Despite the close polls and the surge of the Scottish National Party, the UK election result of a single party majority government is one almost no one predicted. One immediate response is that the electoral system is working again and producing a strong, majority government: the Conservatives can claim that they clearly won the election.

Yet the reality is very different. The 2015 result has produced a considerable divergence between vote share and seats won. The problem is that a 19th-century system of voting in the context of two major parties now seems broken. David Cameron has been hailed for pulling off an extraordinary victory but the fact is that his party has gained 23 seats, becoming a majority party with a swing of only 0.8%. Labour, on the other hand, saw a positive swing of 1.5% but lost 26 seats.

There is a strong argument that the 2015 results are perverse and that electoral reform – such as some kind of proportional representation, where the number of seats are determined by the share of the vote – is much-needed.

The SNP with just under 1.5m votes won 56 seats. UKIP with 3.8m votes won only one seat and the Liberal Democrats with nearly 2.4m votes have only 8 seats. The point is that votes are not equal and many people may feel that their political engagement is irrelevant.

63% of voters did not support the Tories

This result throws up both moral questions and issues of legitimacy. The Conservatives will now come to office claiming a mandate to govern. In his first statement outside Number 10, David Cameron said that as the head of a majority government he can deliver all of his manifesto.

Yet 63% of voters did not support his party. The swing to the Conservatives was minute and they still have just one seat in Scotland out of 59. Their majority is an artifact of the electoral system and not a true reflection of the choices of voters. How can the government claim to represent the electorate with such a small proportion of the vote? No mechanism exists to ensure that the Conservative government takes accounts of the views of those who did not vote for them.

At the same time, millions of Green and UKIP voters are represented by just one MP each. The irony is that while an anti-political mood appears to have influenced many voters to reject the traditional parties, the outcome is that they are less represented than ever. And they can see how directly they are being excluded from the political system.

Hannah McKay/EPA

Again, while the SNP has gained many votes and seats, hundreds of thousands of Scottish Liberal Democratic, Conservative and Labour voters have no representation in Scotland – apparently denying a voice in parliament to the Scottish unionist position.

Not fit for purpose

The problem is that first past the post functioned in a two-party system where party support was spread relatively evenly across the nation. With a multi-party system and considerable regional variation, the electoral system is no longer fit for purpose. Very few voters can make a significant outcome to the electorate, undermining the democratic legitimacy of British government.

The case for electoral reform is stronger than ever. UKIP, the Greens and the Liberal Democrats have a clear interest in proportional representation. Yet, while the Conservatives have benefited most from first past the post they actually have strong reasons for supporting electoral reform.

The election has thrown up the question of the Union more starkly. Cameron has said he is committed to governing for the whole of Britain. Yet, under the current system we have a Scotland with almost no Unionist representation and we could have an system of English votes for English laws with an inbuilt Conservative majority.

Who wants reform

The way for the Conservatives to gain legitimacy across the union and to ensure representation for all English voters would be through a proportional system. At the same time if Labour wants to have representation in Scotland and the South of England, proportional representation would enable them to broaden their support.

The irony for the Conservatives and Labour is that the best way to save the union and engage the electorate may be electoral reform. Yet the 2015 election has demonstrated that with small shifts in voting they can achieve the holy grail of majority government. For Labour, the issue of electoral reform may become pressing. The results in Scotland mean that they either need a collapse of the SNP or a different voting system if they are to get into government again.

For the Conservatives, questions of legitimacy and long-term political strategy suggest they have an interest in reform. But the reality is that they have won a majority on a very small swing and they have a short-term political interest in the current status quo. There will be little or no pressure for reform on the government side and, of course, with a majority they are in a position to veto any attempts to change. Despite the perversities of the outcome, a real prospect of electoral reform will only come if the 2020 election again produces a hung parliament where minor parties may be in a position to press for reform.