Proportional representation and Brown's opportunist ploy

What sort of electoral system should communists advocate? Moshé Machover - mathematician, lecturer in philosophy and leftwing activist - examines the alternatives to 'first past the post'

In what looked suspiciously like a deathbed conversion, Gordon Brown has pushed through the House of Commons a Constitutional and Governance Bill, one clause of which provides for a referendum on electoral reform, to be held within a year following the forthcoming general election. In the referendum, voters will be asked to decide whether the present plurality[1] procedure (popularly known as ‘first past the post’, or FPTP) for electing the House of Commons would be replaced by the alternative vote (AV) procedure.

AV is a special case, or an adaptation, of the single transferable vote (STV); but, whereas under full-fledged STV each constituency elects several MPs, under AV there is just one MP per constituency, as under the present FPTP.

AV, like STV, is a preferential system: instead of putting an ‘X’ against your preferred candidate, you rank the candidates in order of preference, marking them with ‘1’ for your favourite, ‘2’ for your second choice, and so on.

Under AV, a candidate who gets a majority of top-choice votes is elected outright. If no candidate gets more than half of the top-choice votes, the candidate who has the least number of these votes is eliminated; and if you voted for that candidate as your top choice, your vote will now go to your next choice. The process is repeated until one candidate gets a majority, and is thereby elected.

Clearly, this bill is an opportunistic ploy by Gordon Brown. A Tory government will certainly not hold the proposed referendum. If the forthcoming election gives New Labour a majority of seats, then electoral reform will probably be kicked into the long grass. However, in case of a hung parliament, the referendum may help to cement a deal whereby the Liberal Democrats would join a coalition with New Labour or, more likely, support a minority New Labour government.

The Lib Dems have long called for STV, but they will gladly support AV as a ‘step in the right direction’, because it would work to their advantage. Most voters for the larger two parties are likely to put the Lib Dems as their second choice under AV. This may help the Lib Dems win in constituencies where they are now in second place and which under the present FPTP would be won by one of the larger parties with a plurality but not a majority of the votes.

New Labour also stands to gain - or at least not lose too much - from AV. Although Nick Clegg claims that the Lib Dems are equidistant from the Tories and New Labour, it is a fair guess that most Liberal supporters would rank a New Labour candidate higher than a Tory. This may help New Labour win in constituencies where it is now in second place and which under the present FPTP would be won by a Tory with a plurality but not a majority of the votes.

So the Lib Dems are likely to gain seats at the expense of both New Labour and the Tories, while New Labour is likely to lose a few seats to the Lib Dems, but gain some at the expense of the Tories.

The Tories are almost certain to lose from AV. No wonder they are dead against it.

Quirks of AV

Brown’s proposed reform would not be a great improvement: while FPTP is just about the worst and most undemocratic electoral system, AV is not a great deal better. Under FPTP it has happened several times that a party won a majority of the seats while not getting a nationwide plurality - let alone a majority - of the votes. The same can happen under AV.

One of the worst features of FPTP is that a candidate who is the most detested by a majority of a constituency’s voters can still win the seat. Here is a toy example illustrating this pathology. Suppose there are seven voters who must elect one out of three candidates - A, B and C - and whose preference orderings among these candidates are as follows:[2]

3: A B C
2: B C A
2: C B A

(In the present example, the first row means that three of the seven voters prefer A to B and B to C; the other rows should be read similarly.) Here four out of the seven voters - a majority - regard A as the least desirable candidate; but under FPTP, assuming that people vote for their most preferred candidate, A has a plurality of the votes and is elected.

Under AV this perverse phenomenon cannot occur. However, AV can result in rather bizarre outcomes that infringe the principle of majority rule. In the next example there are three candidates and 17 voters, whose preferences are as follows:

3: A B C
2: A C B
4: B A C
2: B C A
4: C A B
2: C B A

Here A is preferred by a majority of the voters to each of the other two candidates: nine voters prefer A to B, and nine also prefer A to C (by the way, B is preferred to C also by nine voters).[3] However, under AV - since none of the candidates has a majority of the top-preference votes - A, who has the least number of these, will be eliminated, and the votes of A’s supporters will be transferred: three to B and two to C. So B will now have a majority and be elected - although, as we have just seen, a majority of the voters (nine out of 17) actually prefer A to B.

This 17-voter example can also be used to illustrate another quirk of AV: an increase in support for a candidate can be counterproductive. Suppose the last two voters, those in the sixth row, were to change their minds, and switch their preference order from (C B A) to (B C A). In that case, C would have the fewest top-preference votes, and be eliminated. The four votes of C’s supporters would go to A, who would have a majority, and be elected. So, purely as a result of getting two additional first-preference votes (at C’s expense), B fails to win, and instead loses to A.

In technical jargon, this kind of phenomenon is called non-monotonicity. One of the few good things that can be said about FPTP is that it does not suffer from this perversity: a candidate cannot be harmed by increased support. So in this particular respect AV is worse than FPTP.

A non-monotone electoral procedure cannot possibly be truly proportional. In practice, AV is not likely to produce greater proportionality than FPTP - possibly quite the reverse. It may favour the Lib Dems compared to FPTP, but like the latter it is specifically designed to exclude smaller parties, unless they are concentrated in a few constituencies (as are the SNP and Plaid Cymru), or are in the ‘moderate’ centre.

These are just a few of the quirks of AV. So the proposed reform would replace a very bad undemocratic system by one that is almost as bad. Whether radical socialists should vote for this reform in the referendum (assuming that one will be held …) is in my opinion a tactical question, on which I would not like to pronounce here.

Opportunity for public discussion

However, the fact that the idea of electoral reform has been put on the public agenda creates a welcome opportunity for the radical left to intervene in the debate and mount a general critique of the limitations of bourgeois (so-called) democracy in general, and of the way it is practised in the UK. It is also a good opportunity for raising the question as to the kind of electoral reform we ought to support.

Let me make it clear that in this article I am not going to discuss the kind of electoral system that would be suitable for decision-making in a communist commonwealth. I have addressed this issue in a recent essay, Collective decision-making and supervision in a communist society.[4] Here I will confine myself to the question as to the kind of electoral reform that radical socialists may advocate and support in a capitalist country, and specifically in the UK. These are clearly rather different questions. A communist society will make possible and require novel structures and procedures for making social decisions, which are not applicable under present conditions. On the other hand, faced with the inherently restricted and largely illusory nature of bourgeois democracy, we should advocate the most far-reaching reforms possible here and now. (This does not make us reformists: reformism is the illusion that capitalism can be gradually reformed away, without a revolutionary break.)

In evaluating various possible electoral procedures, it is necessary, but not sufficient, to apply general criteria as to which system is more democratic in some rather abstract sense, as is done in the academic social-choice literature. Of course, this is important. But we must also bear in mind which system would be favourable to the radical left, particularly in conditions where it is numerically and organisationally weak and struggling to make its voice heard. These two kinds of consideration are certainly not incompatible; but the radical left perspective leads us to dismiss some criteria and assign greater weight to others.

For example, in a non-revolutionary situation, the radical left must not aim at, or let itself be lured into, participation in government; to be truly radical, it must be in opposition. Parliamentary politics is to be used not for taking part in running the state, but as a forum for projecting a socialist message from the hustings and from the floor of an elected assembly. Now, some voting procedures are criticised in the academic literature - and in a vulgarised form in the bourgeois media - for tending to lead to ‘unstable’ or ‘weak’ government. In fact, these arguments are largely spurious; but even supposing they are not, why should we care? Seeking stable, strong government betrays a hankering after a strong state - not a particularly democratic sentiment. Surely, we are interested in promoting a strong left opposition, not a strong government.

Also, in the present situation in the UK, in which the radical left is still small and electorally marginal, it is in our particular interest to advocate voting systems that are fair to small, radical  (‘extremist’) parties. Such systems are not only more democratic in an abstract sense, but would remove much of the temptation that, under the present FPTP system, attracts sections of the would-be radical left to forming unprincipled alliances with reformists and alien class forces.

Two concepts of representation

A great many procedures have been used for electing parliaments and similar decision-making representative assemblies, and many more have been proposed but never used. Before advocating any particular procedure, let me first address the issue of representation in a rather abstract, idealised, theoretical manner.

In what sense is an elected assembly supposed to ‘represent’ the electorate? There are in fact two quite different theoretical answers to this question, each of which is embodied in a distinct mode of representation and a corresponding type of election procedure.

The first mode may be called district representation (DR): every member of the assembly is personally elected to represent a particular constituency, which is defined geographically. Accordingly, there are a large number of constituencies, each of which elects a single representative or a small number - at most a handful - of representatives. Naturally, such a constituency may be, and normally is in fact, quite heterogeneous: its voters may differ considerably from one another in their interests, preferences, tastes and opinions.

The second mode is proportional representation (PR): the assembly is supposed to be a microcosm of the society at large, like a statistical sample, reflecting in true proportion (or as near to it as possible) the various shades of opinion that exist in the society as a whole. Thus it can stand as proxy for a market-place meeting of the entire citizenry; and a vote taken in the assembly may be regarded as a close approximation to a referendum. Here a member of the assembly represents not a geographically defined constituency (which may well be very heterogeneous in the above sense), but a like-minded section of the electorate at large, which may well be geographically dispersed.

The fundamental theoretical defect of DR is that on close analysis the concept itself turns out to be deeply problematic. The question that a DR election procedure needs to resolve is which of several candidates ‘best’ represents a constituency, in the sense of providing the ‘best’ reflection of the preferences of its voters. If there are just two candidates, A and B, the answer seems fairly straightforward: clearly, if the number of voters who prefer A to B is greater than that preferring B to A, then A is the better representative and ought to be elected.[5]

But, when there are more than two candidates, things become much less clear-cut. Suppose there are three candidates, A, B and C. As we saw in the second example above, the electorate can be divided into six distinct camps according to their preference among the three candidates.[6] A profile of the electorate is a list of six numbers, giving the numerical size of each of the camps. If a single candidate is to be elected, then we need a procedure that selects, for each possible profile, the ‘best’ candidate. It turns out that any such procedure must produce in some cases a result that is in some sense unreasonable or unsatisfactory. The same applies a fortiori when there are more than three candidates, one or several of whom are to be elected.[7]

Leaving aside such abstract, idealised considerations, there is a concrete, but general argument against DR voting systems. All those that have been seriously proposed by social-choice theorists, and certainly all those that are in actual use for electing parliaments, are biased against small, radical  parties. They privilege large or middle-of-the-road parties (or both), and are often designed for this very purpose.

For this reason it seems to me that the radical left - particularly in the UK, given the present state of the left - ought to advocate PR.


The single transferable vote (STV) system is an intricate preferential voting procedure. Each constituency elects a small number of representatives - typically from three to six - rather than a single one. To be elected (ie, win a seat), a candidate needs to get a certain quota of votes. (This quota is the least number of votes such that no more than the required number of winners can achieve it. For example, in a three-seat constituency, the quota will be just over 25% of the valid votes.) Votes are then deducted from candidates who get too many first-preference votes (more than the quota) or, in some cases, too few; these votes are transferred to other candidates: namely to those who are the next preference of the voters in question.[8]

STV, which is zealously advocated by the British Electoral Reform Society and is used for electing the Dáil Éireann (lower house of the Irish parliament), is often described as a PR system. This is not strictly true; as I showed in a letter published in this paper,[9] STV, just like AV, is not monotone. Thus, an increase in support for a party’s candidate can lead to the party winning fewer seats. Such a system cannot possibly be truly proportional.

Rather, STV is a DR system that is ingeniously designed to produce less disproportionate outcomes than the extremely undemocratic FPTP; and the approximate degree of proportionality it produces is quite erratic. Also, like other DR systems, STV is biased against small and radical parties.

In the last elections to the Dáil, held in May 2007, Fianna Fáil got 41.56% of the top-preference votes. Under strict proportionality, this would entitle it to 69 seats (give or take one seat, due to rounding) in the 166-seat assembly. But in fact it won 77 seats. Similarly, Fine Gael, with 27.32% of the votes, won 51 seats instead of some 45 to which it would have been entitled under PR. And Labour, with 10.13% of the votes, won 20 seats instead of 17.

On the other hand, the Greens and Sinn Féin got fewer seats than they would deserve under PR: the Greens were cheated of two seats, and Sinn Féin of at least seven. Moreover, although Sinn Féin got considerably more top-preference votes than the Greens (6.94% and 4.69%, respectively) the former won fewer seats than the latter (four and six, respectively).[10] So much for proportionality!

It would be naively optimistic to expect that STV, were it to be used for elections to the House of Commons, would treat a radical socialist party more favourably or fairly than it treats Sinn Féin in Ireland.

Nevertheless, STV would be a massive improvement on the present FPTP, and in my opinion socialists should regard it as acceptable.

Genuine PR

The most consistent PR procedure is the party-list system used in many countries for parliamentary elections and in most EU countries for elections to the Euro parliament. The country is divided into a small number of large constituencies. (In some small countries, such as the Netherlands and Israel, the whole country is a single constituency.) In each constituency a party can present a list of candidates, and a voter casts a vote for one of these lists. The assembly seats are allocated to each party in proportion to the number of votes cast for it.[11] In the ‘closed list’ variant of the list system, the seats are allocated to a party’s candidates in the order in which they appear on its list. In the ‘open list’ variant, voters may indicate preference for a particular candidate in the list of their choice, and seats are allocated accordingly.

The arguments often voiced against this consistent PR system are for the most part specious, if not outright reactionary, and are of no interest to us here. For example, it allegedly tends to produce unstable or weak government (not necessarily true, but if it were, so what?); it is said to encourage the existence of small parties (true, but no reason for complaint if you do not expect to be in a large party soon).

However, the party-list system does have one obvious fault: a representative can only be elected through a party. This tends to give undue power to party leaderships and bureaucracies. However, the weight of this argument is not as great as it may seem. For one thing, under existing DR systems party leaderships and bureaucracies also have, in reality, a major influence on selecting candidates. (In the UK, few maverick candidates are allowed to stand for major parties in safe or promising constituencies.)

Also, the power of a party’s leadership to fix the list of candidates can be overcome to a great extent by using the open-list variant and, more importantly, by holding a primary election within the party (possibly including close supporters) for choosing its candidates. A party with a robust inner democracy has little to fear from such a system.

Weekly Worker readers will not expect me to have many good things to say about Israel. But here is a rare, perhaps unique, exception: Israel has just about the most democratic electoral system possible in a bourgeois state: a consistent form of proportional representation. Under this system, even in the paranoid period of 1950s McCarthyism, the Israeli Communist Party - Stalinist, but nevertheless the most radical leftwing political party at the time - was able to win five to six mandates in the 120-seat Knesset. Minority voices, including that of the Arab national minority, have regularly been heard on the floor of that house.

To prevent misunderstanding I hasten to add: I am not saying that Israel is a highly democratic country. The foregoing remark refers to one narrow aspect, the electoral system. Israel ‘compensates’ for its democratic electoral system by having a racist citizenship law, which discriminates against non-Jews and denies the vote to many non-Jewish residents. The state has occasionally used administrative and judicial devices in order to prevent certain parties - mainly Arab nationalist ones - from participating in the elections. However, the electoral system as such cannot be used for disenfranchising or silencing minorities.

A hybrid system: AM

There are some hybrid election procedures that combine DR with PR, aiming to obtain the advantages and mitigate the faults of both modes. Such is the mixed or additional member (AM) procedure, variants of which are used for electing the German Bundestag (federal lower house), New Zealand’s House of Representatives, the Scottish parliament and the London assembly (elected council of Greater London). Under this procedure, each voter has two votes: one for a representative under a DR system (usually FPTP, but in principle any other DR system would do), and one for a party list. The assembly thus consists of two kinds of member, elected by DR and PR systems respectively; and the number of the latter can be adjusted so as to achieve - or at least approach - overall proportionality.

This system has a number of faults, mainly inherited from its DR component; but none of these are of major importance in my opinion. Its main virtue is that it can produce a proportional outcome.

However, in practice bourgeois states using AM have introduced artificial provisos designed to deny representation to small parties. Thus in New Zealand, in order for a party to get any seat, it must win at least 5% of the party votes or win at least one seat in a DR constituency. The German electoral law is even less democratic: here a party must win 5% of the party votes or three DR seats.

In conclusion: if I were to choose between electoral systems for the House of Commons that are feasible here and now, this side of a socialist revolution, I would opt for the pure party-list system (open version) as my top choice, with the AM system (without any threshold provisos, or very low ones) a close second, and STV third.

Acknowledgment: I am grateful to my scientific collaborator, Dan Felsenthal, for some factual-technical help in writing this article. He bears no responsibility whatsoever for the opinions expressed here.


  1. In the strict terminology I use here, plurality means the greatest number of votes; whereas majority means more than half of the total.
  2. Here and in subsequent illustrative toy examples, I have used small numbers purely for convenience. In each case the same phenomenon can be illustrated with larger, more realistic numbers.
  3. Such a candidate, who is preferred to any other candidate by a majority of the voters, is known as a Condorcet winner, after Nicolas de Condorcet, the revolutionary French philosopher, mathematician and political scientist, who in an essay published in 1785 proposed that such a candidate ought to be elected. A Condorcet winner may not exist, in which case the question as to who ought to be elected is very thorny.
  4. www.zcommunications.org/collective-decision-making-and-supervision-in-a-communist-society-by-moshe-machover
  5. Even this seemingly obvious rule, which implicitly assumes strict majoritarianism, is not entirely uncontroversial: there are apparently reasonable voting systems that violate it. One such system, used to choose the winner in some sporting and artistic competitions, asks each voter to assign a mark, say from 0 to 10, to each candidate; the winner is the candidate getting the highest average mark. A variant of this system uses the median mark (see en.wikipedia.org/wiki/Median) instead of the average. Under both versions it may happen that B wins although a majority of the voters prefer, and award a higher mark to, A. For a simple example, see DS Felsenthal, M Machover, ‘The majority judgement voting procedure: a critical evaluation’ Homo Oeconomicus 25 (3/4), 2008, pp319-34: downloadable from eprints.lse.ac.uk/24213
  6. For the sake of simplicity I have excluded orders of preference that are indifferent between two or all three of the candidates. If indifferences are admitted, there are not six, but 13 possible camps!
  7. For details see, for example, SJ Brams Paradoxes in politics: an introduction to the non-obvious in political science New York 1976; M Dummett Principles of electoral reform Oxford 1997; H Nurmi Voting paradoxes and how to deal with them Berlin 1999.
  8. For details see en.wikipedia.org/wiki/Single_Transferable_Vote#Voting
  9. Weekly Worker November 12 2009.
  10. For all these data, see en.wikipedia.org/wiki/Dáil_Éireann
  11. In practice, a deviation from strict proportionality is introduced by the rounding error in calculating the number of seats, which must, of course, be a whole number. Also, in most places a list obtaining less than a certain threshold - typically set at between 2% and 5% of the total vote  is not allocated any seats, and the votes cast for it are disregarded.