The uncertainty principle. A step by step guide to handling confusing polling in your betting

# The Alastair Meeks Decision Tree

You can access the descison tree here

The EU referendum polling is all over the shop, with a stark divide between the phone polls, which show a clear Remain lead, and the online polls, which show it neck and neck with Leave perhaps fractionally ahead.  How on earth are we supposed to cater for this in our betting?

Here’s how.  We only need to assess two things: what the current state of public opinion is between Remain and Leave; and how it will move in the next month.  True, we don’t know either of those things.  But we can guess.  Or, more helpfully, we can guess what probabilities to assign to the different possibilities.

Above is an example of just such a set of guesses.  First of all I’ve identified five scenarios:

1. All the polls are understating Remain’s lead
2. The phone polls have got Remain’s lead right
3. Remain’s lead is somewhere between the phone polls and the online polls
4. The online polls are accurately recording the battle
5. The online polls understate Leave’s lead

And then in each case I’ve assigned probabilities that the position will change sufficiently to change the result, or not.

In the example above I’ve tentatively concluded that the phone polls might be more accurate and a bit more firmly concluded that the final month might see a swing to Remain.  Mathematicians need not trouble to correct the workings underpinning my implications: there are enough heroic assumptions going on in this already.

By totting up the probabilities of all the green boxes, you reach an overall chance of a Remain victory of 77.7% (or 2/7 in betting terms).  But frankly, I’d be delighted if I were accurate to the nearest 5% either way.

I do NOT (please note the bold and block capitals) hold this example out as either my own estimate or being particularly scientific.  You can alter these assumptions according to taste, and you should do so.  But you should assign probabilities to all these possibilities.  When the pollsters themselves tell you that they don’t know what’s going on, you shouldn’t assume beyond question that the online polls are right and the phone polls are wrong, or vice versa.

Feel free to play around with this as you wish.  At least this should give some structure for people to think about the notional odds that they choose to assign to the two sides’ prospects of success.