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Fundamental operational concepts, jury size, financial ratios and the Greeks


Governance as "juggling" -- Juggling as "governance" (Part #11)

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"Fundamental concepts": In exploring the possibility of such correspondences, there is a case for clarifying what are signified by the "fundamental concepts" of physics. Young offers a set of 12 in terms of "measure formulae". Arnopoulos offers a set of 15. A search of the literature reveals that there are numerous treatises on the "fundamental concepts of physics". Ironically however there appears to be little consensus on what constitutes a fundamental set -- other than at the level of the standard model of particle physics, presumably to be considered irrelevant to further insights into juggling (at least provisionally). A relevant commentary in Wikipedia (Category talk: Concepts in physics) is introduced with an irritable discussion of What is fundamental?

The quest can be framed otherwise by asking the question as to how many "operational concepts" a juggler requires in order to be able to juggle? Or a helicopter pilot to manage a helicopter? How do these relate to the fundamental concepts identified by Young and Arnopoulos? How would a juggling physicist identify the set of such fundamental concepts? Related issues can be explored more generally (Representation, Comprehension and Communication of Sets: the Role of Number, 1978; Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980).

The issue is then how such a set of concepts (insights or functions) can be understood to inform the challenge of "juggling" in governance -- beyond the extremely loose use of the metaphor in the citations above. A valuable indication is presumably offered by the extent to which a 12-fold pattern has been widely valued over centuries in many domains for reasons which remain obscure (Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources, 2011).

This checklist necessarily includes the Greek and Roman pantheons, as mentioned above -- with the particular implications they offer for governance. However, given the tenuous nature of the systemic links between those deities (as noted), there is a case for exploring whether they embody functions which bear a degree of equivalence to those of the set of physical concepts. The question can be explored more generally, which was the initial reason for establishing that checklist (Eliciting a 12-fold Pattern of Generic Operational Insights: recognition of memory constraints on collective strategic comprehension, 2011).

The mysterious enthusiasm for a pattern of 12 is currently illustrated by the bestseller by Canadian clinical psychologist and psychology professor Jordan Peterson (12 Rules for Life: An Antidote to Chaos, 2018), subject to the highly critical review by Adam A. J. DeVille (Jordan Peterson's Jungian best-seller is banal, superficial, and insidious, The Catholic World Report, 3 April 2018). With respect to "why12", the reviewer argues:

And why 12 rules? Here my mind freely associated to the droll story Margaret MacMillan tells in her splendid book Paris 1919 of Georges Clemenceau, with delicious Gallic hauteur and sarcasm, dismissing Woodrow Wilson: God himself was content with 10 commandments. Wilson modestly inflicted fourteen points on usâ-...the fourteen commandments of the most empty theory!)

But why are so many projects framed in that way?

Operational challenge exemplified by jury size: With respect to requisite variety in decision making, insights are emerging in the light of studies of jury size (Evan Moore and Tali Panken, Jury Size: Less in not More, Cornell University Law School, 2010; Dana Mackenzie, What's the Best Jury Size? Slate, 25 April 2013; Jeff Suzuki, Constitutional Calculus: the math of justice and the myth of common sense, JHU Press, 2015). These merit particular reflection, given the fundamental role attributed to juries in the process of governance -- notably the particular commitment to 12-person juries.

As noted by Chris Gorski (The Mathematics of Jury Size, Inside Science, 23 March 2012):

Could different jury sizes improve the quality of justice? The answers are not clear, but mathematicians are analyzing juries to identify potential improvements. Nowhere in the U.S. Constitution does it say that juries in criminal cases must include 12 people, or that their decisions must be unanimous. In fact, some states use juries of different sizes.

One primary reason why today's juries tend to have 12 people is that the Welsh king Morgan of Gla-Morgan, who established jury trials in 725 A.D., decided upon the number, linking the judge and jury to Jesus and his Twelve Apostles. The Supreme Court has ruled that smaller juries can be permitted. States such as Florida, Connecticut and others have used -- or considered -- smaller juries of six or nine people. In Louisiana, super-majority verdicts of nine jurors out of 12 are allowed. However, in 1978 the Supreme Court ruled that a five-person jury is not allowed, after Georgia attempted to assign five-person juries to certain criminal trials.

To mathematicians and statisticians, this offers a clear division between acceptable and not acceptable, and therefore an opportunity for analysis.

In the undertaking of such analysis Gorski notes that no good models exist for how jurors interact with each other: The real challenge is that the data doesn't really exist. Ironically this echoes the problem with other 12-fold sets, including the deities and the set of 12 Apostles (on which preference for a 12-member jury is seemingly based). How might Jesus be understood to have "juggled" (with) the 12 Apostles at the arcetypal Last Supper -- or King Arthur with the Knights of the Round Table?

Much more data and research is available for the size of the committees used in processes of governance. Most recently the optimal group size has been confirmed to be 7, as frequently cited (What is the optimum Board size? Governance Today, 2018; Marcia W. Blenko, Michael C. Mankins, and Paul Rogers, Decide and Deliver: 5 Steps to Breakthrough Performance in Your Organization, Harvard Business Press, 2010). However other factors and data have concluded that 11 is the optimal number (Russell Kashian and Heather Kohls, Committee Size and Smart Growth: an optimal solution, e-Publications@Marquette, 2009).

It might then be assumed that the "jury is still out", and that there may well be greater wisdom in 12. How the number relates to the requisite variety of distinctive perspectives and cognitive skills is clearly a concern, especially if distinctive functions are called for -- as implied by the Six Thinking Hats and the Six Action Shoes of Edward de Bono, and otherwise discussed (Comprehension of Numbers Challenging Global Civilization, 2014). It would appear that there is indeed a possibility of reducing the number recognized to 6, as argued by Edward de Bono (Six Frames For Thinking About Information, 2008) and presented diagrammatically. This reduction may well obscure in some way the need for complementary perspectives which would raise the number to 12, for example.

If it is widely assumed that it takes a jury of 12 to juggle wisely the arguments presented in a trial -- then how (in)effective and (unwise) might the capacity of an executive committee of 7 then be assumed to be? What "balls" might it then tend to "drop"? Is this kind of question of relevance to the functioning of committees with regulatory and oversight responsibility?

Insights from the set of financial ratios and "the Greeks": Governance of a commercial operation typically makes use of a set of standard financial ratios in evaluating and tracking performance. Each is a relative magnitude of two selected numerical values taken from an enterprise's financial statements (Joe Lan, 16 Financial Ratios for Analyzing a Company's Strengths and Weaknesses, American Association of Individual Investors. September 2012).

To the extent that the challenges of governance are defined by a set of risk sensitivities, mathematical finance offers a set of quantitative measures representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. Also known as risk measures or hedge parameters, these are collectively termed "the Greeks" because the most common of these are denoted by Greek letters.

Given their purpose, these two sets of measures can be considered comparable to the set of 12 measure formulae which are the basis for the arguments of Arthur Young -- in the light of the challenge of "governing" a helicopter. Clearly the issue with respect to the "healthy" governance of any collective initiative, is how non-quantitative tools essential to governance are supplemented (if at all) by an array of analytical tools. Arguably the tools can to some degree be considered as metaphors indicative of qualitative modes of cognitive engagement with the dynamics of governance.

The question of how many such tools are considered essential (when used) clearly remains a matter of debate -- especially in the light of distinctions between profit-making and non-profit-making undertakings (Andrew C Holman, et al, The Analysis of Key Financial Ratios in Nonprofit Management, June 2010; Dumisani Hlatswayo, 7 Important Financial Ratios Every Charity Leader Should Know, 20 March 2017; Kevin Leder, Financial Metrics and Benchmarking for Non-Profit Organizations, May 2012).

For the purpose of this exercise, the tools (as identified in Wikipedia) are simply listed to encourage further reflection, notably as to how they might be clustered, combined, ignored or "juggled" in practice.

Financial ratios (see also List of financial performance measures):

Risk sensitivities ("the Greeks"):

  • First-order Greeks
    • Delta: measures the rate of change of option value with respect to changes in the underlying asset's price.
    • Vega: measures sensitivity to volatility. It is the derivative of the option value with respect to the volatility of the underlying asset.
    • Theta: measures the sensitivity of the value of the derivative to the passage of time: the "time decay."
    • Rho: measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk free interest rate (for the relevant outstanding term)
    • Lambda (Omega): is the percentage change in option value per percentage change in the underlying price, a measure of leverage, sometimes called gearing.
  • Second-order Greeks
    • Gamma: measures the rate of change in the delta with respect to changes in the underlying price.
    • Vanna: (or DvegaDspot and DdeltaDvol): is a second order derivative of the option value, once to the underlying spot price and once to volatility.
    • Vomma (Volga, Vega Convexity, Vega gamma or dTau/dVol) measures second order sensitivity to volatility. It is the second derivative of the option value with respect to the volatility, or, stated another way, vomma measures the rate of change to vega as volatility changes.
    • Charm (or delta decay, or DdeltaDtime): easures the instantaneous rate of change of delta over the passage of time.
    • DvegaDtime: measures the rate of change in the vega with respect to the passage of time. It is the second derivative of the value function; once to volatility and once to time.
    • Vera (or Rhova): measures the rate of change in rho with respect to volatility. It is the second derivative of the value function; once to volatility and once to interest rate.
  • Third-order Greeks
    • Color (gamma decay or DgammaDtime): measures the rate of change of gamma over the passage of time
    • Speed (or the gamma of the gamma or DgammaDspot): measures the rate of change in Gamma with respect to changes in the underlying price.
    • Ultima (or DvommaDvol): measures the sensitivity of the option vomma with respect to change in volatility.
    • Zomma (or DgammaDvol): measures the rate of change of gamma with respect to changes in volatility.

In the context of this exploration it is extraordinary to discover the importance of gamma in financial trading. There it offers a measure of the rate of change in the delta with respect to changes in the underlying asset's price. In a world focused on change, gamma is an indicator of the change in the rate of change. With respect to finance, this must necessarily be understood as the change in one of the most tangible forms of value -- if notional and symbolic. Given the argument for the value of playing (as noted above), it is strange that "playing the markets" is a well-recognized phrase and that gamma should be so fundamental to the skills involved.

This suggested further speculation (Psychosocial Implication in Gamma Animation: Epimemetics for a Brave New World, 2013). The argument is notably developed with respect to:

Fruitful gamma resonance within a pattern of mnemonic associations?
Gamma as change in the rate of change of value		 Unsustained awareness implied by gamma inversion
Relational insight dynamics in terms of a "gamma" perspective

As the second derivative of the value function with respect to that underlying price, gamma is an important measure of the convexity of a derivative's value, in relation to the underlying price. It is important because it corrects for the convexity of value. Convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity.

With "the Greeks" clustered in terms of first, second and third-order derivatives, this readily recalls those derivatives in the measure formulae of Young's table (indicated below). They also raise the question of the problematic relevance of "derivative thinking" (Vigorous Application of Derivative Thinking to Derivative Problems, 2013). The requisite vigilance for sustainable governance also recalls the sene in which "finance" can be recognized as a surrogate for confidence and the focus of attention implied by derivatives of a higher order (Investing Attention Essential to Viable Growth: radical self-reflexive reappropriation of financial skills and insights, 2014).

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