Brexit and Arrow’s impossibility theorem

Politics in the UK has been on a rollercoaster ride in the last few weeks over Brexit. There have been many high profile cabinet resignations by ministers who are unhappy with the proposed Chequers plan.  Brexiteers and  Remainers, who are bitterly opposed each other, have managed to find one thing that they do actually agree on. They both vehemently reject the proposed compromise in Theresa May’s Chequers plan for the transition period. Note that this is just the transitional agreement, not the final agreement that will govern the ongoing relationship between the UK and Europe in the future.  For that, we can look forward to another two years of negotiation, political fighting and uncertainty. 

Arrow’s Impossibility Theorem

This turmoil supports the truth of Arrow’s Impossibility Theorem. This states that it is actually not possible to fairly combine peoples wishes into the right outcome. The view of the people can not be forged into a single coherent view. In other words, what the British people want will always be different from what Britain wants.

Kenneth Arrow, a Nobel Laureate, set up three criteria for ‘fairness’ in an electoral system and then demonstrated that no system can be designed that will satisfy all three of these. His criteria were :

  •             If every voter prefers X over Y, then the group prefers X over Y. 
  •             If every voter’s preference between X and Y remains unchanged, then the group’s preference remains unchanged 
  •           There is no ‘dictator’: no single voter possesses the power to set the group’s choice. 

I won’t go into the maths – you can look it up for yourself here on Wikipedia. It all hinges on the fact that there is a pivotal voter who tips the balance and therefore determines the outcome. So that pivotal voter is, in effect, a dictator: what he says goes.  

This mismatch between the voting public’s wishes and the higher level group outcome is a good example of catataxis. We can sum it up in the catataxic maxim :

“As above, not so below”

What happens at the group level is often the opposite of what is happening at the individual level. 

Plus ça change, plus c’est la même chose

We can draw another example by considering the differences between the American Revolution (1775) and the French Revolution (1789). Both happened within 15 year of each other but they had very different outcomes. The Founding Fathers in America made sure they built in checks and balances to the constitution to prevent any dictator emerging. In other words, conflict and argument were baked in at a lower level to guarantee stability at a higher level. 

In contrast, the French Revolution decapitated the state but did not redistribute its powers to other lower entities. So, in effect, the state was still a monolithic structure. This then led to the rise of Napoleon as a dictator followed by the Bourbon restoration which took them back to where they started. 

So maybe the optimistic conclusion to all the Brexit furore is that this vehement disagreement is  necessary. It is the messy process of democracy that guarantees a stable, unified state at the end.    At a higher level, it certainly seems to have pulled the EU together into a more coherent whole, judging by the unanimity from their side of the negotiating table. 

The law of large numbers and the meaning of life

Entropy and life

The Law of Large Numbers is a cornerstone of statistical science. It says that, while it is very hard to predict things on an individual basis, it is much easier to predict things on an aggregate basis once you have enough individuals in the group. The whole statistical toolbox of bell curves, averages and standard deviations exists to offer accurate predictions of random events using the law of large numbers.

For example. I can’t tell you the exact height of the next person to walk through the door but I can confidently say it will be between two standard deviations of 1.78 meters if it is a man and we are in the UK. So, in effect, a random event at the micro level yields a predictable outcome at the macro level.

As above, NOT so below

Consider gamblers in a casino. While it is possible for an individual gambler to get lucky and win big, in the long run the casino will always win because the odds are in its favour. This is the essence of the law of large numbers. A huge number of unpredictable micro events produce an overall system is very predictable. What is more, the larger the system the more predictable it becomes. The key criterion is that the individual events are truly random; that they are not correlated at all. In the casino example, this means that the gamblers are not colluding with each other (or with the dealers) and that the cards or roulette wheels have not been rigged. In mathematical terms, this is expressed as “the system must have independent variables”. So the ‘order’ at the macro level depends on randomness or ‘chaos’ at the micro level which is summed up in the catataxic maxim :

       “Order requires Chaos”

The macrostate and the microstate

This ‘order above, chaos below’ concept was central to the development of Statistical Thermodynamics, one of the crowning achievements of 19th Century Physics. Ludwig Boltzmann managed to forge a link between Newton’s laws of motion and the evolving field of thermodymnamics which examined pressure and temperature phenomena in steam engines. With his kinetic theory of gases, Boltzmann took a dualistic approach defining a ‘macrostate’ and a ‘microstate’ in a catataxic separation of reality.

The macrostate was the description of the whole system, observable by measuring the pressure and temperature of the gas. The microstate was was a description of the gas as a large collection of molecules all in constant, rapid, random motion. By viewing these particles as Newtonian ‘billiard balls’ banging against each other, he was able to derive the macrostate laws of temperature and pressure from the microstate motions of these particles. The pressure of the gas derived from the sum effect of these particles banging against the side of the gas container. But he could only do this by assuming that the particles were random: that interactions between them were negligible except during collisions.

You are just an eddy of entropy

This macrostate/microstate approach led to one of the most important theories in Physics : the Second Law of Thermodynamics. This states that the entropy of the universe must aways increase. Things naturally tend towards a state of disorder. At first glance, this seems to be inconsistent with our experience. How do you explain the evolutionary development of complex creatures such as animals from the primordial soup if the natural tendency of the universe is towards disorder ? The answer to this paradox also lies in changing the frame of reference. Take a catataxic step upwards and look at the bigger macro picture.

Imagine two metal plates, one hot and one cold in a bath of water. As they are different temperatures, the second law of thermodynamics states that heat will flow from the hot one to the cold one until they are the same temperature. This represents the highest state of disorder (maximum entropy) because there are no local ‘pockets’ of difference which would represent some sort of structure. Everything has become uniform and the system as a whole has achieved equilibrium.

Entropy and life

If the temperature difference between the two plates is very extreme, then you might the heat flow by convection rather than simple conduction. In other words, convection cells as in Fig.3 above could spontaneously arise in order to make the transfer of heat more efficient and drive the system towards equilibrium faster. This is an example of structure naturally emerging at a local level to speed the progress towards maximum entropy. An increase in order in the microstate facilitates a decrease in order in the macrostate. As above, not so below again.

So here, at least, is one answer to the meaning of life. Life on earth exists to drive the solar system towards maximum entropy. In the metaphore above, life is the ‘convection cell’ that has spontaneously arisen in order to dissipate the heat of the sun (the hot plate). This is why  the greatest diversity of species occurs where most of the heat of the sun falls – near the equator. If you have ever wondered why you are here, now you know. You are just a little eddy of entropy that exists to dissipate sunshine. Now get out there and start tanning….

If you build it they won’t come

I was working on a local history project in Kent (where I live) when a friend gave me some old photos. They showed men in frock coats handling hops on long trestle tables. These are city workers handling an agricultural product. It took me some time to track down where the photos were taken.  It turns out they were hop factors in the 1920s, working in 15 Southwark Street opposite the Hop Exchange in London.

The vanished hop trade

The hop trade was once a major industry in Southwark. Back when there was only one bridge over the Thames (London Bridge) everyone passed through  Southwark . Its coaching inns and breweries have been famous since Chaucer’s time; this is where the pilgrims gathered before setting off for Canterbury. There was plenty of traffic up the other way too. Kentish hops, grown in the Garden of England, came up the A2 and the Old Kent Road to the market traders in Southwark Street, around the corner from Borough Market.
The hops were dried in oast houses and then tightly compressed into 6 foot sacks called ‘pockets’ and sent up to the middlemen, known as hop factors, in Southwark Street. Each load was sampled by cutting a foot square brick of pressed hops out of one of the pockets. This cube was wrapped in brown paper and secured with brass chair nails. Samples from a particular grower were all strung together with waxed hemp.

Another set of middlemen, the hop merchants who acted for the brewers, came to inspect the samples. These photos show the merchants (e.g. man in top hat on left) examining the hop samples displayed by the hop factors. The room is starkly functional. A big glazed roof lets in plenty of natural light to help the inspection and a big clock to measure opening and closing times. Nothing else. No decorations at all. After all, this is a serious place of business.

Three factors kill the trade

Hop production peaked in Kent in 1878 and has been declining ever since. Kentish hop varieties, such as Fuggles and Goldings, add bitterness to beer and ales, whereas German hops have low bitterness and strong aroma and are used for lager. So a number of trends conspired in the decline of the Kentish Hop industry. First was the trend towards lager over bitter. Second was the decline in exports as Australia and South Africa began growing their own hops. The third blow came in 1973 when Britain joined the Common Market and cheaper continental hops wiped out most of the growers in Kent.

Bomb damage in WW2 meant that many warehouses were rebuilt in Paddock Wood in Kent and the hop merchants moved what was left of the industry down there in the 1970s.The last hop merchant, Wolton Biddell in Borough High Street, closed its doors in 1991. All the buildings have been redeveloped. The area around London Bridge and Borough has become one of the hottest development areas in London as evidenced by the Shard, Europe’s tallest building. The old Hop Exchange has become a general purpose office building.

A magnificent open outcry design

But what a beautiful building. Opened in 1867 and designed by R.H.Moore it is now Grade II listed. When you step inside you can see the vast open atrium and the three tiers of balconies overlooking it. It is designed to allow ‘open outcry’ ; traders on the floor, merchants on the balconies shouting their orders back and forth to each other. Its just like the old stock exchange before it became computerised, or the Royal Exchange where futures were once traded but which is now an upmarket shopping mall. The Lloyds Insurance building has the same “atrium and balcony” design, letting all the brokers hear the stroke of the Lutine bell to inform them of bad news. In the hop exchange, all the balconies bear the crest of Kent – a white horse on a red shield – to remind occupants that this is the trading place for Kentish hops.

I live opposite a oast house and travel to London Bridge every day. The oast house across the road from me has been converted to a spectacular county home. My daily journey encompasses the agricultural history of Kent both at the beginning and end; from an oast with no hops to a hop exchange with no brokers. A palace for a product that no longer exists. There are plenty of brokers getting off the train at London Bridge these days, but they are not broking hops any more but financial products instead.

If you build it, they won’t come

You may be wondering where the catataxis comes in all of this. This tale is not just a personal trip of nostalgia, because there is one more twist to the story: the hop exchange was never full of brokers. The Victorian developers built it in a burst of progressive optimism hoping to capture and consolidate the hop trade inside its walls. But the hop factors and merchants already had their own various premises and saw no reason why they should move. So the hop exchange has only ever been a general office building and not a commodity exchange at all.

The Victorians were keen on making the abstract concrete. Think of the statues of “Trade” or “Progress” that adorn Victorian metropolitan buildings. These are industrial versions of the ancient Greek muses; abstract concepts in female form. The Hop Exchange was an attempt to cast economic activity in architectural form. Sadly, it did not work. This building designed to house speculators was itself a speculative failure. This was a catataxic blunder. Just because a building exists at level 1 does not mean that the trade at level 2 will be captured by it. In this case, the motto is: if you build it, they will not come.

Markets are a bottom up phenomenon; a spontaneous eruption of emergent behaviours. They can not be created top down. Building a building to try capture that magic is a s fruitless as running around trying to capture lightning    in a bottle. That does not stop people from trying. The latest disaster in the making of this type is the King Abdullah Financial District in Riyadh, Saudi Arabia. Some $10bn has been spent building 59 skyscrapers in an attempt too lure international banks into the desert.  These hopes are built on sand.