Conventional wisdom on the next election result

This post is effectively a follow-up to a short passage in one of my previous posts.  In my summary of the various individual party seat markets, I compiled a tally of the par seat outcomes.  I then asked myself how stable that projected outcome was.  On reflection, I felt the answer I gave didn't have very much precision about it and I wondered whether I could do better.  So here goes.

Where are we now?

Once again I've looked at the constituency markets and totted up the favourites in all 632 mainland GB seats to derive the current par outcome.  I used the markets as they stood on Tuesday 25 November, so these are already a little out of date, but the nice thing about this exercise is that it doesn't really matter very much if one or two seats are different or if I've made the odd mistake here or there.  Here's the current state of play:

Conservatives: 273 1/2

Labour: 301

Lib Dems: 31

SNP: 16 1/2

UKIP: 5

Plaid Cymru: 3

Greens: 1

Speaker: 1

(I've attached links to the full tables underpinning this and the other tables in this post at the end of the post for the super keen, but they aren't really very interesting.)

As you can see, not too much has changed in the last couple of weeks.  Labour are some way short of an overall majority, but some way ahead of the Conservatives.

And how stable is that projected outcome?

This is where I've done a bit of further thinking.  Because bookies price in terms of odds, we can derive implied probabilities on the chances of an upset.  There are a number of different ways in which you can do this - looking at how short the favourite is priced is one way.  The method I have chosen is slightly different, but I hope more informative about the chances of all the parties in a seat, not just the favourite.

So I started thinking about confidence levels.  How sure are these seats of being taken by the favourite?  So I retested them, this time marking seats as sure things if the second favourite was priced at longer odds than 2/1.  If a bet is priced at 2/1, that means that the bookie is presenting this as a 33% chance.  But allowing for the bookie's profit margin, this overstates the probabilities in reality [EDITED TO CORRECT OVERSTATEMENT].  So if a seat has no second favourite at or below 2/1, we can treat the favourite as having a pretty fair chance of winning.

If there is a second favourite at or below 2/1, this is a true marginal.  I've presented the results in a tabular format, with the parties' range shown below:

	Conservatives	Labour	Lib Dems	SNP	UKIP	Plaid Cymru	Greens
Conservatives	238	48	13	0	5	0	0
Labour	48	257	5	24	2	1	1
Lib Dems	13	5	18	3	0	1	0
SNP	0	24	3	9	0	0	0
UKIP	5	2	0	0	3	0	0
Plaid Cymru	0	1	1	0	0	2	0
Greens	0	1	0	0	0	0	0
THREE WAY MARGINALS	1	1	1	0	0	0	0
TOTAL IN PLAY	238 to 305	257 to 339	18 to 41	9 to 36	3 to 10	2 to 4	0 to 1

I hope this table is reasonably comprehensible, but in case it isn't, here's how it works.  Each seat has been classified as a safe seat (in which case I have tallied it in the box on that table where the party faces itself - so there are 238 safe Conservative seats, 257 safe Labour seats and so on) or a marginal.  If, for example, the seat is marginal between Labour and the SNP, I have recorded it in both places where those parties meet on the table.  So there are 24 Labour/SNP marginals.  I have treated the Speaker's seat as a safe Conservative seat.

This table wouldn't work quite so well if there were lots of three way marginals, but fortunately there is precisely one seat where three parties are priced at 2/1 or less: Watford.

In the final line, I've put the range of seat outcomes that might be expected for each party, bearing in mind what the constituency markets expect to be seats that are in play in this range.

This table is much more informative than I had expected.  It shows that within this range, the Conservatives are nowhere close to an overall majority.  Labour might creep over the wire, but only if everything goes right for them.

That leads onto the next question: how correlated are the results in the different constituencies?  I suggest that the answer is different for different parties. 

Leaving aside the Greens, the simplest parties to consider are the SNP and Plaid Cymru.  Both will be fighting on their own patch and on their own terms.  Whether or not they succeed will depend on whether their public regard their own prospectuses as compelling or whether they are minded to vote for other reasons.  For the SNP, seat tallies near either 9 or 36 are serious possibilities, depending on the answer to this question.  I see these party's results as highly correlated between constituencies.

I see UKIP's prospects as correlated, but not as much as the SNP's.  Their poll shares do not seem related to local candidates but on the alienation of a substantial chunk of the public.  However, they do appeal differently to previous Labour voters and previous Conservative voters, and it is easy to envisage Labour and the Conservatives having differential success in resisting their appeal.  Most of the seats in this prospect list are currently Conservative held, so there will be substantial correlation.  But for all the enthusiasm of UKIP supporters and a wave of money backing them, the seat tally is not expected to reach double figures on the current market prices.

The Lib Dems' chances are correlated more loosely still.  They campaign as local candidates, and this shows up in Lord Ashcroft's two stage polling in constituencies, where prompting for constituency matters gives the Lib Dems a big boost in seats where they have strong incumbents.  The correlation becomes stronger at the bottom end of the range.  They will start losing a lot of seats if the incumbency sandcastle cannot keep out the waves of national swing.  Incidentally, it is worth noting that the differential performance against Labour and the Conservatives is already largely priced in: Lib Dem held seats like Redcar, Norwich South and Burnley are already in the safe Labour column for 2015.

At the other extreme, we have Labour and the Conservatives.  The Conservatives are fighting on three fronts: UKIP, the Lib Dems and Labour.  These are three very different battles.  It is hard to imagine the Conservatives doing uniformly well against all three, though less hard to imagine them doing uniformly badly.

Similarly, how Labour perform against the SNP has almost nothing to do with how it will perform against the Conservatives or UKIP.  It is conceivable that Labour might sweep the board against both the Conservatives and UKIP even as it flounders against the SNP.  For Labour to get over 326, it would need more or less everything to go right in both of these essentially uncorrelated battles.  That's not a 2/1 shot, that's something closer to a 5/1 shot or longer (and that's accepting the 2/1 bar at face value).

Can you test this stability further?

Indeed I can.  I've also had a look at the position if we use the test of marginality as a seat having a second favourite that is priced at 5/1 or less.  That implies that the second favourite is a 1 in 6 shot, which again is likely to be on the high side, allowing for the bookie's profit margin [EDITED TO CORRECT OVERSTATEMENT].

Here's the equivalent table using that looser test:

	Conservatives	Labour	Lib Dems	SNP	UKIP	Plaid Cymru	Greens	Respect	NHA
Conservatives	197	94	31	0	11	0	0	0	1
Labour	94	205	10	42	5	3	2	1	0
Lib Dems	31	10	2	5	0	1	0	0	0
SNP	0	42	5	6	0	0	0	0	0
UKIP	11	5	0	0	0	0	0	0	0
Plaid Cymru	0	3	1	0	0	1	0	0	0
Greens	0	2	0	0	0	0	0	0	0
Respect	0	1	0	0	0	0	0	0	0
NHA	1	0	0	0	0	0	0	0	0
THREE WAY MARGINALS	13	10	8	4	10	0	0	0	0
TOTAL IN PLAY	197 to 347	205 to 382	2 to 57	6 to 57	0 to 26	1 to 5	0 to 2	0 to 1	0 to 1

This table gets more complicated for two reasons.  First, there are more parties in the mix.  And secondly, there are far more three way marginals: fifteen, in fact.  But I think it is still useful.

As you can see, the range of outcomes has got much wider.  At this level of testing for marginality, the SNP could worry about taking only the 6 seats they already hold - or dream of taking every seat in Scotland.  Either the Conservatives or Labour could have a healthy overall majority or a crushing defeat.

Things look a lot less stable at this level of confidence.  It seems that conventional wisdom is not so certain after all.

Perhaps.  But I come back to the point I made earlier on about correlated contingencies.  For example, it's a hell of a lot more likely that the SNP will tally 57 (or 6) seats than that Labour will tally 382.  The graph of possible Labour seat tallies would look curiously lumpy, with different correlated contingencies interplaying with each other in a largely uncorrelated way.  Either a Conservative or a Labour overall majority look to be firmly outside chances.  Equally, both major parties look most unlikely to suffer a Götterdämmerung.

Some betting observations

If you buy into the conventional wisdom on the seat markets, backing a hung Parliament is a complete no-brainer at any price north of 1/3 and probably shorter.  If the conventional wisdom of the seat markets is right, only Labour look in with any kind of a reasonable shout at an overall majority if the conventional wisdom is correct, and for the reasons I've given above, the odds on that should be long.  Dreams of a Conservative overall majority look to be just that: dreams.

Generally, I think the middle table is the best to work off.  It shows the range of reasonably expected outcomes.  The looser definition of marginals is, however, useful for understanding where the outer risks are.

I've always been keen on betting on a hung Parliament.  I'm now getting very keen indeed.  I've topped up again at 8/15 with Ladbrokes.

If you back any outcome other than a hung Parliament, you should be looking for long odds.  After all, you're going against the conventional wisdom of the seats markets.  You might want to consider the 326-350 seat bands for Labour or the Conservatives, since the odds of either going past 350 look very distant indeed right now.  These are not bets that I'm going to place though.

That's not to say that you wouldn't right to ignore conventional wisdom.  My view is that the markets are underestimating the volatility of seats on low poll shares for the major parties.  As it happens, my view is also that volatility in individual seats will probably cancel itself out in large parts, but you could reasonably take a different view. 

However, volatility for the SNP or UKIP will probably not be self-cancelling: both of these parties might either soar like rockets or fall like sticks.  Because the fortunes of the SNP and UKIP are pretty much completely uncorrelated, we could see both do the same thing at the same election.  At present, the SNP look more likely to sweep the board than UKIP, but I don't completely rule out the idea of a UKIP horde descending on Westminster.

There are a few more easy bets to make.  The SNP are currently 8/15 to win most seats in Scotland with Ladbrokes (or 5/6 over/under 25.5 seats).  You can instead buy the SNP at 21 on Sporting Index.  Using the 9 to 36 span shown by the middle table, you risk losing 12 or gaining 15 with a par point in the middle of 22.5 seats so it is effectively an odds against bet instead of an odds-on bet.  Yes, the best guess of conventional wisdom on the constituency markets is currently 16.5, but the seat markets are scrambling to catch up with the new reality of post-referendum polling.  On this one I prefer to trust the general markets right now (in particular, the prices in Glasgow and the surrounding area still don't reflect the likely impact of the Yes vote in that city on the SNP's chances).  If you can't stand it, pair the SNP buy of 21 with a bet on Labour most Scottish seats at 11/8.  One of these bets must win and both might.  Personally, I'm just buying the SNP.

UKIP next.  I pause, because I've been a persistent UKIP bear, only to be caught out by the markets repeatedly this year.  But the 1/3 that UKIP will tally under 19.5 seats with Ladbrokes looks very sound.  Even on the wider test of marginality, their upper limit looks to be 26.  I'm on.  Selling UKIP on Sporting Index at 9.5 is a good bet too - but be aware that if UKIP do soar like rockets, this bet might look very sickly - and expensive.  This is not impossible, and is inherently more likely than, for example, the Conservatives exceeding the top end of their range, because of the points I have made about correlated contingencies.

I intend coming back to these tables repeatedly in my betting.  I shall be worrying when I depart too radically from them. 

Footnotes for the super keen

Here are the detailed tables underpinning the summaries set out above.  In truth, they're not very illuminating, but I feel I ought to at least make my workings available.

https://drive.google.com/file/d/0Bygi8eZw-4q1TWEyeHZES19DMXMwSDFBZVRILUhmOUdWbG9V/view?usp=sharing

https://drive.google.com/file/d/0Bygi8eZw-4q1OE1YY1NTQk5IbEt2NExJd2ExQlJxTW5RakZN/view?usp=sharing

https://drive.google.com/file/d/0Bygi8eZw-4q1TW9ReTlsWEZPR2VsV1VUR0pFdXpPV2xNeXlF/view?usp=sharing