Author Archive

Habits of ‘Ƭ-rational’ Obedience during Covid

The Prisoners’ Progress

This essay is a brief note from a bigger project that explores the meaning of obedience as a categorical imperative solution in a game of waiting[1]. The original essay and an accompanying stage game has been published[2] elsewhere. Some of my notes are also available for download at the following: focusing on the theme of players as spectators to obedience during Covid designed as a game between you, and Player Unknown, PU. Despite disobedience by Player Unknown, equilibrium behaviour clustered around an obedience payoff. The objective now is to assign payoffs within the aesthetics of game theory to the sensory experience of obedience as a rational strategy to adopt in a game of waiting.

Pre-rational Consciousness

Whether spectators to obedience or prisoners of the plague[3] ‘imprisoned between the sky and the walls’ of our homes we struggle in perpetuity like the characters from[4] Pirandello in search of an endgame. As citizens in this heterotopian[5] ‘world within worlds’ citizens as players are like Precogs in a mysterious game of waiting, because now is the future in this[6] ‘poor old lousy old earth, my earth and my father’s and my mother’s’ and this future we are already living in’. This Blog narrative breaks the fourth wall by asking you the reader to participate as if you were the writer of this essay. You are a player in a game of waiting between ‘Myself’, as a player, and ‘Someone as yet unknown’ to the game labelled[7] ‘the Other’. The relationship between what players say they will do and their actions is highly non-linear. There is a pre-rational consciousness wherein the existence of the Other as a player is the only adjustment to Myself’s frame of mind. A working hypothesis[8] from earlier research on non-linear actions is adopted in that any connection between a sign of obedience and its significance to the playbook is random unless obedience is nested within the algebra of the game. The nest algebra underpins[9] the coding of human behaviour. Each string maps onto the payoffs in the matrices that are generated from a sequence of obey moves.

Like Procopius of Caesarea

Time stamp: July MMXXI: Everything is different. Everything is changed. There is an overwhelming sense of ennui. The Covid-19 regulations have become part of the warp and weft of our daily lives. Our behaviour is under scrutiny. Like Procopius of Caesarea, writing in AD 545, we, relying on statistics, watch and observe others as we negotiate our lives during the Covid lockdowns. As spectators to obedience, we are living in unusual times, waiting for our vaccine that will end the pandemic.. We are fatigued. We learn to adapt and adopt new norms. Although time has lost its meaning, as citizens, we have become players in a game of waiting. We are engaged in what the poet Samuel Taylor Coleridge called ‘the willing suspension of disbelief’ trying to weave meaning from the observations of others.

Our behaviour has become even more personal, more exploratory of time. Folksy stories with visions of lived lives we could have led if only there was no pandemic, generate imaginens that ‘build castles in the air’.  For the time being, life has changed, and our behaviour has had to adapt to life under Covid regulations. Our a priori knowledge of Nature may have to be revised. A gauntlet has been laid down by Nature, a gauntlet that not only has challenged our sense of self in the natural world[10] but also required of us to pause, to wait, and thus obey a set of rules and regulations. Can it really be, as Socrates suggests, that we have no right to disobey, come what may, so that allegiance is owed to a moral duty? The real moral that Socrates pointed to is that acting conscientiously can be painful or costly. Any citizen as a player in this game of waiting is split between a rational and mystical self. Is it ever right to do as you think you ought not to do?

Habits of Obedience

A new axiom of Ƭ-rationality is introduced. During a pandemic there is the phenomenon of command and obey that is reminiscent of John Austin’s command theory of law[11] wherein rules are expressed as ‘habits of obedience’ and regulations involve an expressed wish that something be done with consequences if that wish is not complied with.  Humans are adaptable. Purls of wisdom are stitched into the soul of human behaviour. It is as if there is a Kantian inner intuition, independent of the playbook, where it must be possible for the sign ‘I obey’ to affirm one’s beliefs about the pandemic. Our actions may be so subconscious that one cannot attribute them to oneself. So, in the design of the endgame, obedience is presented as a disguised equilibrium solution to waiting, that is, an equilibrium where opponent’s choice of strategy cannot be divined from the actual outcome or payoff.

Non-Archimedean Memory

There is talk, there is one’s memory[12] of the pandemic. Waiting causes the intertwining of obedience, emotion and memories. We argue that in a game of waiting our memories are not an ordered field like the real numbers in the payoff matrices. A non-Archimedean time dimension is introduced, that is, a player’s memory in a set of memories in the ‘now’ is not within an integer multiple of another memory in the future. Perhaps the ability of our memory to rank order the apparent good and bad experiences of a pandemic displaces the earlier time periods of disobedience. It is as if the player’s brain processes obedience and attaches an emotion through habit recognition so that the memories of waiting become associated with obedience.  In the payoff matrices each cell represents a mini subconscious ‘now’ and the mind-brain behaviour of a player, adjusting into the ‘now’ surreal time, selects imaginens from a pyx of memories. It is as if Myself can eavesdrop on the signs that accompany thoughts by watching the Other.

Mind Disinheritance and Displacement

In the ‘now’ the motif of parallax is robust. A non-Archimedean time dimension is best illustrated in Susanna Clarke’s fantasy[13] wherein she writes: ‘Two memories. Two bright minds which remember past events differently’. At the time stamp the solution is unambiguous that only one choice can be made: obey. The choice is an adaptive learning mechanism. But there is a telescopic effect. The idyll of obedience is more remote in time for the Other for whom disobedience is more recent. The telescopic nature of the game condenses the search for an equilibrium to the signs, the actions and behaviour of Myself and the Other player. It is, as if, obedience pursues the Other. Unable to trust the Other instantly Myself hits a blind spot – there is no adherence to the rules to be seen. There is a crisis of uncertainty. Another day, another week reveals the hidden behaviour camouflaged by what I wanted to see and believe about others. For a moment in time there is a sign of no obedience momentarily before reality hits. As prisoners of the pandemic we experience this intangible mind-bending phenomenon that disinherits an already given belief from our belief system for a moment in time until reality returns and displaces doubt. Is doubt a reflection of the sign of obedience or the significance of disobedience? At that moment in time within the noosphere[14] of truth and lies you could believe that obedience did not exist. It is as if you as a player had a[15] ‘third eye’ in the realm of the human mind, through which you could reflect on the actions of your irreducible self on whether to obey or not.

Surreal Diss[16] Value of Obedience

There is the temptation to disobey and non-conform to the rules and regulations. So, in order to illustrate mind disinheritance and displacement within a noosphere of reason the prisoner’s progress is anchored to what we call the surreal diss value of obedience. The reporting of Covid statistics is de rigeur and thus the first opening move by Nature is public knowledge. As a move, it has happened already; subconsciously the Other is aware of the powerlessness in a surreal state of being surrounded by statistics constantly watched by Myself. This translates to the arbitrary payoffs in Table 1. By way of illustration the two solutions with payoffs (0, 2) and (-1, 2) are defined as ‘co-tangent’ solutions[17] for the Other player in the sense that they both affirm the same strategy, disobey. We promote the[18] pair of payoffs (0, 2) and (-1, 2) as co-tangent adjusted equilibria, adjusted for the reasoned pursuit of obedience as a social value[19]. Research is continuing, but in the interim let’s consider the following hypothetical: let p1 be the probability of obedience. There is a corresponding probability of disobedience (1-p1). For Myself, a mixed strategy {p, 1-p1}, with ½ probability, hints that the Other player will be indifferent between obedience and disobedience. If the Other player obeys, then the payoffs accruing are -1 and 1.

Table 1: Surreal Diss Game

Myself/the ‘OtherS1: ObeyS2: Disobey
S1: Obey2,-10,2
S2: Disobey-1,1-1,2

The expected payoff for obedience accruing to the Other player is computed from the equation {(-1 x p1) + (1 x (1-p1))}: less than 2 depends on value of p1.The Other’s expected payoff from obedience is equal to the payoff from disobedience only when p1, the obedient player’s probability of obedience has a certain value. This value is computed at -½, a value we define as the surreal diss value of obedience. If the Other player truly wishes to disrespect the rules and regulations the obedient player, Myself, has to be twice as likely to obey as not or the Other player will not be willing to give up 2 in exchange for the probability of (1, -1). However, to know our own mind and to explain our own behaviour there is a Hegelian bridge to cross, a bridge between being in the ‘now’ and the ‘beyond effect’ of the future. A surreal diss value embedded in obedience payoffs is contentious as some players disobey. The co-tangency promotes reason and virtue and, in the endgame, like Diogenes, a rational player, adapts behaviour and acts in accord with Nature. There is this liminal space where the Other crosses over as a[20] Beckett player delaying a disobey move whilst thinking of obedience.

Truth-rationality: Ƭ-rational

So what constitutes Ƭ-rational behaviour at these co-tangent payoffs? The Other player would not be acting rationally if a strategy were chosen that does not maximise the payoff. Within the aesthetics of game theory a Nash equilibrium (0, 2) maximises the payoff accruing to the Other player. Albeit, opting to obey translates apparent non-rational behaviour into what we label as truth-rationality, a point of balance in the game when the subconscious mind of the  Other player reasons that a maximum payoff is bounded by the surreal diss value of obedience. Rationality is interpreted here[21] as ‘’the discipline of subjecting one’s choices – of actions as well as of objectives, values and priorities – to reasoned scrutiny’. Although adherence to the rules is a sign of obedience for Myself as a player, the significance of waiting for the Other is to rework the payoffs in palimpsest time by reading the sign that an obedient player has to be twice as likely to obey the rules and regulations in the pandemic. Otherwise an unsynchronised equilibrium – order without equilibrium – obtains in this epistemic mind game. The Other, as a prisoner of the pandemic, is now a producer of obedience, not just a spectator to obedience. Myself contemplates the[22] palimpsest of playbooks as all players are confronted with multiple layers[23] of interpretative[24] memory and imaginens – some still happening in real time.

Human Talk[25]

Our assertion without proof, is that if all players read this sign, obedience becomes a categorical imperative. Myself and the Other player, like Vladimir and Estragon, engage in a variety of ‘human talk’ while awaiting an end to the pandemic. We exhibit idiosyncrasies of rule-guided communication that go beyond non-rational behaviour. This Kantian inner intuition is analogous to an intangible mind-bending phenomenon that disinherits an already given belief to disobey from the Other’s belief system for a moment in non-Archimedean time – at least until reality returns and displaces doubt. Obedience becomes a club good in the tradition of public choice[26]. The penetration of ‘club’ obedience into social life alters the configuration of rationality to the extent of encouraging particular conceptions of imaginens within the subconscious of all players. The socially constructed rules of obedience and compliance slowly transform our understanding of constraints set by Nature. Obedience to rules and regulations rather than cheating, for example, or shirking, evolves as an ordered solution to the Natural problem of waiting.


Reality lies in how you see things. Individual player behaviour in the ‘now’ during a pandemic is viewed as an artefact of the player’s consciousness, and the reality of ‘now’ is beyond the ordinary quotidian drabness of life in a pandemic. The illusions are imaginens ‘like Godard’s camera filming a camera filming a camera’ without origin or end[27]. Myself and the Other are challenged, as you are by what is observed but we create a ‘future’ from the entanglements of multiple realities in non-Archimedean time. Obedience has come to us in this game of waiting to advise on what we ought to do for family, and ultimately for society. In a game of waiting obedience disguises itself as the old man Mentor, whom Odyssey asked to look after his son, Telemachus. The word ‘truth’ becomes a synonym for ‘reality’ during a pandemic and the signs of obedience betray a new axiom of rationality, truth-rationality that spans the arc of adaptable human behaviour. There is a lack of trust and impatience in a game of waiting. Like Orpheus, son of Apollo, many of us are weak. Others, like Eurydice, his wife, run away from obedience, they ‘step on a viper and die’. However, when we omit obedience from a Ƭ-rational playbook then the corresponding nest algebra consists of a sequence of matrices with zero payoffs signifying nothing. In other words, all players in a game of waiting realise at a moment in non-Archimedean time that obedience is making life easier in this game, providing[28] ‘some kind of way outta here’ during the Covid-19 pandemic.

Ode to Bob Dylan : A Poem to Irregular Hopes

Ode to Bob Dylan at 80: A Poem to Irregular Hopes


Enjoining Austin Clarke, Dylan Thomas & Ted Hawkins with Bob Dylan in a poetic ‘strange loop’


Pretty mama, I don’t understand

Tell me what’s so special about this man[1]

As the cherry blossoms curl

To the ground below

A dream twister,

Thran as cloth galluses

His lyrics purl

At mankind’s threads

Along the watchtower.

No more auction block

At 80.

No undertaker’s bell

It is only a number,

Furnished full of tears, still

Ichi-go ichi-e

80 is the lock and life is the key

To the memory palace of memory.

Do not go gentle into that good night,

Old age should burn and rage at close of day;

Rage, rage against the dying of the light. Our poets saw a woman smiling

Her tresses, bright as celandine,

Could not cross the Crana flowing.

Men elbow the counter in public houses

Drink their pints of plain

Bob shall obey the ever known.

Why keep the grape stone

Leave the vine stock?

I know the injured pride of sleep

The strippers at the mocking post.

By the way, that’s a cute hat

And that smile’s so hard to resist.

I was so much older then

I am younger than that now.

So happy just to see you smile

Underneath the sky so blue

Morning has moved the dreadful candle

Appointed shadows cross the nave

Away, decide? What dare we call

Our thoughts, Marcus Aurelius?

Unwanted void or really us?

Tangled up in blue, at dawn, in a wood of sorrel, branchy

Dew-droppy, where sunlight gilded sapling

And silvered holly, or by the bank

Of Breda,

Where our poets saw a woman smiling

Her tresses, bright as celandine

Flashing amber

Sufficient glimpses of someone

Not long ago

Not long aglow

Where our poets saw a woman smiling

Her tresses, bright as celandine

Enjoying Proust’s madeleine.

With their nightingales and psalms

Bu for the lovers, their arms

Round the griefs of the ages,

Who pay no praise or wages

Nor heed my craft or art

You can always come back,

Like the ship of Theseus

But you can’t come back all way.

Like little limes, leaning fruitfully

On a tree.

Lines of limes, little limes.

Lovely lines of life at 80.

[1] Opening lyrics from Bad Dog written by Ted Hawkins from his LP Cold and Bitter Tears 2015.

Playing the Spectator While Waiting for Covid

Across the world we are adjusting and adapting to life under lockdown, furloughed, cocooning, and moving around within an agreed social distance. We are responding to a new world order under Covid, a new normal with a greater degree of mutual interdependence as people observe and respond to each other’s behaviour. While there are computer games[1] to teach the importance of social distancing, we wondered whether or not game theory reasoning could underpin our behaviour during the Covid pandemic. The essay is about game theory reasoning and its putative relevance to rational behaviour under Covid. Related research into the aesthetics of game theory reasoning in literature inspired a reading of Sophocles’ Antigone and Beckett’s Waiting for Godot and Watt. The research[2] into obedience and waiting is ongoing but some thoughts are shared here as we design a game of obedience and waiting with a view to understanding of our own rational behaviour during this Covid pandemic. In these unsettling times, if one can only think of something as unbelievable as invisible Zen archers then there is hope in knowing that we are all facing this together.

Obedience as a Waiting Game

Sophocles’ play Antigone provides an historical canvas. The play is about pride and responsibility but, it is also a story about the rule of law, the role of Government and civil disobedience. Antigone is also[3] a ‘public story’, in terms of obeying a universal law. Should Antigone have adhered to the rule of law, the law of the State, and thus, obey her uncle King Creon? Or, choose not to obey. Like Antigone we have free will. Like Vladimir and Estragon we wait. So, do we adhere to the rules and obey Government guidelines, or do we disobey? The same reasoning would apply to groups and (economic) clubs[4] wherein members adhere to rules and regulations. Rational players as individuals do commit to an organised set of rules.

It has been shown by Schelling[5] that it is ‘not always safe to assume (individual) outcomes accurately express the individual decisions’ as observed.  Therefore in the search for rationality in a game of obedience, there may be a sub-game ‘trembling hand’ equilibrium in waiting, if we can interpret waiting as obedience. Our research has focused on an optimal design of a game of waiting inspired by a reading of Beckett’s Waiting for Godot and Watt. And suffice to note here in our design that the etymology of ‘waiting’ is either an interpretation of ‘hoping’ [Latin verb ‘spero’] as in Antigone’s behaviour, hoping to bury her dead brother or an interpretation ‘remaining in place’ [Latin verb ‘manere’] like Vladimir and Estragon as they wait for Godot. The latter interpretation is applied in this Blog essay. That is, we either obey Government restrictions and wait for further guidance or we disobey.

Ontological Insecurity

But there is an added poignancy to Sophocles’ narrative today during the Covid-19 pandemic as citizens in particular begin to question and debate Government policy. Covid-19 has disrupted individual and collective confidence. It has triggered what sociologists[6] and anthropologists[7] call ‘ontological insecurity’- an anxiety about your safety and security at a moment in time. We are now in a state of perpetual angst. It can be best understood by your answer to the question: how safe do you feel? We need assurance: in the medium term the roll-out of a track and tracing app or the wearing of masks might suffice. Masks or face coverings, for example, provide confidence and security: you wear a mask to protect others and they wear a mask to protect you from Covid infection. A vaccine would provide long term assurance. However, while it is sufficient to observe others taking precautions it is necessary for our own security that others, have confidence in their own survival. Therein lies the mutual interdependence that is characteristic of game theory.

Player Unknown

Like Antigone, we as citizens are now players in a game of obedience. The game is between you, Player 1, and ‘others’, referred to as Player Unknown (PU).[8] The PU allows us to blend the ontological insecurity of rational players into the game design. Antigone did not have to obey her uncle King Creon. She chose not to. Ultimately, like Antigone your playbook is a question of individual choice versus fate. There are many scenarios? What if King Creon did not expect Antigone to bury her brother Polynices? What if Estragon followed Pozzo and opted not to wait for Godot? We opted not to explore these hidden games with mixed strategies in this essay. They are to follow.

We ascribe Covid-19 behaviour as obedience and in an obedience game we have illustrated the payoff to ‘others’ in italics in Table 1 and the payoffs to you are illustrated in bold. Every player is unknown to you and you have zero information on any player. PU provides a cognitive framework that enables you, as a rational player, to anchor your confidence to observed behaviour by any PU. How would you choose your strategy of play in such a game? Players are rational and optimise their choices to get the most preferred outcome. PU would like to avoid the game or transfer responsibility to others. The sub-game payoffs reflect this preference ordering. Although the payoffs in Table 1 are arbitrary cardinal numbers, they do reflect the players’ preferences in a game of obedience. As citizens we have become players in a Covid obedience game. The ethical trade-off, arguably, do X and not Y is reminiscent of the narratives in Sophocles and Beckett. We opt to frame the trade-off as a non-cooperative game.

Trembling Hand Equilibrium

The trade-off is between individual choice and fate. We wait, we obey. Or not. It is a strategic choice with a sub-game perfect equilibrium. In other words,[9] obey as a strategy, is the Nash strategy in the ledger of choice for the duration of the game. Obedience, may well be the sub-game node to the main game of Covid survival over pride. The player’s payoffs take the cardinal form (-1, 0, 1, 2). The equilibrium payoff (2,1), for example, can best be understood by the philosophy[10] of Montaigne: ‘my life has been destroyed by many catastrophes most of which never happened’.

Table 1: Sub-game equilibrium with Player Unknown



Disobey 0, 1 0, 1
Obey 1, -1 2, 1


To obey the rule of law, to obey the Government until lockdown is eased and a vaccine available presents each and every one of us with a rational choice to obey. That choice is best understood by adapting the words of an old Biblical tenet[11] sic ‘I obey because it is absurd’. Playing this game with rational obedience in the playbook will obtain the payoff 2 for you as the rational player. Disobedience is not an option for you. There is no later. Every form of behaviour is shaped by trial and error. Disobedience, however, may obtain an elusive payoff of 1 for PU with an inherent risk of -1. For Antigone, it meant her death. What if she no longer believed in her strategy of disobedience?

Topology of a Playing Strategy

So let us consider two equilibria: the (2,1) payoff and a ‘hidden’ equilibrium[12]. The equilibria are separated by a probability (function) of reciprocal altruism[13]. The selfish outcome is present in both but due to a payoff equation (yet to be defined) it manifests itself differently in the two equilibria. Therefore the altruism function could be a discontinuity that can be developed from the differential form of the equation of life[14].

Definition: An equilibrium is hidden if it does not intersect with a well-defined open neighbourhood of equilibrium points. Or it may be a point in a small open neighbourhood whose closure is compact.

Theorem (to be proven): The (2,1) equilibrium payoff is a subset of a larger group of non-observant ‘hidden’ equilibria corresponding to a topological vector space wherein a convergence is defined in the neighborhood of saddle points.

Corollaries: I: The neighborhood of saddle points include a neighbourhood of 0. II: The vector space would include the payoffs at the default position of selfish behaviour by PU and the payoffs with co-evolution of the players who ascribe to a reciprocal altruism type.


Until further research is concluded, the payoff (2,1) is a trembling hand equilibrium. It can only occur if PU commits to obey as a strategy. So, ask yourself: should you obey? Affirmatively, yes. In a Bayesian game, Nature reports to each player his or her type. Are you Player Unknown? The equation of life in a Covid game is analogous to a Krepski two-move game of chess at a moment in time: opening move is either obey or disobey. If you disobey there is a greater risk of death. Checkmate. But this checkmate can only occur if one player (say, White in chess) commits to a mistake[15] so it seldom happens in practice. An anonymous rational PU in a two-move game does not want to die anonymously. If you obey the rules and guidance, you could evolve as a spectator to obedience, secure in the knowledge of your own survival and the survival of others. Despite disobedience by PU, behaviour will tend to cluster around (2,1) because there are many more rational players like you subject to the Gaussian distribution of rational behaviour. There is hope. The equilibrium point of balance in this stylised obedience game of waiting is realised when you can begin[16] to construct ceremonies out of the air and breathe upon them’. The Zen archers become visible. Keep safe. Keep sane.

[1] Check the Thomas Reuters Foundation article by Emma Batha, ‘Covid-19 Computer Games Reaches Children Importance of Social Distancing’, 19 May 2020

[2] Collaboration with Manfred Holler at LMU in Munich ‘waiting games’ inspired by the literature of Beckett and Brecht and the narratives in both Greek tragedy and Roman comedies, in Sophocles and Seneca respectively. The idea is a Beckett player type delaying and thinking [like the ‘sanyasin’ in Hindu] as observationally equivalent to waiting. Interesting perspective from Kimberley Bohman-Kalaja who published Playing the Spectator While Waiting for Godot at Princeton University Press, 2007.

[3] The view expressed originally by Holderlin who translated the play from Greek into German.

[4] McNutt, Patrick (2002): Economics of Public Choice Elgar Publishing, UK.

[5] Schelling’s Game Theory p241 by Robert Dodge (2012) Oxford University Press.

[6] Framed by Giddens (1990) in his book Modernity and Self Identity as ‘ontological security’ with the earlier original concept of insecurity attributable to R.D. Laing (1960): The Divided Self Penguin, London.

[7] Refer to the R.D.Laing’s research overlap with the grid-group analysis of Mary Douglas and Margaret Mead and application in an earlier article McNutt (1987): ‘Anthropology, Economics and the Socio-Economy’ The Arab Journal of the Social Sciences vol 2 no 1 April.

[8] Adapting the strategy from the gaming fraternity’s Player Unknown Battle Ground (PUBG): worksheets from my lecture notes ascribed to the MBA cohorts who attended Masterclass at both Manchester and Smurfit Business Schools in Manchester and Dublin.

[9] Check out McNutt (2010): Decoding Strategy published by McGrawHill and Holler (2018): The Economics of the Good, the Bad and the Ugly, Routledge.

[10] Selected from Montaigne’s Essais (1595) as translated in the essays in Wikisource.

[11] Adapted from an old Christian tenet ‘credo quia absurdum’ – ‘I believe because it is absurd.’

[12] The term suggested by colleague Manfred Holler at LMU and Hamburg.

[13] From McNutt (1988): ‘A Note on Altruism’ International Journal of Social Economics vol 15 pp62-64.

[14] The equation of life to be a diffusion like equation expressed in terms of the movement from selfish to altruistic behaviour in a Covid-type obedience game.

[15] The game design with a mixed strategy would assign probabilities to a second move for Antigone. What if she no longer believed in her strategy of challenging her uncle?

[16] Adapted from the narrative in Cormac McCarthy’s 2006 novel The Road at page 78 ‘where you have nothing else construct ceremonies out of the air and breathe upon them’.

Artificial Intelligence Transubstantiation

A future beckons where typing may be redundant. In that future, what if your brain could type? Beginning with a sufficiently intelligent algorithm (henceforth AL. Gorithm) we have argued that AL. needs a conscious and wisdom. For the purposes of this Blog essay, a conscious and wisdom are presented as images, allowing us to generalize within a mathematical morphology. A mirror metaphor is used simply to highlight the challenged faced at that moment in time when geometric neuron patterns of a conscious brain are transubstantiated onto a physical object. This Blog essay builds on earlier research[1]. In the game transition, we have chosen to label AL. Gorithm’s coherent  understanding of the word ‘mirror’ as a process of artificial intelligence transubstantiation. Work in progress. There are ppt slides and documentation:




A future beckons with augmented reality, a future where smartphones are replaced with smart glasses, where typing is redundant. In that future, what if your brain could type? A not dissimilar question was posed by Facebook in 2017. By using sensor technology, for example, researchers have enabled a brain-computer speech-to-text interface. Artificial intelligence is on a long path to human intelligence. Albeit, reasoning, common sense, conceptual thinking, cross-domain thinking, creativity, self-awareness remain, for the moment, beyond the reach of algorithms. Many argue that artificial intelligence systems, however mathematically robust, are unlikely to acquire real person wisdom. It’s a fantasy, argues Koch (2020). Until a master algorithm[2] is conscious of itself, Mitchell (2020), who delivers an excellent review of the literature admits that ‘human-like’ intelligence is really far away. We explore some options. Beginning with a sufficiently intelligent algorithm (henceforth AL. Gorithm) we have argued that AL. needs a conscious and wisdom. For the purposes of this Blog essay, a conscious and wisdom are presented as images, allowing us to generalise within a mathematical morphology. We introduce a mirror metaphor to explain. Framing a robotic conscious within the rigors of a Prisoners’ dilemma requires humans to be less selfish in their behaviour that is captured and processed into data packages. AL. Gorithm ‘thinking’ introduces both a philosophical and a mathematical dimension to a debate that can be housed within the dualism of mind v brain, and thus, complementing an underlying game topology. Borrowing a phrase from Mayor (2018), the algorithms are biotechne that is, they are ‘made, not born’. Consequently, there are deep ethical issues on existence, thought, creativity, perception and reality to be unlocked before we can answer the question: what if your brain could type? But what if Facebook’s goal is realised: what if the data patterns of a conscious brain can be translated onto a physical object – isn’t your brain typing?


Mathematical Morphology


If the data patterns are geometric then the artificial machine intelligence (machine learning, deep learning) ultimately relies on the geometry of human patterns and inference. Mathematical morphology is a non-linear approach to image processing that relies on the complete lattice structure. What if the brain-computer interface had an abstract structure that can be studied as a lattice structure? Deep learning neural networks are trained on bits and bytes of labeled data packages; then they use what they’ve learned to mathematically select and identify patterns from images, sounds, or payments. As the robots adjust to changes in their programmed environment the biotechne algorithms ‘think’ in real time. Researchers[3] in the enhancement of brain MRIs have explored the brain-computer interface as a lattice structure. But unlike the human brain, AlphaGo, for example, which beat the world’s master in the ancient game of Go, does not play chess; pigeons, however, do play chess[4].


Mirror Metaphor


What if there is a game dimension underpinning the concept of cognitive connections between brain neurons and a physical object like a keyboard. You can visualize a sentence or word in your mind’s eye but your brain has to project it onto a visual. This is a challenge. Try this simple experiment: write the word ‘mirror’ on a piece of paper. Hold up the word ‘mirror’ against a mirror. Now, look at the image. It is difficult to decipher. The brain is consciously reading or ‘opening’ an image from the mirror but you cannot read the word ‘mirror’. This is analogous to the challenge faced by a thinking biotechne algorithm. The translations of the structuring of the visual image of the word ‘mirror’ create a memory bank of images.


The challenge for AL. Gorithm is to read or[5] ‘open’ the visual images of the word ‘mirror’ so that an image can be unscrambled by a robot and understood as the word ‘mirror’ as if the robot had a thinking, emotional brain. A thinking algorithm has an advantage provided a memory of the image is retained in a memory bank, thus providing the bits and bytes of data that intelligent algorithms require to function.  And in a process not unlike predictive text on a smartphone, AL. Gorithm, by employing morphological filters, will decipher that image of the word ‘mirror’ coherent with a real person’s vision of the word ‘mirror’ at a moment in time.



Artificial Intelligence Transubstantiation


The word ‘mirror’ cannot be understood without reference[6] to the morphology of the mirror image. A circular interpretation of the word or sentence is a technical translation of the substance of the brain and the conscious mind onto a physical object like a mirror, a keyboard, or a robot or a computer. Significant research on brain MRIs and the challenges addressed in mathematical morphology are noted. Early thoughts on the mathematics of the process as a game on manifolds are located in the ppt slideshows referred to above. In the game transition, we have chosen to label the player AL. Gorithm’s coherent  understanding of the word ‘mirror’ as a process of artificial intelligence transubstantiation that is, that a move by AL. Gorithm, as a player, is diffeomorphic to a move by a real person[7]. At that moment in time in the game phase when the biotechne algorithm translates the image of the word ‘mirror’ before a human a transubstantiated robotic ‘bluetooth brain’ is at a point where it is ready to type. The mirror metaphor is used simply to highlight the challenged faced by the mathematicians at that moment in time when geometric neuron patterns of a conscious brain are transubstantiated onto a physical object.


No Meaning No Conscious


Our thoughts, our memory, our emotions – in essence, our mind – and, our search history have become data packages that can be ascribed a geometry. They can be arranged into geometric ordered patterns. But data packages have no meaning for AL. No meaning, no conscious. The master biotechne algorithms – like the ones deployed by AlphaGo or by Facebook’s F8 laboratory or by Neuralink in their plans for brain-reading[8] – will require an ethical boundary. The boundary will only evolve from a coded gesture of human understanding, knowledge, reasoning and wisdom that can be wholly independently ascribed to AL, consciously aware and processed, coded and programmed.  We call this ‘the big equation’. In the Masterclass, we did explore, briefly, ‘the big equation’ as a cognitive awareness (visual) experiment by looking at the Winograd semantics and perception in terms of Kanizsa patterns and illusions. The purpose of that exercise was to identify a link between meaning and conscious and to demonstrate – with cognitive simple visual aids – an axiom[9] of no meaning no conscious.


Transubstantiated ‘Bluetooth Brain’


Facial recognition software, for example, builds on the architecture of the neural networks that specialize in processing data by translating an image into a binary set of visual data. So, is there a Gestalt switch, a diffeomorphism, wherein AL’s ethical perspective can be mapped? If so, at what node in the complex coded pattern of digital behavior does it occur. Our research agenda is to find that switch, analogous to an opening move in a game: because at that switch our memory has (already) been outsourced to AL as we rely exclusively on smart devices. And de facto at that switch our brain ≈ our mind. Our memory is entangled with smart algorithms that have intruded our everyday life. We rely on AL. Gorithm. The AGI dream of an artificial human brain that can run on cloud computing systems requires an artificial intelligence transubstantiation.


Zimmer’s conjecture


The mirror metaphor earlier, is but a first principles approach to understanding a transubstantiated ‘bluetooth brain’. A conscious brain, ordered and reflective, has a geometry. Measured and programmed data patterns are a lower dimension in the geometry. They are programmed in order to inform the feedback loop of the master algorithm. At a higher dimension, arguably, data has meaning only when AL. Gorithm thinks and is consciously aware. Then the data patterns as measured are at a higher dimension in the geometry, programmed to inform the feedback loop of a master algorithm and, coded into an abstract ‘thinking’ biotechne algorithm. At that diffeomorphic Gestalt switch within the network architecture, a transubstantiated robotic ‘bluetooth brain’ is ready to type.




If the research on the  brains’ neurons as an algebraic dual space can be ascribed a game space then could the brain be measured as a smooth manifold with bits and bytes of structured data? The associated algebra and the topology is already embedded in the memorized data patterns in the brain. So in order to recover the manifold structure AL. Gorithm could be programmed as a Player Unknown in the asymmetric game space. In the AGI[10] search for a single piece of software capable of learning almost any human task mathematical logic has been applied. When the rank[11] of the lattice is larger than the dimension of the manifold our brain ≈ our mind ≈ conscious AL. Gorithm. At that point of balance, artificial intelligence transubstantiation would be complete. So let’s solve the big equation.


Our transubstantiated ‘bluetooth brain’ imbued with a deep learning programming code[12] with ethical values, would be ready to type. If, and only if, the Winograd sentence ‘time flies like an arrow’ could be interpreted by AL. Gorithm as a statement of fact and not an expression of love and emotion would the transhumanism fears about ‘the big equation’ be assuaged. This would be a small step in the right direction. The transhumanist dream of downloading one’s mind into a computer circuity processed by biotechne algorithms would have been realized. It is happening; no doubt within Facebook’s F8 laboratory, or at Neuralink, or OpenAI or DeepMind Google Brain significant advances have been made. Was it a car or a cat I saw?





Christian, B & T. Griffiths (2017): Algorithms to Live By Picador Publishers

Koch, C (2020): The Feeling of Life Itself: Why Consciousness is Everywhere but Can’t Be Computed MIT Press

Lee, Kai-Fu (2018): AI Superpowers: China, Silicon Valley and the New World Houghton Mifflin Harcourt

Mayor, A (2018): Gods and Robots Princeton University Press

Mitchell, M (2020): Artificial Intelligence: A Guide for Thinking Humans Pelican Press


Philip Ball ‘Android Dreams’ Article in Prospect Magazine pp57-59 March 2020

Fortune Magazine Europe edition February 24 2020 on Artificial Intelligence.

[1] This short essay builds on earlier work in progress with neotenic data patterns where algorithms are emotionally connected to code. Further arguments in support of interpreting data ≈ data with emotions involved a game between onsumers (online consumers) and a personalized ‘act-like’ a human Al. Gorithm. The tao of robot ethics and related materials are available on my webpage.


[2] Term employed by Pedro Domingos (2015): The Master Algorithm, published by Penguin books.

[3] There are articles on brain MRI in The Journal of Ambient Intelligence & Humanized Computing [read 2019 article by Vikrant Bhateja et al ‘Human Visual System Based Mathematical Morphology’] and early research available at Semantic Scholar by Olivier Lezoray et al (2014): ‘Learning Complete Lattices for Manifold Mathematical Morphology’ and a paper by Carvalho et al (2014) ‘Lattices from Combinatorial Game Theory’ in the journal Theoretical Computer Science, vol 527 pp37-49.

[4] We refer to this as isomorphic asymmetries in a lattice game dimension. The patterns could be presented in geometry a (lattice) game on manifolds, and we refer to torus and neoteny at

[5] The morphological opening of the word ‘mirror’ could be regarded as the opening move in the game.

[6] The reasoning here is not dissimilar to Heidegger’s hermeneutic circle – the idea that neither the whole text nor any individual part can be understood without reference to one another: Heidegger’s work published in 1927 is Being and Time

[7] To be proven by the author and beginning to revisit John Nash’s mathematics on compact real manifolds.

[8] Neuralink is the company financed by Elon Musk to develop brain-machine interfaces.

[9] The axiom holds unless and until AL. Gorithm as an artificial moral agent connects ‘act-like’ human thought and emotions.

[10] AGI is artificial general intelligence with Microsoft and Google competing to develop human-like OpenAI and DeepMind Google Brain algorithms respectively with common-sense reasoning and conceptual thinking. The dream is to replicate the human brain.

[11] Zimmer’s conjecture was solved in 2017 –  symmetries can exist in a higher dimension that cannot exist in lower dimensions.

[12] The values are subject to the constraint of a non-empty well-defined core of ‘the big equation’, the metric equivalent of a gesture of human understanding, knowledge, reasoning and wisdom

An ultimatum game of ichi-go ichi-e

There was an opportunity, one meeting at Osaka for world leaders at the recent G20 summit. A valuable starting point for the policy-makers, faced with a menu of economic theories, is trust in each other and a new inter-disciplinary approach with an emphasis on ethics and economics. Climate change, migration and displacement, IoT and 5G, global income inequality, household mortgage debt, value of drinking water and food shortages present a grand ethical challenge. In 2015 we asked has economics become an illusion? An era of wistful economics:

Taylor Principle

This time, however, global economic policy should be less about money supply and demand, less about central banks modelling and the private sector and more about the strategic interaction between these ethical challenges.  There is an urgent need for coordinated action to stimulate the global economy with fiscal and monetary measures. The EU is fragmenting. Whither the Euro? Today, Federal debt is projected to jump to a record 144% of US GDP by 2049. There is a debt mountain in China reported at 250% debt-to-GDP. As the Scylla of the Taylor principle (of high interest rates when there is high inflation and low interest rates when unemployment is high) causes a modelling whirlpool with the Charybdis of the Ramsey approach to optimal monetary taxation, the appropriateness of an ethical fiscal policy as a stabilisation tool may calm the waters. So, more fiscal stimulus is required.


On a macro level, world politics is more about China’s transition to greater exchange rate flexibility and the internationalisation of the Chinese RMB. We had presented on this point in Shanghai in 2012. It’s a long game. In other words, RMB v US$ is an infinite game of playing the game not a finite game of first mover advantage. . A weaker RMB would probably mean a stronger US dollar and vice versa. We are reminded of Japan’s exit from its dollar peg in 1971 as today the game is one of reserve currency competition, whether or not the US dollar is destined to lose its standing as the preeminent international currency to Sterling, the Euro or the RMB. Trade wars, competitive devaluations, Brexit, military conflict create sudden disruptions to growth at a moment in time.

Productivity Bonus

As a countermove we become risk-averse on currency fluctuations. But there is a curved ball from the EU and the US regulators as their antitrust focus on big tech. Based on the presumption of a negative effect on competition it relies wholly on an attack on monopoly rents as a reward to innovators. Nonetheless, shareholders and investors and pension funds gain too. However, if the model builders could adapt the McKenzie model of classical general equilibrium theory so that technology is available to any company who can supply the resources required, ultimately, by happenstance, competition and innovation will coalesce into a productivity bonus. Big tech and technology could then be viewed as a way to escape classical monopoly by innovating to compete. To do so would require the equivalent of the 1919 Colgate doctrine for big tech, facilitating the introduction of new technology by allowing each of the big tech companies to decide, on its own, with whom to do business. They exercise discretion on innovation and technology; we, as onsumers,  decide. Our behaviour, after all, is less measured by prices, supply and demand but more influenced by small changes in innovation and technology over shorter time periods.

Onsumers & Complexity

Albeit, our policy advisers and central bankers are less likely to ever move away from the standard Ricardian DGSE models of economic analysis. There is a sunk cost to the modelling.  A key assumption in this model is that households like you and I are a homogeneous family of infinitely lived individuals. Really? This is 2019 and a more realistic and heuristic approach would address the fact that individual’s behaviour changes over shorter time periods with innovation and technology. Our well-ordered lives bring the occasional disturbance that can be characterized by an unmanageable degree of complexity. In our real world, we as onsumers, for example, shopping online, continue to bid against ourselves in the search for the best algorithmic deal.  In practical terms we do not behave as hyper-rational beings. At every G20 there is a risk-bucket and world leaders may get a chance to try again at another meeting; at this G20 there was one chance to try: ichi-go ichi-e. The ethical challenges of climate change, mortgage debt, migration and displacement, IoT and 5G, global income inequality, value of drinking water and food shortages all collapse into a generalized ultimatum game in which we as players must agree or we all get nothing.

Do You Want To Eat Grandma?

The eye of Sauron gazes down upon us as we click, search and buy online in an endless feedback loop of transactions. We rely on algorithms for advice, for direction and general guidance and reassurance in our personal lives. Machines and robots are thinking because rational humans have stopped thinking. Consider this thought experiment: mentally rehearse losing your smartphone. It has been stolen by a thief. In this Seneca moment in time your behavioural instincts kick in as you prioritise your stolen data. You recognise the value of your smartphone. In effect you have arranged ‘the thing’ that is your personal data into priority pockets of monetized data. The synchronised interaction between you, the rational online consumer (‘onsumer’, henceforth) and a sufficiently intelligent algorithm, (Al Gorithm, henceforth) is best understood as a game as described recently in a Masterclass:

Neotenic patterns

As a player in the game, rational onsumers outsource memory to smart devices. Likes and dislikes, preferences and options, clicks and cache are the moves in the game. With neoteny later moves in a data pattern resemble earlier moves. By the 6th move[1] in a 16 move sequence, for example, the onsumer has provided sufficient data, enabling Al. Gorithm to decode the onsumer’s type. The dimension of the game is defined by Euler’s equation. Think of your own behaviour in online transactions such as booking a hotel or airline ticket. Faced with an opening buy-it-now price, BIN, and confident that you will do better, the rational onsumer has a tendency to overestimate his or her capabilities. Alas, by the 14th, 15th and 16th move, the final END price ‘moves away’ from BIN. Having dismissed BIN in earlier moves, the onsumer completes the transaction at an END price > BIN.

Lake Wobegon effect[2]

The hypothesis presented in the Masterclass is that the END price (vector) retains the neotenic pattern of a BIN price (vector) as onsumers continue to bid against themselves in their search for the best price. Each move’s ideological direction is either to buy or not to buy guided by a tendency to overestimate one’s capabilities and it is as if each move beyond the 6th move spans across each face of each cuboid in a wrangled entanglement of cuboids as illustrated. The neotenic data patterns unfold within a manifold of cuboid pockets of data ‘things’. The onsumer’s strategy, the sequence of moves is memoised by Al. Gorithm. An inner field is created by the ‘moving away’ motion of END from BIN allowing the cuboids in n-space to gravitate towards a neighbourhood of Nash equilibria, best described as ‘the best you can do’ gravitational magnetic preference. We contend that in smaller neotenic data sets there is a convergence in the inner field to a singleton Nash point.

Data ± Emotions

The ‘moving away’ captures crudely the premise that the emotional attachment between algorithms and data patterns is inevitable during a game. The attachment is wholly intrinsic. At a moment in time Al. Gorithm becomes the onsumer. Albeit, we have discussed this elsewhere we now argue that an emotional attachment to data ‘things’ can be ascribed to Al. Gorithm in the early moves of a game as Al. Gorithm’s behaviour resembles the behaviour of the onsumer. Philosophically, something abstract is thinking. Outsourcing of personal data has become a dominant strategy. It leads to a solution, a Nash equilibrium in the Euclidean space as the END price ‘moves away’ from the original buy-it-now BIN price, such that BIN < END.


Mathematically, the reachability of artificial intelligence is about matching behaviour or mimic patterns but the ‘thinkability’ of artificial intelligence, the quintessence of technological singularity, is more likely to be aligned with neotenic data patterns embedded in the onsumers’ patterns that generate many cuboids of data. This is work in progress as we explore the cuboid geometry and the Euclidean space, extending to simply connected Riemannian spaces, defining the Nash manifolds as the optimal framework of Nash equilibria. As the game unfolds, the cuboids, given sufficient time, drift towards the Nash points in a topological space locally equal to an Euclidean space. This in turn increases the average drift of the cuboids. The hypothesis is that the game reaches the singleton point at which point HUMAN = MACHINE, the reachable thinking equilibrium point.

Decode Winograd

The equilibrium is that much closer by epsilon to a point of singularity. When your data patterns are prioritised as ‘things’ and a Nash equilibrium exists on each edge of a cuboid pocket of data things, a thinking reachable equilibrium exists. Each sufficiently intelligent algorithm behind machine learning is something that could be someone else in a game. At this equilibrium point and only at this point, Al. Gorithm with emotional attachment will possess not only a memory of past data patterns but also the capacity to envisage future events and moves in a game. Ultimately, Al. Gorithm will decode Winograd sentences, so, hopefully, no one eats Grandma!

[1] We are designing a game with a betrayal of type by the 4th move at time period t, requiring 11 moves of historic (t-1) data patterns to satisfy Euler’s law at time period t+1.

[2] David Myers coined the expression to explain a natural tendency to overestimate ones capabilities: retrieved from  or in McNutt’s Decoding Strategy (2014) it is the dilemma described as ‘in trying to do better you end up worse off’.

Could Labour Win? Condorcet Loser in UK Election

A recent YouGov poll last week, Tuesday 30 May, provoked a discussion of a likely ‘hung parliament’ in the upcoming UK election. Voters are challenged, faced with many candidates across a spectrum of issues, as the old left-right dichotomy breaks down.

In the literature on voting theory, there is a phenomenon called the Condorcet Loser. If there is a candidate that loses in a 1:1 comparison to each of the other candidates, then that candidate should not be the winner of an election. But it could be the winner. Often ignored in the literature as the Cinderella of the election forecasting ball, a Condorcet Loser candidate could win if a unique set of circumstances prevail. One such circumstance is the voting rule. The UK election will be decided on plurality voting. Plurality voting, known as first-past-the post (FPTP), violates the Condorcet Loser criterion. In other words, there is the probability that in some constituencies a Condorcet loser candidate could emerge as the winner under FPTP.

If a sufficient number of Condorcet Loser candidates are Labour candidates, and if rational voters re-order their preferences along the lines of our stylised example below, then Labour could win the election. How is it[1] possible? Yes, anything is possible. There are many candidates across many constituencies in the upcoming election.

Lexicographic Voter Preferences

Lexicographic preferences exist when different voters have different orderings in their voting preferences such that different voters rank candidates in different ways. In economics, you may choose a bag with less fruit because it has more apples than oranges. This is the win set. So, for example, a Labour/Leave voter might rank a Conservative Brexiteer candidate higher than a Labour candidate or a Conservative/Remain candidate might rank a Green party candidate higher than a Conservative candidate. The more traditional left-right win set is created when candidates’ promises are in sync with left-right voter preferences. To get elected, a candidate, has to position their manifesto in a win set. So, a right-wing candidate promises tax policies and a left-wing candidate promises welfare funding. However, a distinctive feature of this election is that the traditional left-right has been displaced across the spectrum by leadership style and integrity v trust and security, coupled with Brexit. It is neither left nor right but lexicographic: as the candidates send signals to recipient voters it is possible that a Labour/Leave voter might rank a Conservative Brexiteer candidate higher than a Labour candidate because of trust and security or a Conservative/Remain candidate might rank a Green party candidate higher than a Conservative candidate because of leadership style and integrity.

These lexicographic preferences translate into discontinuities, a range of factors (assumptions), if you will, that could facilitate a Condorcet Loser in this election:

  1. Faced with a range of issues such as social care, taxation, jobs, pensions inter alia, the win set is boundless.
  2. With so many issues there is the risk of independence of irrelevant (boundless) alternatives facing the electorate.
  3. Polls for or against a candidate, whether leave or remain are irrelevant, if they display a latent collective irrationality of voter opposition to a candidate, that is, independent of any political party, Brexiteers will always vote for Leave candidate, Labour or Conservative.
  4. Brexit has endogenized the household balance sheet into the voter preference as rational voters discount their future incomes as argued in the Blog[2] on wistful economics.

If we add in other political parties and a disparity in age-specific voter turnout ratios then it is probable that the UK election process could create a Condorcet Loser candidate in some constituencies.

What if? Stylised Example

A fuller discussion of voting paradoxes in the economics of public choice can be found in both[3] Mueller (2003) and McNutt (2002). Here, by way of a stylised example adapted[4] for the UK election, we assume that the Condorcet Loser is Labour/Leave (LL). The Condorcet Loser is LL since every other candidate is preferred by 2 out of 3 voters in this example. Using the convention in the voting literature of representing preference by the > symbol, each line reads as the voter’s preference so the ordering in line (i) reads as follows: first preference is a Conservative Leave (CL) candidate, second preference is a Conservative (C) candidate, third preference is a Labour Leave (LL) candidate and least preferred is a Labour (L) candidate.

  • CL > C > LL > L
  • C > L > LL > CL
  • L > CL > LL > C

Based on the assumptions 1 to 4 earlier, we place ourselves in the mind of the rational voter with lexicographic preferences on election day. We take a representative sample of rational voters who discard their least preferred choice based on their linear preferences as follows (i) Conservative ‘Brexiteer’ (CL) would never vote for a Labour (L) candidate; (ii) Remain voters would never vote for a Leave candidate, independent of political party and (iii) Corbynites would never vote Conservative (C).

If these conditions held in the mind of the voter on election day then we have a re-ordering as follows:

  • CL > C > LL
  • C > L > LL
  • L > CL > LL

In this scenario, LL is the Condorcet Loser but not a winner. No surprises.

Loser as a Winner Phenomenon

Earlier we had introduced the assumption of ‘leave neutrality’. This could manifest itself in the mind of the voters as they weigh up leadership style and integrity v trust and security into a lexicographic ordering. If the Labour/Leave candidate’s policy platform is minimally differentiated from a Conservative/Leave candidate then a rational Leave voter could rate both candidates nearly equal but ranks Labour/Leave over Conservative/Leave.

If they are equally likely the following re-ordering could happen in the mind of the voter with lexicographic preferences:

  • CL > LL > C
  • C > LL > CL
  • CL > C > LL

By the Condorcet winner criterion, CL > LL by 2:1 and C > LL by 2:1 implying that LL is the Condorcet Loser.

However, with leave neutrality, assumption 2 and the possibility theorem, if the rational voter least preferring LL also rates CL and C low, and if sufficient other voters rate LL close to their preference in the win set, LL could be elected as a majority Condorcet Loser winner. And a Labour candidate takes the seat. So, it goes.

[1]An answer depends on three voting rule requirements: Leave Neutrality: a rational Leave voter rates Conservative and Labour candidates nearly equal but ranks one over the other. Independence of Irrelevant Alternatives: the choice of a candidate in some constituencies is independent of Remain/Leave. Possibility Theorem: the possibility of voters with lexical preferences orderings across n ≤ 5 candidates. Adaptation of McNutt (1993): ‘A Note on Calculating Condorcet Probabilities’, Public Choice vol 75 pp357-361.


[3] Denis Mueller (2003): Public Choice III Cambridge University Press, Patrick McNutt (2002): The Economics of Public Choice, Elgar Publishing, UK.


Who Buttoned My Waistcoat?

Who did button my waistcoat, a human or a sufficiently intelligent algorithm, (SIAL)? At Manchester and Smurfit business schools we explore the economics of the sharing economy from a game theory perspective. We have shared observations and experiences of online transactions. They represent data patterns that are embedded in the clicking and scrolling behaviour of shoppers in cyberspace. Additionally, we would also like to understand, why it is that online rational consumers – we call them, the ‘onsumers’ –  appear to bid against themselves during online transactions. In other words, a final price, the END price, is more frequently higher than the opening bid, the buy-it-now or BIN price for an online transaction.

Is it a behavioural conundrum? Is it rational? Our research continues as we test the hypothesis:

BIN price < END price

Sufficiently Intelligent Algorithms

Online purchases are guided by search algorithms. Price is an important signal. As the ‘onsumer’ arrives at the landing page of the online site he or she clicks and scrolls up and down the screen up to a tipping point. In that quantum moment in time the clicking behaviour of the ‘onsumer’ has created a pattern of online behaviour, a pattern that has been captured by the algorithm. The pattern is a valuable tradeable asset of information.

The scrolling and clicking behaviour diverts from the original purchase and has allowed the algorithm to add in menu and scroll costs that are not discounted by the online shopper. In reality you are likely to be bidding against yourself as you search beyond the BIN price on offer, as you continue to click and compare, discuss with others, price compare the BIN offer in related sync’d online sites. As you deliberate and prevaricate, the sufficiently intelligent algorithm captures all this behavioural information in a moment in time, ∆.

Your before and after pattern of behaviour can be represented as a first order difference equation, the early building blocks of an intelligent algorithm:

Bt+1 = Bt + ∆

Rational ‘onsumers’ may choose to discount transaction costs to zero but the sufficiently intelligent algorithm does not. There is a revenue purse to be shared amongst the online digital advertisers. Data patterns are a tradeable asset. They are embedded at ∆ into your online price, influencing your online behaviour in a subliminal bidding war against yourself: a final price, the END price, is higher than the opening bid, the buy-it-now or BIN price.

If we can identify the sources of the online transaction costs (TC) that are incurred by a rational consumer, then we might find an explanation for the divergence between BIN and END prices. If a rational ‘onsumer’ knows that TC > 0 then he or she will make every effort to minimise the transaction costs. If so, why is it that BIN < END? Is it unique to specific online transactions such as hotel or holiday bookings?

Non-Observable (Online) TC

Whatever the heuristics involved we believe that there are additional non-observable online TC complementing the data recovery by the SIAL.  There are at least two nonstandard transaction costs at ∆ in your online purchases that require some attention:

  • a rational ‘onsumer’ booking a holiday may be part of a group of friends but the algorithm is sufficiently intelligent to pick up an individual’s click as correlated with a group set of clicks leading to a purchase – call this a herding effect; and


  • rational ‘onsumers’ are inclined to repeat purchases online from the same airline or hotel or from the same online platform with stored auto-fill information on address and credit card details and again the algorithm is sufficiently intelligent to know this – call this a hard commitment or no-switching

You Are Your Own Opponent

Allowing SIALs to influence your behaviour deprives you of a sovereign right as a rational consumer to choose freely. In bidding against yourself you have become your own irrepressible opponent[1]. Do we as rational ‘onsumers’ discount these non-observable costs at zero? Yes, we do because buying online generates latent or hidden transaction costs (TC). It is a different experience to the transaction of buying an apple at the fruit market. Consequently, an online purchase is always perceived to be cheaper than in the (offline) store in the shopping mall. This may well be the case for many products and services purchased online. But do you necessarily end up buying the product or service at a lower online price? The jury is still out. The pricing is less transparent than at your local bookstore (if it is still in existence) where buying a book presents a degree of transparency on the price paid. It too has opportunity costs but they are observable – for example, car-park ticket or bus fare to the book shop or time spent browsing in the store.


Anecdotally, paying others to wait in the queue line[2] is evidence that the transaction costs are not discounted to zero. In fact, they are positive; and if they are observably positive then a rational consumer would be prepared to pay up to the discounted value of their opportunity cost in order to be in the queue to secure an iPhone or a bargain priced 4K Sony TV. With online transactions, there may be a herding effect and a non-switching effect identified in the data patterns. The SIAL can translate them at ∆ into non-observable waiting time costs and queue costs. Unknowingly, the rational ‘onsumer’ discounts them to zero and BIN < END price. Machines ‘think’ because humans have stopped thinking. Memory as well as patterns of behaviour have been outsourced to smart devices. It is not inconceivable that an unwitting thief in the digital age of the Turing thinking machine may have buttoned my waistcoat. Honestly, I can’t remember!

[1] Check out an early idea at





Polar Bear & Seal Dilemma in the Apollonius Circle


Polar bears pursue seals. But polar bears cannot swim as well as seals. As the ice cap melts, there is less ice caps for the seals to rest. Both have to survive. With melting ice caps, the seal as victim should adapt to the same speed as the pursuer, the polar bear. In the language of differential games equal speed preserves the distance in the Apollonius circle Swimming at equal speed means survival. A valuable lesson – more cooperation, less conflict.


One of the classic illustrations in the game theory literature is the Prisoners’ dilemma. Faced with the option of whether to cooperate or compete with a rival depends on what each believes the other is going to do. In the playbook of a rational player competing is a dominant strategy supporting a Nash equilibrium wherein both are worse off in the long term.  Is there an equilibrium we all prefer? In nature, there are many games and different equilibria: the polar bears hunt seals; the seals swim to avoid the bears: This ice game of pursuit results in a Darwinian outcome of survival of the fittest.

Does it have to be so? Can the rules of the game be changed? What if the polar bears and seals signal mutual cooperation in order to survive? They cooperate because their behaviour is directed by the fact that the ice is melting. The amount of ice is no longer infinite. The newly observed patterns of behaviour in nature are too complicated to understand. New insights are being discovered in the BBC’s Planet Earth So, what if cooperating is a signalling solution to the polar bear and seal dilemma, how can we rationalise this solution from a game theory perspective? And how can we observe a degree of cooperation?


As the ice cap melts, there is less ice caps for the seals to rest. Less resting places makes it harder for the polar bears to capture the seals as they spend more time swimming in the waters. Polar bears cannot swim as well as seals. So, do polar bears spend more time on fewer ice caps waiting for the seals to rest or do they improve their ability to swim longer in pursuit of the bears?

For the seals, knowing that polar bears cannot swim as well and as long as they can, the optimal action is to stay longer in the water. But they risk capture by the polar bear, who, knowing that the seals believe that polar bears cannot swim as well as they, adapts to swim better, pursues the seals until they rest on an ice cap in the belief that there will be no polar bears nearby or the seals believe that the bears cannot swim as well as seals.

 Thief of Nature

In a post-Darwinian world of melting ice caps more seals stay longer in the icy water. If more seals stay longer in the icy water polar bears unable to swim as well as seals, will fall in population as they lose a vital food source. Fewer seals will survive. Fewer seals means fewer polar bears, so as the ice caps continue to melt it appears to be a no-win outcome for both the polar bears and the seals. This ‘thief of nature’ no-win outcome obtains since neither are responsible for the ice cap melting.

So, is there a lesson for the seals and bears faced with the dilemma of survival? There is the Darwinian outcome of survival of the fittest. However, since climate shapes their environment[1]  whomever adapts better to the melting ice caps has a greater probability of surviving. But what if they signalled to each other – the predator bear signalling to the seal?

Avoiding Bad Choices

Fish congregate in the centre of the frozen ice pack where the ice is thinnest. You, the reader and I, as humans, we know that if either of us falls through the frozen lakes of Siberia in temperatures approaching 60 degrees below zero we will die of hypothermia, or if you rescue me, my body will freeze immediately and I will die of shock. Same fate applies to you, I’m afraid. It’s nature’s own Siberian dilemma. We both know that this outcome of very bad choices to be true.

A higher payoff is represented by avoiding thin ice, by avoiding bad choices. The seals probably know by now that both will obtain the higher payoff if the polar bears stop pursuing them. And the polar bears believe that the seals believe this to be true.  Neither benefit from thin ice and both need the ice pans to survive. So, the polar bears unable to swim as well as the seals adapt to new food sources. The bears signal to the seals and both survive by adapting in the game of melting ice caps. A signalling strategy represents a payoff-dominant Nash equilibrium for both. By surviving they could both reach a payoff-dominant Nash equilibrium.

Swim at Equal Speed

In order to understand this signalling strategy we need to transpose the dilemma into a pure search game. A solution is for the seal as victim to adapt to the same speed as the pursuer, the polar bear: equal speeds equals survival in the equation of climate change. Same equal speed minimises capture provided each follow a pure strategy of avoiding thin ice. In the language of differential games equal speed preserves the distance in the Apollonius circle. The animals may rely on chance to choose their paths to survival. Seals can swim; polar bears need to learn to swim as fast as seals. The sole decision rests with the seal, the victim in the search game: how fast should she swim? Not swimming is not an option. Swimming too often or too fast is tiring and with the increase in thin ice, resting ice packs are less promising.


The life history of seals and polar bears is a cumulative process of adaptation of means to survival that change as the ice caps melt. What is possible is whatever isn’t necessarily not the case[2], so possibly, seals and bears swim at equal speed. Logically, that means that there is at least one possible world in which the sentence ‘seals and bears swim at equal speed’ is true. Albeit, since you and I are responsible for the melting ice cap, we too, need to adapt. We need to avoid conflict. There is at least one possible world in which the sentence ‘to avoid conflict’ is true. There may be and it is our 21st century world with finite resources and infinite data.

[1] On polar bears: and on seals


[2] Excellent read is Daniel Dennett (2003): Freedom Evolves

The Dark Pool of Empty Markets

Many have commented that the job market has become an enigma over the past few years. The jobless rate is low, but pay has risen slowly. Are we[1] measuring pay imperfectly? Vacancies co-exist with unemployment and the old phenomenon of under-employment and the new challenge of a zero-hours contract have emerged to colour the landscape. Many workers have had no real increase in wages in years. At Starbucks recently the Spanish barista and I chatted about job opportunities. She had an accredited certificate in the teaching of English as a foreign language. Additionally, she and her two friends were recent language graduates who had opted to move overseas to work as baristas in Ireland. They had no job opportunities as teachers in Spain. Coincidentally, a few months earlier, the vacancies page of a national paper carried notices for Spanish teachers at senior level to deliver a course on Spanish language and literature to the level prescribed by the Department of Education. The baristas applied for the vacancies and were not successful. It is not an unusual occurrence in the jobs market except that it was reported that in one of the schools Spanish was discontinued as a foreign language. French and German continued to be on the curriculum.

But why was Spanish discontinued? At one level there could have been a mismatch in the qualifications and skills required in the teaching of the Spanish course. At another level, maybe there was no demand for Spanish language at the school. Or maybe the more senior teachers, including French and German teachers, exercised a ‘hold-up’ on curriculum development until they retire. In a simple twist of fate one of the baristas had heard in the grapevine that there was a staff shortage in the school. On reflection there could be another explanation. Theoretical physicists have long believed that empty space is not empty at all[2]. The theory holds that radiation leaves energy in its wake when passing through the empty space. By analogy, in the economics of the jobs markets, Spanish baristas leave a skills set behind when they pass from one job at Starbucks to the next job at a Spanish restaurant creating an empty market of skills and talent in language provision. The transition creates an empty market of skills and talent in the provision of goods and services.

There are no actual jobs in an empty market. But with retirements and aging populations, Europe, for example, may have to rely on the dark pool of skills and talent in the empty market. It is not about the qualification per se rather it is about the misallocation of resources in an empty market that co-exists with the dark pool of skills and talent. In an efficient allocation of resources an individual with skills and talent enters an empty market at one level, (say) as a barista who is Spanish and qualified as a Spanish teacher, and exits at another level as a Spanish language teacher. It is an optimal outcome in a two-sided market of an aging European population and refugees, refugees that  qualified as doctors, engineers, teachers, nurses, writers, painters, plumbers, electricians inter alia who leave behind a skills set as they pass through an empty market as a doctor or engineer or plumber to become a refugee. Until policymakers accept the empty market phenomenon it is unlikely that baristas or refugees will have the opportunity to secure jobs that match their skills and talents. As Starbucks[3] CEO Howard Schultz commented ‘in a nation of latte makers and latte drinkers, you need more of the latter’. Europe has the demand for skills and talent; there is a dark pool of skills and talent, there is a new phenomenon of the empty market. The existence of an empty market could give rise to a misspecification in the economic analysis of labour data. In the econometrics of a wage equation, for example, the co-integration of earnings, prices and productivity will now require an effective hours’ variable[4] to accommodate hours worked in the new labour market of zero-hours contract,  underemployment and working in the grey and black markets. Otherwise a wage equation is just a re-parameterisation of a regression of the level of wages on the current and lagged levels of predicted wages and excess demand. In our view this could have implications for macroeconomic planning in an age of empty markets. The fact that there is a transitioning of skills and talent into an empty market right now should be recognised by policymakers and they should tap into and legitimise that dark pool, sooner rather than later.

[1] The question posed by Mark Glassman and Peter Coy in their vignette ‘Wages: Another Way to Look at Pay’ in Bloomberg Business Week July 22 2016.

[2] Article in The Irish Times ‘Magnetic Masters Bring Data Storage to a New Level’ by Dick Ahlstrom, July 21 2016.

[3] Cited in Time magazine July 11-18 2016 pp81

[4] Introduced in McNutt (1994): ‘Ownership and the s-firm’ in Andrew Burke [Ed] Enterprise and The Irish Economy Oak Tree Press, Dublin.