There’s a great piece in The Independent, Random acts of madness: all the things that Dominic Cummings is getting wrong about game theory, by Abhinay Muthoo a Professor of Economics and Dean of Warwick in London.
Game Theory, while observable in many economic experiments and real world events, relies heavily on a narrow scope of influence with all the players. The Theory tends to be seen after certain events, based on the economic principals of “self interest” in all the players or in controlled experiments that aim to understand more about decision making.
So it’s no surprise that Dominic Cummings, adviser to UK Prime Minister Boris Johnson, was firstly incorrect to have used Game Theory so pervasively as part of the Vote Leave campaign and then into his role in Government and incorrect in exactly how he set up his ‘experiment’.
Firstly, if you were an economist and were asked to construct a model based on a vote for exiting the European Union you would need to build up knowledge of the key players. As Muthoo suggests in his piece, Cummings failed to understand that one of the players was able to manipulate the game in a greater way than he could. This is a miscalculation in how weights play a part in a data modelling and comes from only a basic knowledge of how Game Theory works.
The classic Prisoners example involves two prisoners who know that if both confess, they will have the lowest jail time, if the other prisoner confesses and they don’t, they’ll get a higher term than the other and vice versa and that if both deny they’ll have the maximum sentence. It’s a classic risk reward scenario and one that demonstrates how, in theory, individuals and businesses make decisions based on risk/reward and their knowledge of the other players.
The issue with the Cummings interpretation is that he put no weight on the risk to the UK versus the risk to the EU. “It’ll be worse for them than it is for us” is loosely valid when the stakes for all players are the same, but when one player can take a hit and another can’t then the weights of decisions change. In business we can see some enterprises taking a large risk financially because the rewards will match that risk, whereas another player can’t afford that risk even if they compete favourably with product and placement.
In Machine Learning, this kind of decision making or scoring can be determined with an Artificial Neural Network.
This sort of process, in various forms, is how banks approach loans, business approach credit worthiness and investment firms approach trades to name but a few applications. Rather than being a classic formula taking various metrics and classes and determining a score, Neural Networks and other ML methods take learning and determine certain weights to those variables to isolate the most possible outcomes (or risks). This is applicable to Game Theory until we get to that weight point.
Cummings aimed to create more risk to the EU than the UK, but used the same measure. “The EU won’t want to lose trade with the UK” was a common argument, but the weight for that variable for the UK was greater than for the EU. Basically, the UK had more to lose.
While an intelligent tactic, use of Loss Aversion, Cummings failed to apply an intelligent weight to some of those risk arguments. If an economist had been consulted and created a decent model, used ML to score the rewards against the risks, then that model would have told Vote Leave that they shouldn’t have even started their campaign.
And of course we know that the economic arguments wouldn’t have stood up on their own, hence why additional variables were added or given more weight by the campaign but not modelled, only used to win the vote itself. Looking beyond those variables and their weights, it was never going to be a good outcome for the UK.
Consider Loss Aversion. This is the concept used in advertising and various industries that suggests the emotion (to use the advertising definition) of losing something is greater than the emotion of gaining something. This is what has created free trials and free for x day promotions, because advertisers know that you’re more likely to spend money on something you have than something you never had, regardless of the strength of your pitch.
The Vote Leave campaign initially at least failed to include this as a variable. Their argument was “it’ll be better outside of the EU”. But that wasn’t quite enough – the argument for keeping the status quo on economic terms, even if not as strong as the Vote Leave plan for a post-EU UK, needed to be substantially more appealing to overcome that aversion.
So what do you do when confronted with Loss Aversion not working in your favour? You treat the status quo as a ticking clock that will eventually lead to a loss. And Vote Leave, along with tabloid media and various social media users, began the true Project Fear of the Brexit debate in which the UK public were told they risked using the Euro, being enlisted into an EU army, having more power over them sent to Brussels, etc.
Loss Aversion is a reason people wait a long time to sell homes, as an example. We wait and see if we can sell at the buying price at least, without thinking about cutting the losses. But imagine if you were told your house would be part of a compulsory buying order or would be devalued substantially for whatever reason – you’d be more compelled to cut your losses, and indeed to settle for less, because you had been given this ticking clock argument.
Vote Leave created a new variable during their campaign because they knew that the status quo typically won.
But while they won the referendum, their model (if one was used, and even with missing variables and weights), and their game theory tactic (which wouldn’t even be considered a valid experiment by economics), wasn’t compatible with an EU negotiation where their is a player holding more cards and chips of higher value than theirs.
In a Neural Network, whether not something happens or doesn’t happen is accompanied by a weight. If I plan a trip tomorrow, I’ll have many variables – can I afford the commute and is it expected to rain to use two possible ones. Now if using a typical model, I observe the probability of each outcome based on those variables, but whether or not I have the money is the highest weighted because if I can’t afford it nothing else matters. If it’s raining or not, I may still go out so that’s a minimal weight.
By approaching the EU using the same model with which they won the referendum campaign, they were applying the wrong variables with the wrong weights to the EU as a a player in the game. For the UK, getting a trade agreement with the EU was considered a “yes/no” alone, not a weight of 100 against anything else, and for the EU the weight was a lot less, because for the EU they may lose a market, but competition to UK businesses in the EU would welcome a country of competition disappearing and member states would welcome increased businesses setting up in their countries.
Think about that…the UK expected the EU to want a trade deal with the UK as much as the UK wanted a trade deal with the EU. They were told “no trade negotiations until you leave” (which is something they only had to ask about before the referendum), and for the EU they would actually benefit in other ways from Brexit.
The UK says “you buy from us, we buy from you” and makes that a 100 weighted part of their approach, the EU puts that as 50 because there’ll be less competition and greater opportunities for them within the single market.
Cummings used Game Theory to win a referendum, built a decision making model to follow that would convince voters to side to leave, determined that the narrative had to change because on its own the model suggested the argument to leave wouldn’t work because of loss aversion, then forgot to treat the EU as the top player in the game.
Do you have access to voting/polling datasets for the Brexit vote? Would you be interested in developing a model to show how the Vote Leave and Remain campaigns changed tactics based on that data? Get in touch at firstname.lastname@example.org.