How an increase in Lib Dems could mean less coalitions

Some people are unfortunately unable to work out the maths behind why an increase in the Lib Dem seat numbers is just as likely to mean lower chances of hung parliaments as higher chances. Let's take a deeper look...

Using the UNS (you can play with an interactive version here...) we can see a likely result under FPTP if polling remained the same (and assuming that boundaries don't change) would be this..

Lib Dems: 20
Labour: 363
Tories: 242
Others: 24

This gives a Labour majority of 76 seats. Under AV the Lib Dems might pick up another 20-60 seats depending on local marginals. So, does this mean more coalitions? Well first of all the maths show in all likelihood that even if all those seats came from Labour there still wouldn't be a coalition. But what if Labour had a smaller majority? In theory the Lib Dems could force a coalition by their existence with AV where it wouldn't have happened under FPTP?

True. But it could also do the opposite. Depending on where people live and how they intend to vote (and especially considering the weakness of the Lib Dem vote) it could be that the Lib Dems win more of their seats from the Tories under AV, and on top of that the Lib Dems being a weak force could mean their supporters transferring more votes to Labour to force Labour wins where the Tories would have won with FPTP.

Far from increasing coalitions, this increase in Lib Dem seat numbers would at worse mean that there is no change in Labour's majority, and at best mean that Labour also end up increasing their majority because of the transfers and support they get.

Take 1997. Studies (flawed as they are with lack of true information) show that the Lib Dems would have picked up an extra 69 seats with AV, more than doubling their result under FPTP. Coalition causing? hardly, because the shift in mood towards Labour was so large, so popular, that Labour also would have gained an extra 26 seats, with the Tories losing 95 seats more than under FPTP. In doing this Labour's majority, already large, would have grown in 1997 under AV, a hung parliament even further from reality.

EDIT: For the hard of thinking, an increase in Lib Dem seats, if it happens, will only cause a result closer to a hung parliament than FPTP if it wins more seats off of the LEADING party than the leading party wins off of every other party. It is entirely possible for the Lib Dems to increase their seats and make no difference to the resulting majority if they win all of their seats off the second placed party (in net terms, that is, they could win seats off the leading party too, but the leading party wins just as many seats off of the second placed party too). It could still result in a result FURTHER from a hung parliament than FPTP if the separate measure of how many seats (net) that the leading party wins is increased too. An increase in one party's seats, when talking about three main parties, is only one half of the equation.

The reality is that AV promotes popular governments to be stronger than in FPTP (increasing the majority, weakening the chance of coalitions) and weakens unpopular governments (decreasing the majority, increasing the chance of coalitions). In basic terms, AV only delivers a greater chance of a hung parliament when the country as a whole isn't pulling strongly in one direction for one of the top two parties or another, when the country as a whole is saying it can't decide on one party to be an out and out winner.

The fact that Lib Dems are increasing in numbers plays a very small, tiny, part in whether a coalition is needed or a hung parliament occurs. Much more important is which way transfers go, to the Tories or Labour, this is more to do with how popular Labour is versus the Tories and vice versa.