On May 6, the United Kingdom held one of its irregularly scheduled elections, with an inconclusive result. The Conservative Party got the most seats in parliament, but not enough to form a majority.
Coalition Governments in the United Kingdom
The issues this poses don't exist in the American political system.
We have only two viable political parties, while the United Kingdom has three national political parties, several parties devoted to local federalism issues (a Scottish nationalist party a Welsh nationalist party, a Unionist party in Northern Ireland, and two Irish Republican parties in Northern Ireland), and also has a unionist leaning independent in Northern Ireland, a "union-republican neutral" Alliance party in Northern Ireland and a single Green Party MP in Southern England.
More importantly, we elect our chief executives separately. In the United Kingdom, the Prime Minister and his (or her) cabinet are chosen with the support of a majority of the House of Commons and their maximum five year term can be cut short at any time if that majority support is lost.
When no political party receives a majority, in the U.K., there are two options. The MPs elected can negotiate to form a multi-party coalition that governs as a single temporary ruling party subject to agreements on sharing power, or the party with the most seats can form a "minority government" that doesn't include other parties. This puts a Prime Minister and cabinet in place, but is inherently fragile. The last time the U.K. had a minority government, in 1974, a majority of parliament decided to call a new election eight months later. Other parliamentary systems have similar experiences with the fragility of minority governments.
The problem the Conservative Party faces is that it has few potential coalition party. It is actively opposed to the Scotish and Welsh Nationalist movements. The Sein Fein MPs never take office because they aren't willing to swear their oaths of office. The remaining Irish MPs aren't numerous enough to provide the Conservative party with a majority, and the Green party is the natural enemy of the Conservative Party - they agree on almost nothing. The Conservative Party ran against the Labour Party, which is the second largest party in the country, and the U.K. is facing no overarching threat to its existence, so a grand coalition government of the two parties isn't viable.
Thus, the only way the Conservative Party can secure a majority is with an alliance with the quite Liberal Democratic Party. But, the Liberal Democratic Party's price for making a coalition is election reform, a price that the Conservatives, unsurprisingly have been unwilling to pay.
Political Reform Politics in the United Kingdom
Like most U.S. jurisdictions (except Louisiana and Georgia), in the U.K., legislators are elected from single member districts and only a plurality is required to be elected. In a two candidate race, the is identitical to a majority vote. But, in three or more way candidate races, this causes the candidates who are most ideologically similar (usually Labour and the Liberal Democrats) to split the vote and tip the race to the most ideologically distinct party (usually the Conservatives).
A "first past the post" system as it is called in the U.K. doesn't hurt political parties that are strong in only one region that much. But, the Liberal Democrats, received 23% of the vote (compared to 29% for Labour), but won only 8% of the seats (57 v. 258 for Labour), because its support is quite evenly distributed, while the Conservatives came only a little short of a parliamentary majority with just 36% of the vote. The main beneficiaries of the first past the post system are the Conservative and Labour Parties.
The reality of politics in the United Kingdom is that the electorate is securely left of center, and that without a first past the post system, that Conservatives are able to exploit through the relative unity and geographic concentration in parts of England and Wales outside central cities, the Conservatives would probably be a permanent minority party. The only way Conservatives would have a prayer in the long run would be to grant the Scotish independence, because Scotland delivered just one of its fifty-nine seats to the Conservatives (and didn't have a single change of party in the 2010 election); something the Conservatives are committed to opposing.
The only reforms that really make sense in the long term for the Conservatives would be some sort of half measure reform that would give Liberal Democrats a few extra seats if their popular vote percentage is much less than their number of seats (Scotland's legislature and New Zealand have similar systems), and the creation of rump parliament comprised only of English representatives to serve as a regional government for England to parallel that of Scotland, Northern Ireland and Wales.
But, this would be cold comfort for the Conservative Party. It is already challenged to get a majority in parliament and doesn't want to make it harder for it to do so (although gains for the Liberal Democrats might be offset by gains for England's two far right parties which together received almost 6% of the vote, but won no MPs). If the current trend of gains for Liberal Democrats and declines for Labour cause fewer U.K. voters to strategically vote Labour even when they prefer the Liberal Democrats continue in the short term, a new election in a year or so might see a decline in support for both center-left parties as they further split the vote, pushing the Conservative Party to an outright majority.
Even this is a gamble for Conservatives, however. A new Labour Party leader and the Liberal Democrats, during a Conservative minority government, could agree to run on a fusion ticket with a pre-agreed coalition plan in place, depriving Conservatives of the advantages that the two party system gives them. The natural tendency of first past the post single member district electoral system is for a two party system to emerge in the absence of regional parties.
An increased say in an English only rump parliament for domestic affairs would help conservatives in the long term; but its signature issues at the moment are national ones like staying out of the Eurozone, avoiding deepening of European Union authority, and opposing immigration. The Conservatives have a domestic agenda, but those aren't the main issues producing support from their base. Even Conservatives in the U.K. aren't willing to go too far in upsetting the British welfare state.
The center-right Conservative Party and center-left Liberal Democratic Party are not natural long term coalition partners, and the Labour Party is the Conservative Party's long time archnemesis. Labour and the Liberal Democratic Party, in contrast, are natural long term coalition partners, similar to some extent to factions with the Democratic Party in the United States.
The Labour Party, which spearheaded major initiatives to grant more power to regional governments in Northern Ireland, Scotland and Wales, is also a natural ally to some of the federalism oriented parties of the United Kingdom. It would probably have given Scotland full fledged independence if it didn't need the support of Scotish MPs in the U.K. parliament.
The result is that it seems more likely to me that the Liberal Democrats, Labour Party, Green Party, and some of the regional federalism oriented parties will form a coalition government.
The sensible and simplest reforms for that coalition to adopt would be (1) runoff voting, in which the top two candidates in races where no one candidate received a majority would compete in a runoff election, and (2) increased autonomy for Scotland and Wales. This would probably produce center-left coalition governments in the short and medium term by strenghening the Liberal Democrats vis-a-vis Labour, but would also increase their joint share of the pie by significantly reducing Conservative Party strength in parliament. If these reforms yielded save majorities for the Labour-Liberal Democratic Party coalition in England in the next election, this might even lead to Scotish Independence (Wales is far less equipped to go it alone).
Runoff elections aren't the only way to secure multi-party politics in a parliamentary system. Bonus seats for underrepresented political parties, true proportionate representation systems (a la Israel), or proportionate representation with a floor percentage required to get any seats (a la Germany) are alternatives. But, those systems are all greater deviations from the very simple system that the U.K. has traditionally used in its elections and risk opening the doors of parliament to far right neo-facists, something that Labour and the Liberal Democrats would prefer to avoid.