David Cameron will hope UK voters agree with JK Galbraith’s phrase that ‘nothing is so admirable in politics as a short memory.’ It seems an aeon ago that the Conservatives launched their election campaign broadcast from the fictional ‘Hung Parliament Party’. They argued that if the electorate failed to give a single party a majority, it would result in indecision, weak government, closed-door politics and a paralysed economy.

When Cameron finally emerged in the rose garden at Number Ten with Nick Clegg on 12 May, it was to announce a new politics, which put the national interest over party interest, and with this ‘historic and seismic shift in our political landscape,’ the cynicism of the past was put firmly to rest.

He was right in his latter analysis – there has been no dramatic slide in the value of the pound or in the FTSE over the last two months. The coalition government has had its moments of tension, of course, but hasn’t appeared weak or indecisive. Unlike some political systems in the rest of Europe, there wasn’t a protracted period of internal horse trading in the UK, and with the constant buzz of 24-hour news and Twitter, the media seem more than able to hold the government to account.

There are, of course, some unique points to working with a coalition government, which everyone who seeks to engage with the administration should bear in mind. There is suddenly new power for both minority parties (and not just the Liberal Democrats) and for special interests. The tighter the parliamentary vote, the more obscure the local issue that could decide the outcome. To give one historical example, the minority Labour government in the 1970s led by Jim Callaghan tried to secure support from two Ulster Unionist MPs during a crucial vote of confidence in 1979. The Prime Minister was prepared to promise a multi-million-pound fuel pipeline between Northern Ireland and the mainland in order to secure the vote.

While it can seem somewhat bizarre to many in the public that great issues of state could hinge on such parochialisms, this style of political discourse gives new entry points for astute campaigners. Many of us are used to working with coalitions in mainland Europe or in the devolved legislatures in the UK, but it is something of a culture shock for those accustomed to the strong executive in Britain, with the focus on briefing ministers and their advisers.

Inevitably in a coalition, the executive becomes more dependent on the legislature. In order to maintain coalition unity, various compromises are needed, giving more power to backbenches and minority interests. This means there are more points of entry for outsiders. Although nothing like their powerful equivalents in the US Congress, UK parliamentarians now elect their select committee chairs, having previously been in the purview of party whips and therefore the government of the day. However, with 251 new MPs in the Parliament, they may not have the experience to hold the government to account in the early stages. The Commons majority for the coalition is currently healthy at 75, but votes will be on a knife edge if there is disagreement between the Liberal Democrats and the Conservatives.

Unlike the myth of deals being stitched up behind closed doors, coalitions actually lead to greater public debate and discussion on key issues. Not only is compromise more necessary, but the process is often more open. Detailed scrutiny of legislation will still happen at the committee stage, and the Conservatives will need the Liberal Democrats for a majority. With so many budget cuts planned, constituency issues become even more important if the MPs involved tip the parliamentary arithmetic. We are also seeing think tanks such as Policy Exchange and the Centre for Social Justice on the Conservative side and Centre Forum for the Liberal Democrats becoming more influential.

The decision-making process also becomes far more complex, something that will need to be communicated in communiqués back to national capitals. With the need for agreement not just inside a government but with another party, predicting a political outcome becomes more difficult. For the Liberal Democrats, who operate a federal decision-making structure, coming to a major political decision doesn’t just require an agreement by the key players, but often a protracted discussion with their parliamentary party and ratification by the grassroots membership – as we saw when the coalition agreement was being negotiated.

Having often been ignored, the Liberal Democrats are now more relevant than they have been since the 1920s. When Danny Alexander came to visit our offices at the end of last year, he was responsible for the Liberal Democrat manifesto, something in previous elections he could have been confident he would never have to implement. But he has seized the opportunity of a coalition and, following the resignation of MP David Laws, is now the Chief Secretary to the Treasury, one of the most powerful positions in government.

With so many new MP’s and minister’s names to learn, it’s important to remain focussed. But working with a coalition government still has many of the same facets as a single-party administration. Briefing ministers is still critical, as is having a positive relationship with special advisers and civil servants. Not all members of the coalition are created equally either, so efforts should be focussed on the senior partners to be effective. And finally, it is critical never to try to play two parts of the coalition off each other – that is a sure route to failure.

There are many places we can look for guidance on how to engage with the Con-Lib government. The European Parliament has no majority as such and our work in Brussels has always been based on building cross-party support and negotiating compromises between the major groups, which is why many complain about the ‘watered-down’ nature of EU political decisions. In practice, this can often mean a lot of framework legislation with implementation measures on a technical or geographical basis being required to bring legislation into force.

In the Netherlands and Finland, there have been coalition governments since the First World War, as is the case across much of Europe. But the Westminster-style parliamentary system in New Zealand provides a better comparison to Britain. New Zealand adopted a PR system in 1996 and has been mainly ruled by coalitions in various guises ever since. The coalition agreements have an ‘agree to disagree’ clause, much as the Con-Lib agreement does over tuition fees, Europe and Trident. There is a formal dispute resolution process and a twinning process for ministers from both sides to ensure grievances can be aired. Cabinet collective responsibility is more relaxed, though secrecy rules are strictly enforced. And just like the UK, the Prime Minister and Deputy Prime Minister relationship is critical.

Learning the lessons of how to approach coalition governments requires us to re-learn many of the skills of engagement and communication – and to make them appropriate for the new political reality. The UK hasn’t had a formal coalition government since the Second World War, so we are witnessing history in action. But with electoral reform a real possibility in the UK, coalitions may well become the norm.

Learning the lessons of how to approach coalition governments requires us to re-learn many of the skills of engagement and communication – and to make them appropriate for the new political reality.