The changes from last September are predictable, given how the Lib Dem poll ratings have continued to decline since then – Clegg’s approval rating is now at minus 29 compared to plus 8 a year ago, the proportion of people who support the coalition agreement is down to 34% from 43% a year ago. Asked to pick from a list of positive contributions the Liberal Democrats have made to the government, 40% say nothing at all, compared to 34% a year ago.

The more subtle and interesting movements come in the list of statements about the Lib Dems that were repeated from January. YouGov asked if people agreed with various statements about the Lib Dems, 5 broadly positive for them, 5 broadly negative.

Two of the statements sought to measure perceptions that the Lib Dems had broken people’s trust or betrayed their supporters – agreement with both of these fell. The statement that people “could never trust the Liberal Democrats, even if they left the coalition” had net agreement of +13, down from +25 in January. Net agreement with the statement that the Lib Dems have “broken their promises and betrayed their supporters” was down to +32 from +43. There was smaller movement on the statement that the Lib Dems had sold out their principles, or were propping up an extreme government, but nevertheless, it suggests some of the public are starting to view the party through less of a prism of betrayal, some of the hostility is starting to fade.

Less good news is on how distinctive they are. “I’m no longer sure what the Liberal Democrats stand for” was the most agreed with statement (63% agreed), and its net agreement was up from +29 in January to +41 now. Tempering that slightly, 30% agreed with the statement that the Lib Dems offered “different and distinctive policies from the other two parties”, up from 25% in January.

Looking at agreement with the more positive statements, 26% of people agreed that by entering coalition the Lib Dems had managed to get “real Liberal policies put into action”, 36% agreed that they had made the coalition more moderate and centrist (up from 33% in Janary), 41% agreed they had done the responsible thing by entering government at a time of crisis – the most agreed with positive statement, but marginally down since January.

YouGov asked if people thought the public or private sector were suffering more in the economic downturn – respondents were slightly more likely to think that public sector workers have suffered more than private sector workers (by 27% to 17%), but 49% of people think both groups have fared much the same. On public sector pensions 44% think the government’s changes are right (marginally down from when the question was last asked), 39% wrong, 49% of people oppose public sector strike action over pensions, with 38% of people in support (pretty much unchanged).

On the Liberal Democrats and the coalition, almost half (48%) of people think that entering the coalition was the wrong decision, a proportion mirrored amongst those who voted Lib Dem at the last election (although amongst the remaining Lib Dem supporters 71% think it was the right thing to do). There is a similar split in opinion on whether they should stay in the coalition now – 36% think they should stay (including 78% of their remaining supporters), 45% think they should leave.

Despite Nick Clegg’s low approval ratings, 41% think he should stay as Lib Dem leader compared to 32% who would like him to stand down. A majority (63%) of people did not know who would make the best replacement leader for Clegg (unsurprisingly given the relative low profile of third party politicians – Vince Cable was the top choice, but with only 16%, and this was probably because he was the least anonymous).

On the question of how much influence the Liberal Democrats have within government, most Conservative and Liberal Democrat supporters think they have a little influence, with Conservatives thinking that is about right or too much, and most Liberal Democrats thinking the party should wield greater influence. Labour supporters tend to see the Lib Dems as not having much influence in government. Overall they are seen as somewhat more influential than they were when we asked the same question in May – back then only 8% thought they had a lot of influence, that has now risen to 15%.

46% of people see the Conservatives as having benefitted the most from the coalition, compared to just 19% who see the Liberal Democrats as the main beneficiaries. Looking to the future, 36% of people think that the Liberal Democrats have permanently damaged their party by entering the coalition, 23% think they will recover in time, 21% think they will eventually benefit from having been in government.

On a seperate subject, Labour are seen as the party that best understands and reflects the concerns of women, by 25% to the Conservatives’ 11%. However, 31% of people said no party reflects the views of women. Asked about the leaders, there is very little to choose – Miliband leads Cameron by only 16% to 13%, with 35% saying none of the party leaders understand or reflect the views of women (amongst women respondents, this rise to 43%). Labour are in a better position when people are asked about whether women are well represented in senior roles in each party. 47% of people think women are very or fairly well represented at the top of the Labour party, compared to 33% who think the same about the Tories.

Broadly speaking, uniform national swing has been a pretty good predictor of elections – or at least, a good starting point to analyse elections and where parties have done better or worse than average. However, it is mathematically inelegant, particularly when it comes to the extremes. Say a party loses 5 percentage points in its national support – what happens in a seat where they only had 4% at the last election? On a UNS model they’d get minus 1% support, which is clearly impossible. Generally speaking though UNS doing odd things to parties with minimal support doesn’t matter, as it is all about the marginal seats and predicting overall seat numbers, how well it models changes in support in safe seats is irrelevant.

However, it has been playing on my mind how it will work with the Liberal Democrats at the next election if they maintain their present low levels of support. How would it cope with a drastic collapse in support for a party? It varies from pollster to pollster, but roughly speaking the Lib Dems have lost about half their 2010 vote, about 12 points or so. To start with there were 57 seats where the Lib Dems got less than 12% support in 2010, they can’t lose 12% in those. Equally, if their vote did collapse to what extent would their sitting MPs be insulated from the fall?

The Scottish Parliamentary election gives us a chance to see. Below is a scatter chart of the Lib Dem performance in 2011 – plotting the change in the Lib Dem share of the vote in each seat against the share of the vote they recieved in 2007. Gold dots are those seats that were notionally or actually held by the Lib Dems in 2007, blue dots are non-LD seats.

The green line is what we would expect to see if there was a uniform swing – the Lib Dem vote falling by 8% in each seat. The red line is what we’d get if the Lib Dem vote fell proportionally to their support in 2007 – basically if they lost half their support in each seat. The actual distribution of dots is clearly closer to the proportional line than the uniform swing. If this was repeated at a GB general election then the Liberal Democrats would do even worse than a uniform swing would predict.

On the other hand, look at the distribution of the blue and gold dots – in seats where the Lib Dems had incumbency the Lib Dems did better than a proportional loss would have suggested (and they do worse than than this in seats without incumbency) – while the Lib Dems did end up losing all their mainland seats in Scotland, they did actually perform somewhat better in the seats they held… just not by enough to save them.

I wouldn’t presume to make models or predictions about what would happen to the Lib Dems at a general election on this basis… just that UNS national swing may not be a very good predictor if the Lib Dem vote does remain in dire straights at the next general election.

There were large majorities of party members thought that Chris Huhne and Vince Cable were performing well in office. There was similar backing for the Prime Minister, David Cameron. Liberal Democrat party members were, however, evenly split over Nick Clegg – 50% think he is doing well as Deputy Prime Minister and Leader of the Liberal Democrats, 50% think is is doing badly. Asked about his future, 45% think he should remain leader of the party at the next general election, while 35% think he should stand down at some point before the election

Turning to how well the Coalition Government is managing various issues there was strong support for the Government’s handling of taxation (75% thinking the government had done well) where the Liberal Democrat aim of increasing the personal allowance is being implemented. 67% also thought the Government was managing public spending well. A majority of Lib Dem party members also thought the Government was doing well on crime, Europe, overseas aid. Predictably, a large majority – 77% – thought that the Government was doing badly on student fees. Lib Dem members were almost as unhappy about the Government’s NHS policy, where 73% of party members thought the Government was doing a bad job.

Despite these misgivings, overall 79% of Lib Dem members viewed the Coalition as having been good for Britain. 88% thought it was good for the Conservative party… but 66% thought it had been bad for the Lib Dems (including 21% who thought it had been disastrous). Despite this, a large majority (91%) thought that joining the Coalition was right, and 57% thought that the right deal had been struck under the circumstances

There is hardly any support amongst Liberal Democrat members for ending the Coalition – just 7% want to pull out now, and 6% to pull out in a year or two’s time. 63% of party members want to see the Coalition last for the full five year term of the Parliament.

While these figures represent overwhelming support for the Coalition among Lib Dem members, it is worth remembering that these represent only the responses of those people who have remained in the party. Many Liberal Democrats who opposed the Coalition may have resigned or failed to renew their memberships – among those respondents we contacted who are no longer members of the party, 35% opposed the Coalition and 40% think the party should leave the Coalition within the next year or two.

Tonight’s YouGov/Sun voting intentions are CON 39%, LAB 41%, LDEM 9%. While there is the normal variation from day to day, we’ve now had three YouGov polls in the last week showing the Labour lead down to 2 – it looks as though the local election may have lead to a slight narrowing of the polls.

Here are the actual voting intention figures from back in 1988-1990, as you can see, there are plenty of points (November 1989 for example) when the Lib Dems would have been averaging in single figures. Of course, the key point is that the Lib Dems are in a pretty poor way, but nevertheless, Lib Dem support is NOT at an all-time low.

(The mistake may have com about from adding up the support of the Liberal Democrats and Continuing SDP during this time – my tables only show support for the Liberal Democrats themselves post-1988)