Could the Conservative government fall over sex scandals? That’s the question being asked after two MPs have been accused of inappropriate behaviour, and a redacted list containing at least 34 further Conservative MPs made its way onto the Guido Fawkes website. ITV’s Robert Peston raises the possibility over on his Facebook page that it could bring about the end of the Conservatives’ hold on power.

It’s certainly possible. It’s very easy to see how the scandal could see the government lose its majority on paper, if enough MPs are caught up in it, have the whip removed and notionally end up sitting as independents. Both Anne-Marie Morris, who lost the Conservative whip for using the word “nigger”, and Jared O’Mara, who has lost the Labour whip due to sexist remarks made over a period of years, are notionally independents and it is unlikely that either will be the candidate in Newton Abbott or Sheffield Hallam next time, but both vote with their former party in the Commons.

But MPs can only be removed from parliament against their will if they are found to have broken the law, which has a much higher burden of proof that the political parties’ may have in their own internal investigations. The case of O’Mara is a good example here: he admits that he made sexist and homophobic forum posts throughout his twenties, which many in Labour have taken as evidence that recent accusations that he called a female constituent “an ugly bitch who he wouldn’t touch with a woman’s manky cock” are true. That may well be enough circumstantial evidence for Labour’s ruling national executive committee to decide he has brought the party into disrepute and that they have a better chance holding Sheffield Hallam with a fresh candidate, but it is nowhere close to being able to prove whether he actually said those words to his constituent.

Or take the expenses scandal itself: Labour barred four MPs from standing for the party again, a further ten opted not to stand again, but just two MPs were charged. On the Conservative side, nine MPs opted not to run for re-election following the expenses scandal, but none were charged.

The expenses scandal produced just three by-elections across the 2005-10 and 2010-15 parliaments, all in Labour held seats. Labour lost the Norwich North by-election in 2009 but held Barnsley Central in 2011 and Rotherham in 2012.

So for by-elections to be forced upon the government, one of two things have to happen: MPs have to resign voluntarily, or they have to be convicted of wrongdoing. The latter is a problem for the government in 2020, not today. The former is unlikely because politicians tend not to want to hurt their own side, particularly not with the battle between the big two so finely balanced. And for it to tip the balance of power from the Conservatives to a Labour coalition, the Conservatives need to lose just seven seats in by-elections.

But in practice, even allowing for the fact the opposition parties tend to significantly outperform its general election performance in by-elections, Labour need those by-elections to occur in one of the 180 seats that they or the Liberal Democrats could, theoretically, hope to win even on a big swing. So we are talking about a lot of ifs here: if there are more named MPs, if those MPs voluntarily resign, if those MPs are in seats that Labour or the Liberal Democrats can hope to win, if they then win every winnable seat, then potentially, the scandal could lead to a situation where the government is vulnerable in a vote of no confidence.

The Conservative who is vulnerable is Theresa May, who, if it does turn out that she was aware of allegations against sitting Conservative MPs, may find that she is unable to lead the country through the Brexit talks, let alone afterwards.