The UK electoral system is 47% efficient.

The Centre for Thinking Futures (CTF) announces its report on the UK electoral system.


In the closing weeks of the 2017 UK general election, the Centre for Thinking Futures at Thinking.Institute has analysed the efficiency of the UK electoral system.  Answer: it is very inefficient,  so undemocratic.


Much has been made by such as the Electoral Reform Society of how unequal (unfair) the current UK electoral system is to parties.  This Thinking.Institute analysis shows imparity for the individual voter.



Efficiency is defined as the extent to which voters’ choice is evenly counted in the allocation of seats.  In a 100% efficient electoral system, every vote would count equally towards the final seats allocated to parties.  While this is an ideal, it is (probably) impossible to achieve in practice.   But, the UK electoral system does not come close. Voters are not getting even treatment. With a CTF Efficiency Index of only 47%, over half the votes are not taken into account. Moreover, the CTF Power Index shows that different seats are grossly unequal for voters. Is that fit for purpose? If the standards of Unfair Trading Act were applied, the system would be in the dock.


Changing this system requires the majority parties to agree to do so. But why would favoured incumbents vote to reduce their gross advantage? Perhaps because they believe in democracy?


For a full list of efficiency calculations visit this page.


Key facts

  1. Over 50% of electoral votes make no difference to voter representation.  They do not improve legitimacy at a seat level and do not translate into MP representation. Our intra-constituency index shows a mean efficiency of only 47%.
  2. The CTF Efficiency Index measures how well voter choice is translated into representation within the seat.   A low efficiency means a relatively large number of votes count for nothing.  The CTF UK Efficiency is the average of all 650 seats, weighted according to the size of the turnout.
  3. To compute the seat, or constituency, Efficiency, all the votes of the winning MP are counted up to 50% of the votes cast.  If the winner gained 50% of the vote the efficiency would be 50% since none of these votes would contribute to direct representation in Parliament. For margins above or below 50%, an adjustment is progressively made.  The reasons and method for this are outlined in the report. In brief: In the case of minority winners (where the winner gets less than 50% of the votes cast), the argument is that the smaller the percentage gained by the winning candidate the less legitimacy and therefore efficiency.  In the case of majority winners (where the winner gets more than 50% of the votes cast), a good winning margin contributes to legitimacy,  but the votes make no difference to the results at a practical level.  A party that wins in one constituency by 20,000 votes and loses in 10 seats by 2000 votes each might prefer to see its votes better distributed.  And the electorate might prefer to see their votes making a difference. Since this is a real factor in the electoral results, it should not be skated over.
  4.  The CTF Power Index measures the relative Power of votes in constituencies of different sizes.  The very largest constituencies are more than twice the size of the smallest and yet each returns one member of Parliament.
  5.  Together these factors mean that where you live makes a difference to your representation. That is undemocratic.
  6.  6. 42 constituencies have an Efficiency Index of 33% or less.  Two thirds of the vote is essentially thrown away.  153 have an efficiency of less than 40%.  More than half of the vote counts for nothing in more than half of the constituencies (328).
  7.  Constituencies vary in size. The Power Index (the relative power of votes in different constituencies of different sizes) shows that the 15 largest constituencies are on average almost twice the size of the 15 smallest (Power Index Equals 1.93).
  8.  In a constituency like Ynys Mon, an MP can be elected with only 10,781 votes.  It is the ninth smallest electorate and has an Efficiency of only 22%.  78% of the votes did not count.
  9.  By contrast, in West Ham, the winning MP gained 36,132 votes.  West Ham is one of the 15 largest constituencies, so, despite having a relatively high efficiency (59%), West Ham voters had less bang for their vote.
  10. The case for the current system argues that MPs represent all of their constituents and not just those who vote for them.  But in fact the party political system means that they tend to vote with their parties.  However much MPs may represent all constituents on minor local matters, on the big issues, they  routinely stand with the party.


Almost a quarter of the votes were given to parties other than the established three: Conservative, Labour and Liberal Democrat.  If we add the SNP, as the leading Scottish party, to the list of established parties, then just over 20% of voters produced less than 4% of the seats.


The results below show just how unequal votes can be for parties (although this was not our focus):






 Liberal Democrats






% votes










% seats




















It is obvious that on a simple reading that the allocation of seats in the current system is not proportional to the national interest.  This means that Parliament does not represent the country as a whole but rather a series of skewed local situations.  The method used to decide who gets to Parliament exacerbates this.  The winning candidate at one extreme received 24.5% of the constituency vote.  At the other extreme it was 81%.  9,560 voters produced the same result as 31,222.   More than half of the seats (333) returned a candidate who got less than 50% of the vote.  If this truly reflects the wishes of the people and leads to a government more capable of reflecting the needs of the whole country, then such considerations would outweigh a simple mathematical analysis.  But it seems reasonable to conclude from recent events and the analysis of the that many people do not feel that the government that as elected nor the actions of those governments in the past have met the needs of the people, as a whole, as opposed to selected minorities.


The stance and approach the Centre took

The report is neutral with respect to the parties:  it is clear that both UKIP and the Green party do very poorly ( UKIP came second in 120 seats, yet got only 0.2% of the seats, 1 MP). The Electoral Reform Society have a telling graph, which shows the votes per MP of the parties. UKIP needed almost 4 million.  The Green Party over a million, LibDem over 300,000, while Conservatives needed only 34,243. Supporters of minority parties might reasonably believe that their votes are of less worth.


This analysis is ambivalent on the position of nonvoters,  who constitute a third of the electorate.  On one view, they should be ignored as they absent themselves from the process.  But if they regard the process as unrewarding – either because their candidate will obviously win or will obviously lose – then it is the system itself that leads to their absence and should be recognised as an increased inefficiency. The analysis is therefore the minimum level of dysfunction.


In order to produce this result, it was necessary to develop a formula for calculating efficiency and apply it to the actual data provided by the government.  This formula is based on facts and reasonable  analysis of when votes actually make a difference and when they do not.  They do not make a difference when they are (considerably) more than are needed for the candidate to win, or when they are given to a candidate who loses.  They do make a difference up to the point where a candidate wins and potentially when the candidate wins by a “decent margin”, specifically by getting at least 50% of the votes. Details of the formula (algorithm) are given below.


It is argued that this analysis reflects the level of satisfaction or dissatisfaction that a voter could reasonably feel about how much their vote actually counts. Voting is not the same as shopping.  But in the world of shopping – and business generally – analysts and managers have long had to consider the question of whether a customer gets value for money.  Does a UK elector get value for his or her vote?  If business applied the same kinds of conditions as the electoral system does, customers would soon be dissatisfied.


Changing this system requires the majority parties to agree to do so. But why would favoured incumbents vote to reduce their gross advantage? Perhaps because they believe in democracy?


The UK system is inefficient. Better systems are possible.

In order to have an efficiency of close to 100%, in which every voter is satisfied that their vote counts (equally) towards the allocation of the seat, it is necessary to have proportional representation.  It is also necessary for all of the votes in the whole country to be counted together (as in a referendum) and then divided out proportionately among the seats available.  In the present UK system with 650 seats, that would mean that every one sixth of a percent of voters would elect a candidate.  In the last general election, 30,697,525 votes were cast.  That would mean every 47,227 voters for a particular party would give that party a seat.  But since seats cannot be divided, some small party with only, say, 15,000 voters would get no seats.  So even this would not be 100% efficient.  But if we wanted a “fully efficient” system this is what we would do.

So why do we not?  One of the main reasons is that this divorces the candidate from the local region and constituency.  It is impossible for a voter in most cases to be able to say, “I elected this candidate”, or “This candidate belongs to me and others in my community”.  The allocation of seats to a constituency might seem arbitrary.  It is felt that it is important that there is a connection between the candidates sitting and the area.  Whatever there might have been originally (when members of Parliament were essentially aristocrats from specific areas), there still remains the strong sense of constituency in UK politics.  But it is important to analyse the effect of this and in particular the effect of the particular method that is currently used.

 Do MPs really represent all of their constituents?

A member of Parliament may in principle be intended to represent all of the people in his or her constituency, but the party political system tends to destroy this.  The combination of the whipping system, social pressure and career success (access to ministerial and other positions) being linked to toeing the party line means that while an MP may take up a small local issue they tend to vote on the large national issues that affect people according to the wishes of the leaders of their parties.  This really means that if someone is elected with only 40% of the vote (say), their consideration of the other 60% on most votes is likely to be relatively minor compared with the position that the party has taken on it.

Does the system represent the people?

Of the 136 parties that contested the last 2015 general election, most (91) received less than 1000 votes and arguably were never really serious candidates: they may have had a serious point to make but they probably never really expected or intended to become a member of Parliament nor did the voters who voted for them expect this.  Possibly it was for fun but in many cases it was simply to make a point, or several.  In the proportional representation system discussed above – Full PR –  120 of these would effectively “lose their votes” exactly as they do today because they received too few votes to get even one seat.

But a more serious problem occurs with something like the Greens.  The SNP got 4.738% of the vote.  The Greens got 3.771%.  But the SNP got 58 seats while the Green party only got two. It is not the purpose of this paper to analyse the efficiency of parties, but rather of the respect for voters intentions.  On this analysis, a voter for the SNP got more respect than a vote for the Green party. On a “100% fair” proportional allocation, the Green Party would have got 25 seats,  SNP 31, LibDem 51 and UKIP would have got 82 seats. Only the SNP with its concentration in Scotland received a proportional, in fact positively disproportional, result.

A better electoral system

More efficient systems are possible. These would be based on true proportional representation (PR) based probably on regional allocation. This would retain MP relationship to an area while giving fairer distribution of seats and allowing citizens better access to MPs that reflect their own position.


Analysing the efficiency:  The Approach of the Centre for Thinking Futures

 From a naive perspective, the UK system cannot be more than 49.99% efficient.  It is a first past the post system, which means that if there were two candidates and one got one vote more than the other, he or she would be elected.  All the votes for the losing candidate would be “wasted”, i.e. inefficient.  Equally, all the votes the winning candidate gets beyond this margin are unnecessary to getting elected.  A party with an ideal distribution would win every seated gets by a margin of one vote and the really unlucky party would win no seats but lose every seat by one vote.  That is not quite what happened, but the Green party was more like the second unlucky party while the SNP were more like the first  well-distributed party.


Additional If there were three roughly equal candidates, almost 2/3 votes would be “wasted”, the selected candidates would not get elected.  In this simple system, all that would be needed would be to take a percentage of votes given to the winning candidate away from the total (100%) and that would be how inefficient it is.  If the winning candidate got 40% of the votes, it would be 60% inefficient, or have an efficiency of only 40%.

But is this the right way to calculate it?  A formula was developed by Angus Jenkinson, which is used in this report.  This describes the logic of the formula.


Consider two seats

1             2

A 25%   A 4%

B 27%   B 17%

C 29%   C 12%

D 19%   D 67%


If the constituencies are the same size, then D gets a total of 43% of the votes, and wins one seat.

C gets just over 20% of the votes, and also wins one seat.

B gets 22% of the votes, and wins no seats.

A gets over 19% of the votes, and also wins no seats.

Is this an efficient way to allocate seats?  How inefficient can we say that it is?



 1.  Constituencies are not in fact the same size.  The smallest constituency is the Na h-Eileanan an Iar,  with 21,769 voters on the electoral roll.  The largest constituency as the Isle of Wight with 108,804 voters.  That means a vote in the smallest constituency is five times more powerful than a vote in the largest constituency.

 2. Votes cast for the winning party in any constituency are in principle positive, i.e. not wasted.  But this turns out to be a simple case.

 3. In fact, votes received by a party more than a simple majority become ‘increasingly useless’.   The voters for party D in constituency 2  in the above example may get some satisfaction from the huge winning margin, but from the big picture (most of) the votes were unnecessary to appoint their member of Parliament. Their intention for the government would have been more efficient if they could have given their votes in a different constituency. Thus the larger the margin the less the additional votes count.

 4. In the present system it is common (>50%) for a member of Parliament to get less than 50% of the votes in a particular constituency, as in the case of constituency 1 in the example.  The 71% of voters who voted against party C might legitimately be aggrieved not only that so many of their votes have been wasted but that a party with a minority of the votes got elected.

 5. Thus votes for a winning party up to a 50% of the voters certainly has legitimacy, but in the present system, votes beyond that should be considered increasingly less efficient.

 6. The corollary of this is that the total percentage of votes for the losing parties if they increase beyond 50% also become even more inefficient than they are already (they already produce no candidate).  The party that only gets 300 votes never expected to win, but if you receive 27% and the winning party receives 29%, that is a relatively close margin yet it is not a close decision in the allocation of seats: it is binary.


The algorithm that was used

The following calculation was made:


  1. All of the votes given to to the winning candidate up to 50% were counted towards efficiency.
  2. Votes given to the winning candidate above 50% were considered to contribute to legitimacy with a declining effect.  The calculation applied a power of 3/4 (0.75) to the margin above 50%.  A power of two multiplies a number by itself.  Fractional powers reduce the value of a number.  The graph below shows the effect.
  3. When the winning candidate gained less than 50%, their legitimacy reduced as did efficiency.  This meant that instead of an efficiency of say 40%, the calculated efficiency was about 35%.  Thus the candidate in the Isle of Wight who gained 40.7% produced an Efficiency of 35.4%. The same power factor was used.
  4. The national average was weighted by the size of the turnout (valid votes) in each constituency.


The graph below shows the power curve for votes above 50% (blue line).

General Information

The Centre for Thinking Futures at Thinking.Institute is an independent socially-concerned research organisation directed by Angus Jenkinson.  It researches methods for social renewal, organisational life and the interfaces between social and natural ecologies.  It has books in preparation on: how to think (ecologic), the life of organisations (social science) and the design of change.

About the author: Angus Jenkinson was one of the pioneers of the digital revolution, particularly in the field of customer information management and service.  He has been a professor of integrated marketing and is a fellow of the RSA, the Chartered Institute of Marketing and of the Institute of Direct & Digital Marketing.

The Centre is generously  supported by the Partners at Thinking.