Posted by Simon Hix and Nick Vivyan.

We have updated our election prediction model, based on national voting intention results from all polls with fieldwork up to and including 5 May. As of the morning of the election, we have the standing of the parties as follows: 35.5 per centfor the Conservatives, 27.6 per cent for Labour, and 27.4 per cent for the Lib Dems.

Here’s how these national vote shares might translate into seats under three different assumptions: (1) a uniform change in party support across constituencies; (2) differential changes in party support in each region of the country, based on YouGov regional polling data; and (3) differential regional swings, adjusting for marginal seat effects, using YouGov data from Labour held seats where the Conservatives need a swing of 3-7 per centto win.

Hix-Vivyan Seat Projections for 6 May

These numbers are the ‘mean’ predictions for each version of our model.  To get a sense of the range of possible outcomes, model 3 predicts that the Conservatives will secure between 293 and 324 seats, Labour will secure between 200 and 230 seats and the Lib Dems will secure between 84 and 107 seats.

What do these ranges mean in terms of potential post-election scenarios?  As a guide, here are some of the key seat thresholds to consider tonight when the results come in, and how likely these scenarios may be.

326 With 650 seats in the House of Commons, a party needs 326 seats to command a majority of seats (i.e. 650 divided by 2, plus 1).  If no party wins 326 or more seats it will be the first ‘hung parliament’ since February 1974 and only the third since universal male suffrage was introduced in 1918 (1923, 1929, and Feb 1974).

Likelihood that the Conservatives get 326 or more seats: 2 per cent(using model 3, above).

323 Our colleague Paul Mitchell predicts that Sinn Fein will win 5 seats in Northern Ireland and that these MPs will not take up their seats in Westminster.  If this happens, the real ‘winning post’ is 323 (650 minus 5, divided by 2, rounded up to the nearest whole number).

Likelihood that the Conservatives get 323 or more seats: 4%.

314 Also following Paul’s predictions, the DUP look set to win 9 seats in Northern Ireland.  If they support Cameron for PM, then the Conservatives only need 314 seats to command an ‘effective majority’ in the Commons (323 minus 9).

Likelihood that the Conservatives get 314 or more seats: 26%.

310 If parties other than the Conservatives, Labour and the Lib Dems win 32 seats, then the Conservatives need 310 seats to have more seats than Labour and the Lib Dems put together (650 minus 32, divided by 2, plus 1).

Likelihood that the Conservatives get 310 or more seats: 44%.

295 If the “others” win 32 seats, then the Conservatives need 295 seats to prevent Labour and the Lib Dems having enough seats to form a coalition government with a majority of seats in the Commons (i.e. 326 minus 32, plus 1).

Likelihood that the Conservatives get 295 or more seats: 96%.

<295 If no party wins 295 seats or more, then we will be in the ‘deeply hung parliament’ territory, where things will start to get really interesting!  In this situation, the Lib Dems will be in a pivotal position, as they will be able to choose whether to form a majority with either the Conservatives or Labour.

Likelihood that the Conservatives will get less than 295 seats: 4%.

These predicted probabilities are based on the third vote-seat translation method presented above (model 3, which adjusts for regional effects and marginal seat effects), which tends to allocate more seats to the Conservatives.  Of course, each of the other two vote-seat translation methods yield different predicted probabilities.  For example, take the ‘deeply hung parliament’ scenario: according to our uniform-national-swing model (model 1) there is a 98 per centchance that the Conservatives will secure less than 295 seats, whereas according to our differential regional-swings model (model 2) there is a 32 per centchance that this will occur.

Finally, the usual caveats apply.  Namely, these predictions are based on polls up to 5 May and people can change their mind on election day!  We have assumed that polling companies are on average correct, which might not be the case in such an exceptionally volatile electoral atmosphere.  And, our models are inherently blunt instruments, so may not accurately capture the way national vote-shares map into constituency-level results.