So the first stage of the denouement is over with May's deal finally put out of its misery. I had expected it to go down by about 30-40 votes but in the event a larger margin. We now move on to the critical day, which is Monday. We will either see a Condorcet Winner emerge through preferential voting or we will find there is a real cycling effect and no winner will appear. In that case I think we will leave without a deal.
The people who are now on the spot are the advocates of a second referendum. This was being cast (in Margaret Becket's amendment) as a confirmatory vote between remain and a deal (presumably May's). That is quite popular because there is probably a majority in the House for putting any final deal to a vote of that kind. The problem is that the people behind it want to use it as a way of reversing the decision to leave and therefore don't want it to be a choice between remain and an exit that might win such as a soft Brexit. In particular they are dead against having leave with no deal on the ballot. I think they maximised their support under that strategy at 268. If they were prepared to have a straight remain versus leave with no deal ballot they might get a majority because quite a few ERG people would take that. They could also get over the line if they were prepared to have a three way choice with transferrable voting (no deal, an agreed soft brexit, and remain). That would mean supporting something like a customs union and insisting on a confirmatory vote as the price for that.
However I am pretty sure not enough of them will do either of those things. So I would expect a straight second referendum to fall, by about 50-60 votes. I think we could then see a majority for some kind of soft Brexit. Right now it looks as though a customs union has the best bet (so-called Turkey option). The only problem is it's not clear the EU will agree to that as a reason for extending the extension. In addition the Hard remainers are now once again crucial. If they support any particular soft Brexit as their second choice it will get a majority, just about. Most of them would probably go for Common Market 2.0 although they would take Customs Union as well. So I think it is likely one of those two options emerges as the Condorcet winner. However, if the Hard Remainers vote against it (given the Hard Leavers will also vote against) it will be defeated and we will have no Condorcet Winner. That's a very dangerous strategy from the Remain point of view as it makes a no deal exit much more likely.
If we do get a soft Brexit as a Condorcet Winner what then? The problem is you need a government to take that forward and there is no single party that will do that. The Tories can't because they are too divided and would have to depend on Labour votes to get that through. Labour might say they will run with this but I can't see Tory MPs who support a soft Brexit agreeing to support Corbyn as PM. That would be needed because there are enough die hard Remainers on the Labour benches for that to be necessary. The way out would be either to have a national unity government supported by MPs from both parties with a remit to stay in office only for the purpose of getting the deal over the line or an election like the 1918 Coupon Election with supporters of the deal given the 'Coupon'. Either of those would cement the realignment and a radical party reconstruction.
If there's no Condorcet Winner then a no deal exit becomes the most likely, not least because the EU will probably go along with Macron this time and say "Look you've had your chance, time to leave" and refuse any extension. They might even agree to a short extension but only to manage a no deal exit. You might at that point get a second referendum through but if and only if it had no deal exit on the ballot, given there won't be a deal to vote for. I think though there would be a narrow majority against a referendum even in that scenario.