Nominations are open, and will close a week on Friday, so the latest YouGov-Cambridge poll commissioned by the Royal United Services Institute is well-timed to give that final push to prospective Independent candidates balancing the decision to run against the temptation to hold on to that £5,000 deposit.

The poll (with full results here, analysis here, and Martin Beckford's Telegraph commentary here) revealed a range of views as to whether the public believe that Police and Crime Commissioners will help or hinder the fight against crime, whether the public feel they understand the PCC role and whether they are likely to vote at all – all interesting stuff – but crucially they were also invited to express a view on whether they approved of the involvement of political parties.

Overall, 61% said they disapproved of candidates being supported by a political party, rising to 74% for the over-60s, which is important as, while respondents of varying ages were roughly equally likely to say they would vote, previous experience suggests that the over-60s are more likely to actually show up on the day. Only 11% approved of party political support, and only 19% were undecided.

The hearts of Independents across the country will be cheered by this news. Are they finally catching a break? Is this confirmation that the anti-politics feeling they may feel themselves is widely shared by the general population?

Perhaps.

But I'm going to retreat to boring political-scientist-mode now. While the anti-politics feeling may be widespread, how deep is it? We don't know yet whether this disapproval is strong enough to outweigh other considerations, such as actually knowing anything at all about the candidates, or having had some form of contact from them, which is what the red, blue, yellow and purple labels and the bunches of dedicated leafleters provide. And we don't know the dynamics of how this works in the polling booth, where the temptation to back someone for positive reasons has to do battle with the temptation to vote for an otherwise less-favoured candidate in an effort to keep someone else out. Nor do we know whether this represents a general feeling of anti-politics, or something specific to an election that involves policing.

What we do know is that this is an election where having a second preference available means that voters can better afford to vote how they feel, before retreating to a safe option for their alternative vote. Though we don't know how many of them appreciate this. And we know that the Centreground ComRes poll in May showed only 26% thinking they would vote for an Independent, though this seemed to hit Conservatives more than other parties.

Talking to some Independents shows they have a clear strategy of seeking to come at least second in the total of first preference votes, and then benefitting as supporters of parties prefer an independent to that of a different party. It could work, particularly if political party votes in an area are fairly evenly split between maybe four fairly non-descript party candidates, and if voters have a single clear Independent choice who is able to make their presence felt. Whether and where that happens depends on what nominations actually come in over the next two weeks.

And yet my favourite question from this poll is not about parties or voting intention, but about the impact of PCCs. Respondents were asked whether the reform would mean that some areas would have worse policing than others. Why not ask whether some will be better, or some better, some worse? Does this reveal the bias of those commissioning the poll, or do we just expect more truthful answers from the British public when we assume pessimism and grumpiness?