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: http://www.patrickmcnutt.com/blog/playing-the-spectator-while-waiting-for-covid/ 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

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.

Prognosis

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.

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: http://www.patrickmcnutt.com/news/the-tao-of-robot-ethics-artificial-moral-agents/.

Introduction

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.

Prognosis

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?

Bibliography

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

Citations

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 http://www.patrickmcnutt.com/news/meso-data-omega-circles-origami-manifolds/

[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

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.

[2] http://www.patrickmcnutt.com/blog/wistful-economics-201516/

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

[4] https://en.wikipedia.org/wiki/Condorcet_loser_criterion

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.

Prognosis

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 http://www.patrickmcnutt.com/blog/game-vision-you-are-your-own-irrepressible-opponent/

[2] https://www.theatlantic.com/business/archive/2014/07/the-growing-market-for-getting-paid-to-wait-in-line/375083/