffling power between them. However, both sides declare victory and try to convince the media that they deserve to govern (again, similar to the UK). Yet, it will be up to the majority in parliament to decide....


So, what can we learn for the UK? Nothing much, I am afraid. Australia has in most parts a two party system with the third party (Greens) being much weaker than the third party in UK politics (LibDems), not to mention, Plaid Cymru, Scottish Nationals and UKIP all of which received strong support in regional or European elections. Thus, the dynamics of second preferences in the UK would likely be much more complex. However, I have earlier predicted that the overall shares of seats in parliament is unlikely to change substantially if AP is introduced in the UK (May).  Based on my observations in Australia, I stick to this prediction - apart from noting that we might have a handful of independents. Thus, I would not expect AP to boost the LibDems number of seats in Westminster!



Alternative Vote System (1): Changing Dynamics

April 3, 2011


On May 5, Britain goes to vote on a referendum on (small) changes in the electoral system. The proposal is for an Australian style 'alternative vote' (AV) system, where voters rank their preferences rather than simply select only their most preferred local  candidate. Why do many think this change is necessary, and how is it going to change  elections?


The basic problem is that for the last three decades, including the eras of Maggie Thatcher and Tony Blair, Britain has been governed by parties that had received less than 40% of the popular vote. While they had a more or less solid majority in parliament, they did not have a majority of the people behind them. The current coalition government is an exception. In the 1950s, over 90% of voters voted for one of the two big parties; in the last couple of elections, only about 70% did.  In consequence, governments lacked legitimacy.


An obvious solution to this problem would be to shift to some form of proportional representation. Yet, this would radically alter the power structures in the country (see May 8, 2010), and the vested interests of those in power in the country (not just the political parties) make such a radical change politically infeasible. 


The proposed AV system is simulating a run-off election: The votes for the least successful candidate are redistributed to the candidate with most votes until one candidate achieved at least 50% of the votes. Hence, any MP would have support by at least 50% of the voters - even if this is only a second-best sort of support. Situations of candidates representing a constituency with less than a third of the votes could not happen. In areas of Britain with strong regional parties, notably Scotland and Wales, such situations are quite common. In London, the MPs from Hampstead was elected with 32.8% of the votes - so two third of voters were against their representative...


What are the consequences of the AV system? I believe the main changes are in the dynamics on the local level.

  • As candidates in most constituencies need at least some 'second preference' votes, they need to be careful not to alienate supporters of other candidates. In the simple majority system in place now, it is OK if half of the voters hate you as long as you have a strong group of core supporters and the others don't all vote for the same other person. Under AV, a polarizing candidates is likely to get few second preferences. Consequently, parties are less likely to put forward candidates with radical views supported by their core supporters but few others.

  • Incumbent MPs always have an advantage because they are already known to voters, while challengers typically have yet to build their reputation. When an incumbent looses support, under the simple majority system there are two scenarios.  Either multiple challengers end up competing with each other, making it easy for the incumbent to be re-elected. Or, the locally largest party puts forward a candidate, who then received votes 'against the incumbent' rather than because voters consider him/her as the best candidate. Under AV, voters are not limited by the decision of the locally-largest party as to who shall be the challenger. They can rank multiple challengers on top. In consequence, it will be easier to vote an incumbent out of office! And that's probably why so many sitting MPs are opposed to AV.

  • Under simple majority, it suffices if the vote for others is divided, or opponent voters don't show up at the election. Under AV, having two equally strong candidates from the centre left does not help the right wing candidate, nor do two equally strong centre right candidates de fact help the left wing candidate. Hence, there will be more competition as to who will represent the 'centre left' or 'centre right' sort of position - and voters have more choice.  

  • In the so-called safe constituencies, where the winning candidate won last time with more than 50% of votes, nothing much will change (there are surprisingly many of those, including 32 of 73 constituencies in London). As before, hardly any serious campaigning will take place and voters will be taken for granted. However, seats may marginally get 'less safe', which is good for voters in the sense that they receive more attention from Westminster.

  • Under simple majority, many voters vote tactically not for the candidate who they like most, but vote for the candidate who is the 'least bad option' of those two (rarely three) who has a realistic chance given results at the last election. Under AV, they can record their true preference with their first preference, and still ensure that their 'least-bad-option' gets ahead of the candidate they really don't like. This means voters can communicate a much more differentiated opinion to their politicians that under the simplistic current system.    

In conclusion, I do not expect AV to change the majorities in parliament. Yet, it will change what sort of individuals will be representing these parties. And, it will make it easier to throw out sitting MPs. These dynamics of course threaten the interests of some of those currently in power. As with any proposed form of electoral rules, those who benefited from the old system are opposed to it. The question is whether the British people want the preserve those power structures, or give voters from options to trigger change.



Alternative Vote System (2): Qui Bono?

April 4, 2011


In the run-up to the referendum, there has been quite a lot of speculation as to which party would gain. In particular, the Conservatives seem to be running scared that any system other than the current one would undermine their ability to run the country. Well, most of what is being said in the media on this topic is, in my humble opinion, nonsense. 


The essence is that candidates that appeal to more than their core supporters have a chance of overtaking candidates on the basis of second preferences. While this may impact on the kinds of candidates that the parties put forward, I believe this will only have a small impact on the distribution of seats in parliament.

  • While the media seem to expect the LibDems to gain about 20 seats, my own simulations do not support this view. I simulated an AV system for all London constituencies (see May 11, 2010), and found the LibDems not getting close to gaining any seats in London, while the Conservatives had a net gain from Labour of 2 seats.

  • In principle, the second preference votes are likely to help candidates who take a centrist position. In the British context, this might help independent candidates representing local interests and a distaste for 'Westminster politics' in general (a common sentiment). Results from Australia, where AV has been used for a long time, suggest such a possibility: there 4 of 150 MPs were independents (plus 1 Green who counts as sort of independent) (see August 22, 2010).

  • If voters see LibDems as being "between" Labour and Conservatives, they might be able to pick up a large share of second preferences, and hence seats. However, during the Blair years, the LibDems actually moved to the left of 'New Labour' on some issues, while now in government they support the Conservatives. So it is not clear how popular they will be as second preference. I would rather put it in a different way: under an AV system, the LibDems have strong incentives to position themselves as a party of the political centre

  • Will the AV system help smaller parties? Small parties that have radical views supported by a hard core of supporters but hated by most others - say Socialist, Loony or BNP - are going to find it even more difficult to get any seats (which would be a good argument for extending AV to local elections).

  • Small parties that offer positions of broad appeal, i.e. in the political centre, may benefit from second preference votes in specific constituencies where the candidates by the big parities (whoever is big in the particular constituency) are highly unpopular. They would then play a role similar to independents and tap into the 'anti-Westminster' mood. Thus, conceivably, UKIP or the Greens may get a seat or two.

Based on this analysis, I suggest that the shift to AV is really about local dynamics, not about majorities in parliament. So, it hard to see why the Conservative party is so opposed to giving voters more power. In Scotland and Wales they should actually be able to pick up a few seats. Perhaps they really think that the "everyone-but-Conservatives" vote is very powerful.




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