What are the chances?

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Flamingods

St Stephen’s Church

1 Saint Stephens Lane

Ipswich, Suffolk

IP1 1DP

23rd February 2024

You walked into the party like you were walking onto a yacht

Carly E. Simon

“But you are traffic”, I was gently chided after moaning (sanctimoniously and again) about the number of cars heading into town this evening and causing the jam of which I was now very much a part. Of course, this happens every rush hour, and, of course, I should have left earlier; but I took some slight solace in knowing that trying to take a different route would, most likely, not have got me to the gig any quicker. That’s because I was simply obeying Wardrop’s first principle, as named after its originator, the English mathematician and transport analyst, John Glen Wardrop who, after a stint at British Bomber Command during WW2, helped set up and then headed the (now privatised) Traffic Section of the Civil Service’s, Road Research Laboratory. But only slight solace because Wardrop’s first principle which he defined as:

The journey times in all routes actually used are equal, and less than those that would be experienced by a single vehicle on any unused route.

is also know as the "user or selfish Wardrop equilibrium" as it becomes established when each driver chooses the route that they perceive is the best for them, and them alone, under the prevailing traffic conditions. After everyone has successively adjusted their route choices in this way, an equilibrium is reached when no one can improve their travel time any further through unilateral action. In simple terms that means, left to our own devices, each of us will act in self interest to try to reduce our own travel time and costs, even if that means ultimately – as it inevitably does - sitting in congestion. However, everyone’s journey time, irrespective of route, is equal. To deviate from these user equilibrium routes would simply increase your own journey time, making you even later for wherever you needed to be ten minutes ago.

I shall be telling this with a sigh

Somewhere ages and ages hence:

Two roads diverged in a wood, and I—

I took the one less traveled by,

And that has made all the difference.

Robert Frost: The Road Not Taken

So what’s the alternative? Well, Wardrop saw that question coming with his second principle – also known as ‘system optimal’ or more prosaically, "social Wardrop equilibrium" which, when/if achieved, means the average journey time is at a minimum, rather than the selfish equilibrium where all journey times are equal, even though that may be longer. To establish social equilibrium, all users would have to behave co-operatively in choosing their routes to ensure the most efficient use of the whole system. But what does that need for it to happen? Well, most people could still use the wide, faster road into town, but a smaller number of people would have to travel for longer on minor streets to avoid causing congestion on the wide road and so ensure the most efficient use of the whole system. We all know, though, that’s not going to happen without, for example, some kind of omnipotent – almost certainly political and unpopular - central routing authority dictating route choices, perhaps by marginal cost road pricing or designated days/times for certain subgroups to use the faster route? It’s certainly not going to happen without such controlling oversight, as proven explicitly by that bloke in the Audi who’s just selfishly charged up the outside lane, even though he knows it’s shut in 400 yards meaning he’s going to have to barge his way into the queue of patient and polite drivers in the open lane. But he’ll get to wherever he’s going quicker his way, even though he’s slowed all of us up.

The potential fall in efficiency from social to selfish equilibria is an example of the so-called, price of anarchy, as described in economics and game theory but easily extended to other systems. In the case of my getting into town for the gig, the price of anarchy is the ratio between the time my journey would take if it were made according to Wardrop’s first or second principle. And here’s where our second mathematician and third equilibrium comes in. John Forbes Nash, Jr. (John Nash) was an American mathematician who made fundamental contributions to game theory, geometry, and partial differential equations. Nash was awarded the 1994 Nobel Memorial Prize in Economics but is probably better known as the person portrayed by Russell Crowe in Ron Howard’s 2001 film of Sylvia Nasar's book, ‘A Beautiful Mind’.

In game theory, the Nash equilibrium is the most common way to define the solution of a non-cooperative game involving two or more players where each player is assumed to know the possible equilibrium strategies of the other players, but no one has anything to gain by changing only their own strategy. Nash reasoned that you can’t predict the choices of multiple people (‘players’) by analysing their decisions in isolation, but instead you must consider what each person would do through their expectation of what everyone else would do and expect them then not to change their mind. Wardrop equilibria are essentially applications of Nash’s equilibria but played at scale, being related to the larger size of the ‘game-playing’ population (drivers), many more alternative strategies (roads) plus the potential for congestion, such that the action of any single individual has no influence on the population average.

“Sounds like a party in the desert where everyone’s invited”

Loud And Quiet

The most classic example of a pure strategy, Nash Equilibrium is the two-player, two-strategy game, such as the Prisoner’s Dilemma or the Stag Hunt. Taking the Stag Hunt as our first example; here, two very hungry players must choose, independently, to hunt either a stag or a rabbit. The stag provides considerably more meat than a rabbit. However, whilst a rabbit can be hunted alone, the stag can only be hunted cooperatively, so if one player chooses to hunt stag when the other chooses to hunt rabbit, the stag hunter will totally fail and go hungry, whereas the rabbit hunter will catch and get to eat a rabbit. If they both choose to hunt rabbit, they will both catch a rabbit each to eat. Consequently, each hunter’s optimal strategy depends on their expectation of what the other hunter will do. If one hunter trusts that the other will hunt stag, they should also elect to hunt stag. However, if they think the other will hunt rabbit, they should also choose to hunt rabbit. This is an example of social cooperation whereby many of the benefits an individual gains from being in a society depends upon cooperation and trust with everyone acting in a manner corresponding with cooperation.

But what would you do? Let’s try the Prisoner’s Dilemma. You and someone that you have no loyalty to are arrested on a charge. Unbeknown to you, the police have no evidence for a major charge and agree that looking to get you both a one-year sentence on a lesser charge would be a good outcome for them. However, they try this first. Both of you are isolated and told that if you testify against the other prisoner, you’ll be let off free and the other one will get three years for the major charge. However, if you both testify against each other, you’ll both get two years each. If neither of you testify and stay silent, you’ll get one year each on the lesser charge. Your only concern is to minimise your sentence. So what do you do?

Hmmm …

In this scenario, and counter to what may provide you with your more optimal outcomes i.e. going free or getting just a one-year sentence, the only strong Nash equilibrium in this scenario is where you both testify against each other and get two years each. This is because regardless of what the other person decides, you both get a higher reward by testifying against the other. Why? Well, the other prisoner can only either stay silent or testify. If they stay silent, you should testify, as going free is better than serving 1 year. If, however, the other prisoner testifies, you should also testify, as serving 2 years is better than serving the 3 years you’d get if you stayed silent. So, either way, you should testify since testifying is your best response regardless of the other prisoner’s strategy. Parallel reasoning will show that the other prisoner should also testify. Testifying – or defection - always results in a better payoff than staying silent – or cooperation – and so it is a strictly dominant strategy for both players. Mutual defection is therefore the only strong Nash equilibrium in the game. Since the collectively ideal result of mutual cooperation would be irrational from a self-interested standpoint, this Nash equilibrium is not the best possible outcome for either prisoner.

Another oft quoted example is doping in sports. Taking drug X improves performance and can confer advantage to the athlete taking it, but only if the other athlete does not - albeit with some personal legal/medical risk to the drug taker. If neither takes the drug, neither gains advantage. If both take the drug, again neither gains advantage but both are now at risk and in a worse position than if neither had taken it.

More critically for us as a species, this kind of ‘dilemma’ scenario often plays out at an international level. Take for instance the impasse often seen at global conventions to discuss crises such as climate change. Clearly, all countries would benefit from a more stable climate, but any single country is often hesitant to curb their own carbon emissions, as the maintenance of their present behaviour is deemed more beneficial to themselves than the purported eventual benefit of all countries changing their behaviour. Better to be free than have two years in prison. The difference between the Prisoner’s Dilemma and that of the climate politicians, however, is one of uncertainty. The prisoners’ or indeed the hunters’ payoff for collaboration is easily iterated and readily understood; that for cooperation around climate change much less so. Consequently, there is even less rationale for Governments to cooperate, so further reducing our chances of avoiding the global catastrophe that is very much heading our way.

So anyway, I make it to the gig being held in the beautiful surroundings of St Stephen’s Church in Ipswich. Sadly, I’ve missed the support act but I’m in plenty of time to grab a beer and find a spot to watch the Flamingods on the East Anglian part of their UK tour. The band do not disappoint. The Bahrain-raised and London-based psychedelic-rock four piece display their multi-instrumental talents with three of the band members gradually revolving around frontman, Kamal Rasool, and his eclectic selection of instruments from the Middle East and Asia (think tabla drums and pungi woodwind) to each take up a range of guitars, drums and synthesisers, whilst playing tracks from their back catalogue as well as the brilliant new album, Head of Pomegranate. Trippy, fuzzy and danceable, but above all great fun and an impressively tight set. It shows that these boys have been together since they were 16 years old. A great night out and potentially a brilliant night out; save for the people around me. “You are traffic” I recall, but I’m certainly not the one to my left shouting to the girl they’re trying to impress, raising my volume each time the band plays louder. Bring a mate, not a date! Nor am I the guy wearing a rucksack (!) and standing dead still to the right of me. I’m also not the person directly in front of me, raising their hand high into the air to record the entire show on a phone. I think, why me? It certainly doesn’t seem random that wherever I stand at a gig, or even at the football, I’m always right by the loudest, most annoying person in the crowd. Or is this just an odd case of confirmation bias whereby chance coincidences happen more often than you might expect due to the direct influence of desire upon beliefs. Can it be as simple that because I expect to be surrounded by annoying people, I end up believing that to be true? Like a sort of inverted wishful thinking! Am I just confirming my own prejudices and so becoming a ‘prisoner of my assumptions’? Given that confirmation bias is strongest for desired outcomes, for emotionally charged issues, and for deeply entrenched beliefs, as well as being fairly insurmountable for most people, the answer is probably, yes! It’s not too much of a problem for me at a gig but can lead to serious outcomes for example in police investigations and medical diagnoses. Let’s be clear though – my gig experience is not a behavioural confirmation effect, the so-called ‘self-fulfilling prophecy’, whereby one’s expectations influence your own behaviour to bring about the expected result. That is, I don’t wonder around at a gig until I find the most annoying person and then stand next to them!

The most difficult subjects can be explained to the most slow-witted man if he has not formed any idea of them already; but the simplest thing cannot be made clear to the most intelligent man if he is firmly persuaded that he knows already, without a shadow of doubt, what is laid before him. Leo Tolstoy

That all said, there’s no doubt that audience behaviour seems to be getting worse. There is a theory that things have got worse since the pandemic, because audiences became de-socialised by lockdown. Dr Kirsty Sedgman of the University of Bristol notes how during lockdown we got increasingly used to policing each other’s behaviour and calling out bad behaviour, leading to aggressive responses by those being called out. She notes that we were also starved of “cultural effervescence – the opportunities to ‘engage in and experience collective joy, sociable joy’. Thus, what we are experiencing as bad behaviour at the theatre or at concerts arises from a renegotiation by audience members of what it means to be part of a collective. But it’s likely poor behaviour goes back much further than that and we are now just experiencing the amplifying, echo chamber - confirmation bias - of social media. There is also no doubt, that some of the publicity around the ‘incorrect behaviour’ at cultural events arises from anxiety felt by traditional audience members (think, white, think middle-class) as a new, less elite, more representative audience begins to attend such events in number. But there is no doubt that, as actress Lucy Eaton states, “There were some appallingly behaved people before, just as there are now.” Perhaps even worse: in the 1840s, a rivalry between two Shakespearean actors, England’s William Charles Macready and the American Edwin Forrest, involved Forrest’s fans throwing “half a dead sheep” at Macready during one stage appearance that culminated in the Astor Place Riot leaving over 22 dead. Certainly, my getting annoyed by someone wearing a rucksack to a gig pales against that, but, nonetheless, it does seem that we should reconsider gig etiquette.

So what’s the correct behaviour? My personal experiences from going to the football could summarise what’s needed by the simple chant of “Sit down, shut up” but that likely won’t easily translate to a gig where the audience isn’t split into two sets of fans. No, better would be to take advice from musician, Lucy May Walker whose three, I believe very reasonable, and gently made points were:

• Don’t talk during the show (in an intimate setting, even the band can hear you)

• Be in the moment (take a few photos / short video; turn your flash off; don’t block anyone‘s view)

• The audience have not paid to see you (read the room before singing along; if you must leave, wait till the end of a song)

Needless to say, she received some backlash from – I presume those folk who prefer Wardrop’s first principle – who felt her request to be condescending with some going as far to say that if she didn’t like it she should “stay in her bedroom, sing there and stream it”. But all she was wondering was why anyone would buy a ticket to a show and then talk through it. I agree. Why not write off the cost of the ticket and go to the pub instead? Or hang out at the bar? Long time, music journalist, Simon Price, says that behaviour at gigs has been getting objectively worse and believes Lucy May Walker might not have gone far enough and advocates a zero- tolerance approach to transgressors. He recalls a time when such transgressions were self-policed and obeyed an unwritten code and summarises his points under the catch-all rubric of Don’t Be a Selfish Idiot. He puts the change down to two things: narcotics and narcissism, driven by the proliferation of Class A drugs and a ‘me-me-me’ culture where many people don’t so much want to be at the gig as want to be seen at the gig.

In an atomised society, all anyone cares about is their own pleasure. Simon Price

Price acknowledges the counterintuitive aspects of making rules for liberating spaces where self-expression and abandon should be permissible but accepts that the time has arrived for a more militant approach and his three principles are:

1. Shut up

2. Put your phone away

3. Don’t be a dick.

Fortunately, however, he signs off his code with ‘Break At Least One of These Rules. It’s rock’n’roll, not the ballet’, thus providing me with the escape clause needed to secure my memories to the cloud and subsequently to this blog. So next time you go to a gig think how nice it would be if everyone might be able to have stag for dinner and next time an Audi speeds up next to you just think “Don’t be a dick!”.