I Just Don’t Get Proportional Representation

As we’re potentially heading for a hung parliament or a very closely matched parliament, I wanted in my mind to consider the idea of proportional representation as it is something that’s going to be on the table in any post-election discussions that involve the Liberal Democrats.  As I see it, the Liberal Democrats want proportional representation as they perceive it to be a fairer way to allocate power based on the proportions of votes received by each party, while the Conservatives are against it and want to stay with the first-past-the-post system as (arguably) they do better under that voting method; the Labour Party seems to be fudging their position as they are currently pro first-past-the-post but have been against it in the past.  This suggests that Labour would deal on it, so the possibility of a referendum or legislation on voting reform must rank very high.

Now in my mind, I see that first-past-the-post is a simple and logical concept.  You divide the country up into small parcels then get each parcel to vote for who they want to represent their interests politically; the smaller the constituency or parcel gets the more representative the elected person is of the wishes of the constituency until you get down to a constituency of 1 person who represents themselves.  What’s good about this system is that the constituents get who they vote for and in return the MP must look after the interests of the constituents firstly to ensure re-election and secondly as in the UK you vote for MPs and not for governments or prime ministers.  I know that most people believe that we vote for political parties and prime ministers but that’s actually not really the case as we’re electing our representative, i.e. MP, in the national parliament.

However, the third party (i.e. Liberal Democrats) argue that this is unfair as the number of MPs does not correlate back to the percentage shares of the vote.  This is because the Liberal Democrats tend to come second everywhere and so get a relatively high overall vote but don’t win comparatively many constituencies.  My quick analysis of the 2005 election is in the table below:

  First past post Seats Overall votes
Labour 55.1% 356 35.3%
Conservative 30.7% 198 32.3%
Liberal Democrats 9.6% 62 22.1%
Others 4.6% 30 10.3%
Total 100.0% 646 100.0%

So by going for an extreme version of proportional representation as you get in Israel, where there is one constituency for the whole country and then the vote is apportioned by share of total vote, the Liberal Democrats and the other parties would double their MPs within the Houses of Parliament.  The downside of this approach is that you allow the extreme parties to have positions in the corridors of power, as well as the more hippy parties like the Greens, so you get the big parties and the rough, smooth and cuddly of the smaller parties.  Also, you completely lose any linkage between voters and their representatives with your local MP being chosen from a central list – in my mind, this would be like having someone from Cardiff representing Harrogate or in an imaginary European Election having a Greek MEP looking after the Yorkshire and Humber Region.

As a consequence, parliamentarians have invented more complex versions of proportional representation that involves the idea of first preference votes where after voting for your initial number one choice the prospective candidate with the lowest score is eliminated and his/her votes reallocated to the next choice candidate on those ballot papers and so on until one candidate gets 50%.  This just seems to me to be a case of people being too clever for their own good in trying to slice and dice the voting system to get an answer that they want, rather than really meeting the needs of the people – a triumph of bureaucrats and the political class over normal people, the hoi polloi.

Then there’s the maths.  We all have been explained the iniquity of first-past-the-post versus proportional systems as in the table above.  However, there are mathematical issues with all proportional voting systems – if you read this week’s New Scientist, there is a good mathematical analysis of the voting system at http://www.newscientist.com/article/mg20627581.400-electoral-dysfunction-why-democracy-is-always-unfair.html.    The key conundrum is that it is impossible to allocate a whole number of seats in exact proportion to a larger population, and so it is possible that, as you increase the total number of seats available, it will actually reduce the relative representation of individual political parties even when the population is unchanged.  In the end, none of the maths of any of the systems actually stacks up completely, so it simply comes down to your personal judgement about each voting system rather than anything to do with fairness or maths, i.e. no voting system is actually completely fair or perfect for running a country and we as citizens just have to live with whatever are the results that each election throws up –

“So we are left to make the best of a bad job. Some less fair systems produce governments with enough power to actually do things, though most voters may disapprove; some fairer systems spread power so thinly that any attempt at government descends into partisan infighting. Crunching the numbers can help, but deciding which is the lesser of the two evils is ultimately a matter not for mathematics, but for human judgement. (Source: New Scientist with above Internet reference)”

The way I have come up with to characterise the question is via a football team.  Imagine that you are to select a regional team to represent where you live, so I am looking for a team to represent the North East and I can pick people from Newcastle United (obviously the best, but I’m not biased), Sunderland and Middlesborough.  Now for simplicity’s sake, we have 1 player from each team for each position and there are 100 people who will decide on the team we pick to represent the North East versus a team from London, picked from Arsenal, Chelsea and Spurs.  Each voter has to rank secretly each player as their first, second and third choice.  Now the way, they pick them is as follows:

Position First choice Second choice Third choice
1 Newcastle Middlesborough Sunderland
2 Newcastle Middlesborough Sunderland
3 Newcastle Middlesborough Sunderland
4 Newcastle Middlesborough Sunderland
5 Newcastle Middlesborough Sunderland
6 Newcastle Middlesborough Sunderland
7 Sunderland Middlesborough Newcastle
8 Sunderland Middlesborough Newcastle
9 Sunderland Middlesborough Newcastle
10 Sunderland Middlesborough Newcastle
11 Sunderland Middlesborough Newcastle
  Newcastle/1st Middlesborough/2nd Sunderland/3rd
Overall vote 45% 35% 20%

Under first-past-the-post, you pick the the team based on the First Choice, which is a mix of Newcastle and Sunderland with a Newcastle Captain.  Under first preference choice, you would pick a team of all Middlesborough players with a first preference vote of 55% (i.e. 2nd column vote + 3rd column vote), and under proportional representation you get 5 Newcastle players, 4 Middlesborough players and 2 Sunderland players. but note that you really are after them in order 4.95 : 3.85 : 2.2, but people and positions do not divide up into neat integers.  In fact, true proportional representation is weirder and you have to vote (in this case) for the team you want but without knowing the players, so in the end you just vote partially, i.e. I vote for Newcastle etc, and then the players are selected from a list that has the top Newcastle players, top Sunderland players and so on in order of preference, so you end up with a team of perhaps 7 forwards, 2 goalkeepers and 2 midfielders, which wouldn’t be much cop. 

Clearly you should go for a team of the best players and then really choose the best captain, so first-past-the-post is the right system while the other two are fraught with problems.  Not least of these issues is which players do you actually choose to represent you after you know that you need to squeeze them in to accomodate the voting quirks.

Now this issue of who represents the constituents is a big one for me.  There is nothing I hate more than to have a centrally chosen candidate foisted on me – I will always choose a local candidate over a centrally chosen candidate or will abstain from voting.  I want someone who knows and cares about the area, an ex-councillor is ideal; someone who will actually come back to the constituency and care about his/her constituents whatever the flavour of political party.  Our MP used to be Phil Willis of the Liberal Democrats and he was ideal – ex local teacher, ex councillor and then put up against Norman Lamont of the Conservatives, who lost resoundingly; under these so-called fairer voting systems Norman Lamont would have won. 

A proportional respresentation system will give you people you don’t know or want to represent you as your MP, plus you’ll never get rid of the leaders or inner cabals, because however the percentage votes are cast you will always get the senior party candidates being given their seats first and then the favoured central party people second, so it is the new blood and interesting non-standard candidates that will not be given seats.  In the end, the candidates will all be London groomed, party groomed and all the mavericks and free thinkers refused seats, so your politics will become greyer and unchanging except for an overhyped moving of the political deckchairs. 

What first-past-the-post gives you is candidates that need to look after their constituents and the chance for us – the electors – to kick them out (especially with changes expected to be put into place after the election) – every election giants are felled by their constituents and this election will see many political giants banished to the wilderness of the real world, or Europe, or the House of Lords.  Under proportional representation these political heavyweights cannot be easily removed, so you ossify a political oligarchy into place.  It is the crude cruelty of first-past-the-post that professional politicians hate as it creates a sort of lottery where the electors can punish sitting MPs and remove them, while political leaders like to be able to plan ahead and know that their key MPs are guaranteed to win, which is what true proportional representation does and so to a lesser extent does the first preference system.

Finally, while the politicians kid themselves that it is the political system that’s the issue, I think it’s the policies and the parties.  In the end, as a elector, I don’t like everything about every party, but rather bits and pieces of policies from each party.  So I like the Liberal Democrats over all, but believe in nuclear energy being important, I like a nuclear deterrent of some sort and hate proportional representation, while I am intrigued by the potential of genetically engineered crops; I like much of Labour’s policies but in the end I believe that an individual should be free and able to chose to keep most of what he/she earns to spend as they wish and then to pass on to future generations, with the individual and family coming way before the state; for the Conservatives, I like their starting point of individuals and families first then the state, but I hate their immigration policies as I come from a family that fled from Denmark from the invading Germans in the 1850s and I don’t know what this Big Society idea is really all about.  My ideal would be a patchwork party that doesn’t exist and I am not convinced that voting reform will create this fictional party, because my views on policies are not up for negotiation.

In the end, if it ain’t broke then don’t change it, so I think it’s best to leave the current system alone.  If the politicians do want to fiddle with our political system, then they must not just change the basic electoral system but they should look at the whole system of governance in the UK in its totality, so they must look at the House of Lords, the House of Commons, the Council Systems and the European Parliaments, including the Council of Ministers (all curently unelected), which of course they won’t do – will they?

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12 Responses to “I Just Don’t Get Proportional Representation”

  1. Bob Richard says:

    First-past-the-post *is* broke, perhaps more conspicuously in the U.K. than anywhere else, but broke everywhere it is still in use. You write, “A proportional representation system will give you people you don’t know or want …” Actually, the purpose of PR is to everyone (or as many voters as possible) a representative who agrees with them on the issues, and can therefore advocate for them effectively. What good does it do me if my representative is someone who lives next door to me but is going to vote for legislation I oppose and vote against legislation I support? It’s first-past-the-post that gives me “people I don’t want …”

  2. Wayne Smith says:

    There is much that is wrong with this analysis, but let’s concentrate on the main thing you don’t get, as illustrated by these comments:

    “You completely lose any linkage between voters and their representatives with your local MP being chosen from a central list.”

    “There is nothing I hate more than to have a centrally chosen candidate foisted on me.”

    “In fact, true proportional representation is weirder and you have to vote (in this case) for the team you want but without knowing the players.”

    “A proportional respresentation system will give you people you don’t know or want to represent you as your MP.”

    “In the end, the candidates will all be London groomed, party groomed and all the mavericks and free thinkers refused seats.”

    Perhaps the most common misunderstanding about proportional representation is the idea that first you vote for the party, and then the party chooses the candidates. In fact, in a proportional election, just as in any other type of election, first the parties put forward a slate of candidates, and then you decide how to vote, based on your judgment of the candidates put forward, as well as the party leader and manifesto.

    The entire point of proportional representation is to ensure that, as far as possible, everyone is represented by somebody they actually voted for, in contrast to the current system, where most of us are “represented” by people we voted against, and most MPs “represent” mostly people who voted against them, as well as a huge number of people who couldn’t be bothered to vote at all.

    As you have correctly noted, no voting system is perfectly fair. Nevertheless, some are vastly more fair than others.

  3. Axel says:

    This is my first look at PR as it has never actually been something of huge concern/interest to date, but I thought I better start looking into it, so I profess nothing more than that I have a right to start considering it.

    I would ask you to help me understand it then – is it correct, therefore, in Israel where there is one constituency only that you get a local MP to represent your local concerns or is it all done centrally? Also, what happens for each constitency under a proportional system, are there places where you must put in an MP against the local voters’ wishes to accomodate the national relative sizes for each party? Under the first preference system I get that linkage works, but not under PR which is your point.

    Finally, while the first-past-the-post system has it big failings, I have a much bigger personal constitutional issue with the structure of government, i.e that the House of Lords is not really elected, nor does the House of Lords have genuine power to change the legislation proposed by the Government, plus I do not like how the Government and a small. central cabal within the ruling party based around Number 10 generally controls the country and the House of Commons is often pretty ineffectual body of scrutiny rather than genuinely holding the leading party to account. For me, it would be better starting point to strengthen the House of Lords and make it fully elected via proportional representation and have it as an Upper House that can hold the Commons to account.

    The present system usually gives the winning party almost complete control over legislation in the country – an elected oligarchy – except perhaps today when it looks like the result will be undecisive.

  4. Axel says:

    I think every system gives some people representatives that they don’t want and I am not advocating any system over another, simply trying to work through in my mind (for the first time I have to admit) what PR actually really means and first preference entails. For me, I think that my biggest problem with the whole political system relates to your point “a representative who agrees with them on the issues, and can therefore advocate for them effectively” and while I like Liberal Democrats as a base of political ideas, ie freedom and fairness, they have specific policies that I don’t like, eg on nuclear power. Therefore, I am trying to rationalise in my head how you get round the issue that I would really like a pachwork MP to represent me who has pieces of policies from each party stitched together – I suspect the only way around that is to become involved in local politics and try and get my views across within a political environment rather than putting words into a blog that has no power over legislation.

    Going back to the voting system, Kenneth Arrow (an American economist) set out what he felt were the general attributes of an idealised fair voting system: (i) voters should be able to express a complete set of their preferences; (ii) no single voter should be allowed to dictate the outcome of the election; (iii) if every voter prefers one candidate to another, the final ranking should reflect that; and (iv) if a voter prefers one candidate to a second, introducing a third candidate should not reverse that preference. Overall I reckon that no system can meet all 4 requirements, so to quote Abraham Lincoln “You can please some of the people all of the time, you can please all of the people some of the time, but you can’t please all of the people all of the time”.

  5. Peter says:

    Take a look at the Australian PR system – or more technically, instant run-off.

    What we want to do is elect a representative who enjoys a mandate from a majority of electors. Under FPTP, this frequently does not happen – if A gets elected on 35% ofthe vote, they cannot truly claim a mandate as 65% of electors wanted someone else.

    So consider a French presidential election starting with, say, 5 candidates. If in any vote, a candidate achieves a majority, they are automatically elected. However, say in round 1, no candidate gets a majority; the lowest scorer is eliminated and the electorate is asked to then vote on the remainder. This is repeated until the vote is between only 2 candidates.

    In this way, a candidate will be returned, who has achieved a majority of votes; that is, s/he has been ‘preferred’ by a majority.

    The Australian system allows all this to take place on one day, rather than at a number of elections potentially over weeks. Rather than just ticking a box, a voter lists their ‘preferences’ on their ballot – eg. 5 candidates, you number them 1 to 5. If A gets a majority of ‘1’ votes, they are the winner. However if no-one gets a majority, then preferences are distributed; this means that a voter essentially get to say “I want A, but if they don’t get in, I’ll be happy with B”.

    If no majority is achieved on the first count, then in each round, the candidate with the lowest ‘1’ vote is eliminated and their votes are redistributed according to the second preferences as indicated by the voters on their ballots. This is repeated until a majority is achieved by a candidate.

    Yes it’s technical, but you don’t get a situation where a majority of voters actively do not want a candidate, but that candidate wins.

    I cannot understand why the Tories are so against PR. It’s served Australia well for well over 100 years, it’s not apparently inherently biased against any party (as FPTP seems to be against the Tories) and, because they have to indicate how their how-to-vote preferences will flow prior to the election, the smaller parties have to say what they will do – meaning that such post-event ‘horse-trading’ as we’re seeing now in the UK, is unnecessary. Under an Australian PR system, David Cameron would have been in Number 10 last Friday morning without having had to speak to Nick Clegg. PR would have delivered a result by now.

    In his speech of 26 May 2009, DC rejects proportional representation thus:

    “PR would actually move us in the opposite direction, which is why I’m so surprised it’s still on the wish-list of progressive reformers.

    Proportional representation takes power away from the man and woman in the street and hands it to the political elites.

    Instead of voters choosing their government on the basis of the manifestos and leadership put before them in an election campaign…

    …party managers would choose a government on the basis of secret backroom deals.”

    The speech also leans towards fixed terms.

    I am an Australian / UK dual national, with experience of both systems; I have voted Liberal (ie. Tory) in Australia and would’ve voted Tory on May 6 last had UK citizens living overseas not been disenfranchised.

    PR seems to work well in Australia:
    – it has not entrenched minority parties;
    – it has not prevented unpopular governments getting booted;
    – I feel personally empowered being able to list my preferences rather than rely on post-election deals (such as being hammered out now, presumably in a “back room”).

    So what is the problem? It works perfectly well at the national level in Australia and Canada and in every Australian state.

    However as for fixed terms, look at NSW…

  6. Axel says:

    Thanks for that Peter as I am now much clearer as to how it all works, or could work, and I have to say that it does seem to be better than the horsetrading that we are currently having, plus I think looking at recent election results the Tories would have done better than the results that they have been getting.

    I think the lack of clarity is in the wording as everyone here talks about proportional representation which is more like the Israeli system, whereas the Australian and Canadian system is a preferential voting mechanism.

    In Scotland, the system used for one-third of the seats seems closer to the traditional proportional representation where “the overall allocation of seats is proportional to the number of votes received” per http://www.aboutmyvote.co.uk/how_do_i_vote/voting_systems/scottish_parliamentary_electio.aspx and similarly for the European Elections proportional representation is used and not the preferential system that you are describing and “the overall allocation of seats is more proportional to the number of votes received. The first seat that a party wins goes to the first person on its list, the second seat to the second person, and so on, until the party has either not won any more seats or has run out of names on its list. An independent candidate is treated as though he or she were a party with only one name on its list.” I also am slightly concerned that this is determined by a list rather than you getting who you vote for. This comes from http://www.aboutmyvote.co.uk/how_do_i_vote/voting_systems/european_parliament_elections.aspx.

    I think that the system that you are suggesting seems to be a developing on first-past-the-post rather than necessarily being seen as a wholesale change, which seems to have been chosen in the other two cases in the UK.

    But I am still only just to grips with this all as I expect we will very shortly be looking at some programme of change in electoral system in the next 2 – 3 years.

  7. Winston says:

    I was hoping to cite your article as an argument against PR, but I find it so full of basic misconceptions that it’s difficult to know where to start. Similarly, I found Ian Stewart’s New Scientist article flawed (and, I suspect, disingenuous), but was unable to comment since I am not a “subscriber” (another case of flawed democracy?).

    All I can suggest is that you read the Electoral Society’s pamphlet called “PR Myths”. It might correct some of the misleading statements you made in this article…unless you’ve already made your mind up.

    I’ve been a programmer, interested in politics, for more than 30 years, and if there’s one thing I DO know about the business of political reform: it has +everything+ to do with maths – the only science that is likely to be able to give an objective viewpoint on the +fairness+ of any given voting system, with no baggage or tradition or past governments or vested interests to worry about.
    And, time and again, they point to PR; not because it’s simple, but because it’s +fair+.

    And who can say fairer (no pun intended) than that? The rest is up to politicians and us who vote them in.

  8. Axel says:

    I don’t state that I know very much about proportional representation but that I am trying to understand it, so I suppose I am looking for people with greater experience to guide me through. It’s important that the misconceptions are explained as it perhaps now the most important political question around, but if simple, unsophisticated voters do not understand it how can a referendum be just and fair as it will simply have been a vote on what hype seems best at the time. I will read the Electoral Society’s pamphlet on PR Myths and hopefully it will remove my “basic misconceptions”, but I remain none the clearer as to what they are as no-one will tell me except to state that “you are wrong”.

  9. Winston says:

    Someone wise once said: “To every complex human problem, there is a simple solution….and it’s almost invariably wrong.”
    If you want simple, stick with FPTP (first-past-the-post) because, God knows, it’s simple. What it +isn’t+ is fair.
    However, to answer your question, there are, as I understand it, and if you assume that you’re voting as a large group for “parties”, four basic forms of vote:

    FPTP (see above) – I assume you understand that.

    AV (Alternative vote) – Very similar to FPTP, except that voters are asked to +rank+ the candidates with a number. If no candidate gets 50% on the first count, the candidate with the fewest votes is eliminated, and his/her votes get allocated to the remaining ones according to their 2nd choice. This process continues until one candidate gets 50%. I should ad that this is NOT a PR system.

    MMR (Mixed Member Representation) – Used in Germany and lots of other European countries, and for the Scottish parliament (it’s called the “Additional member” system here). Basically, you have fewer constituencies (about 40% fewer in Scotland), but you are given two choices on the ballot: a candidate and a party. Constituencies are counted as a normal FPTP election, but the remaining seats are filled to make up the difference between the number of candidates returned from constituencies, and the number of seats the party +should have+ received based on the percentage of party votes cast. This IS a PR system.

    STV (Single Transferable Vote) – This is probably the one that gives you the maths headaches (and it IS difficult), but the idea is quite simple. The ballot is similar to an AV ballot (you have to rank the candidates); however, constituencies are much bigger, so you are usually voting for anywhere between 4 and 10 seats and therefore have a lot more candidates to choose from.
    If you have several seats (say 4), you can’t expect a candidate to get 50% of the vote. And if they do, what do you do with all those wasted votes, since they’re bound to be miles in front of the next 3 candidates?

    Answer: something called the “Droop Quota”
    In a multi-seat constituency, a candidate is only required to get
    v / (s + 1) votes, where v is the number of votes cast and s is the number of seats up for election. So, in a constituency that has 100 voters and returns 4 seats, the DQ is 100 / (4 + 1): ie, 20 votes.

    Other than that, the counting is rather like AV, except that +excess+ votes are counted first. So:
    1. First choice votes are counted. Anyone getting over the DQ is “elected”.
    2. The elected candidates’ +excess+ votes (ie, the ones that they didn’t need to get them past the DQ) are divvied up according to their 2nd (or remaining) choice. If, as a result of that, any other candidate gets elected, their votes are similarly divided and the check is done again.
    3. If there are still candidates to be elected, the one with the fewest votes is eliminated and, like in AV, their votes are divvied up according to the highest remaining choice.
    After that, Steps 2 and 3 get repeated until you have ‘s’ people elected.

    STV IS a PR system, and is generally considered the “fairest”, especially when each constituency has 5 or more seats (for why you’ll have to Google, because some of it involves pretty sophisticated maths). The problem is that candidate lists can get quite long, which makes the ballot look imposing.

  10. […] was roundly castigated for being a political ignoramus with my first look at electoral reform, which was probably sound.  However, far from being deterred, I still want to continue to try and […]

  11. […] my first foray into considering the election system during the General Election in May 2010, and having favoured the first-past-the-post system was roundly criticised for my lack of real thought, which was harsh but perhaps fair.  I followed […]

  12. politik says:


    I Just Don’t Get Proportional Representation | Axel and Sophie Steenbergs Blog: News, Views and Chat about Spices, Tea, Recipes and the Environment…

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