SO DO you know the old Liberal Democrat joke? No? OK, a motley crowd of LibDems are assembled. Up goes the chant. “Whadda we want?”

Back comes the reply. “The Single Transferable Vote in multi-member constituencies”.

“When do we want it?” “In due course, after mature and prolonged consideration of the options.”

I take your point. Little bite. Still, the LibDems achieved exactly that aim for Scottish council elections, after mature and prolonged pressure upon Labour, their coalition partners in the early days of the Scottish Parliament.

And so it is under STV that folk will cast their votes next week. Or, rather, those who still go to the polls in person. Nearly a quarter of the electorate, some 23 per cent, registered in advance for postal ballots.

READ MORE: Boris Johnson will, ultimately, be judged by his peers – and by the people

Those who have already voted can calmly ignore the increasingly frenzied appeals from the parties in these final days of a curious, overshadowed campaign.

The advocates of Proportional Representation say it more fairly reflects the popular mood. Critics say it can be indecisive and can dilute the link with individual ward councillors.

Either way, it is more likely to generate hung councils, prompting the need for cross-party coalitions – or for negotiation around particular decisions.

So a system born from coalition can lead to localised inter-party dealing. However, in advance of Thursday, the party leaders are, understandably, reluctant to talk about post-election deals.

For two reasons. One, they do not want to be seen to be pre-empting popular choice. Voters tend to prefer to make their own decisions, for their own reasons.

Two, the nature of contemporary politics. On all sides, there is sharp division. Over the economy, over governmental performance north and south of the Border – and, of course, over independence, the core fault line in Scottish discourse.

The talk is of shutting out their rivals. Of closing the door upon…..enter loathed party here. I canvassed views on the prospect of local coalitions, in this atmosphere.

READ MORE: Not interested in politics, eh? How about schools, bins and public transport? These elections matter

Labour’s Anas Sarwar has said his party will not enter any formal pact with any other party – to the dismay of some local stalwarts on his own side who fear they could be giving up a degree of clout (plus, of course, the prospect of council titles.)

Partly, this may reflect the controversy which attended a pact in Aberdeen between Labour and the Conservatives. It led to the suspension of nine Labour councillors, later rescinded. But it had Scotland-wide impact.

More to the point, Mr Sarwar’s guidance reflects his broader strategy. He wants Labour back in the game as a leading player. To do that, he needs to oust the Scottish Conservatives from second place in Scottish politics, behind the SNP.

And to do that he needs to declare a plague on both houses, Nationalist and Unionist. He needs to depict Labour as offering a fresh approach, to invite the voters to consider his two main rivals in tandem.

Hence the declaration of “no deals”. It may well pose difficulties locally but it is designed to advance a Scotland-wide single transferable strategy for Labour.

Now, there are caveats to all this. An individual council group might appeal to Labour’s Scottish Executive, although Mr Sarwar seems adamantly against formal pacts.

Within that general proscription, individual bargaining on individual policies is not ruled out. Indeed, Mr Sarwar says it could be a new way of doing politics: considering issues afresh, without pre-ordained coalitions determining the outcome.

In saying that, I think he is largely reflecting that wider strategy and, of course, reflecting Labour’s current lowly status, unable to dominate Scottish local governance as it did in the past, at least in the central belt.

The SNP, in line with standing policy, rule out any deals with the Tories. Again, their broader strategy is to counterbalance their party offer against Westminster Conservative rule. They are open to working with other parties although, as with others, they stress their own policies to bolster local services.

Ditto the Greens who indicate their willingness to work locally with others but rule out a formal coalition with the Conservatives. In practice, the Greens’ aim will be to enhance their presence in local government.

Douglas Ross, for the Conservatives, has flirted with cross-party co-operation in the past, hinting at the prospect of pro-Union parties working together.

However, little came of it and, for these elections, he is offering no advance prospectus while remaining potentially open to local negotiations, should that arise.

In practice, given the stance taken by others, that might involve working with the LibDems. However, two points should be borne in mind. One, all parties are cautious ahead of polling and, two, the outcome might drive the need for compromise in local areas.

The LibDems have a predilection towards co-operation which, of course, reflects their Scotland-wide standing. Frankly, they need to project a positive role for their party.

They stress that, in keeping with their philosophy, it would be up to local council groups to determine local decisions. However, sources suggest that they would be unlikely to support the SNP in retaining control of Glasgow and Edinburgh, condemning their rival’s record in Scotland’s biggest cities. (Naturally, the SNP dissent.).

As always in politics, there is the question of momentum. Can Labour, for example, usurp second spot from the Tories and provide a boost to their own wider prospects, with UK and Holyrood general elections on the horizon?

Douglas Ross has not had his troubles to seek of late, mostly inherited from the Prime Minister, but he insists that he will see off Labour in this contest.

And, again as always, there is the issue of independence. My colleague and chum Professor John Curtice has drawn attention to one facet of the STV system. Supporters of independence may be relatively content to switch between pro-indy parties, such as the SNP and Greens, in this election.

By contrast, supporters of the Union may be more reluctant to switch between, for example, Conservative and Labour. Which could give a little added momentum to apparent support for independence.

I note that school students sit their Modern Studies SQA exams on Thursday, polling day. They should have much to contemplate in future.