Section 3: Designing TokenSpace: A Conceptual Framework for Cryptographic Asset Taxonomies

Section 3: Designing TokenSpace: A Conceptual Framework for Cryptographic Asset Taxonomies
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Contributors (1)
Published
Aug 10, 2019

3.1 Introduction & Problem Statement of Taxonomy Development

Much of the taxonomy development methodology developed here is based on the work of Nickerson et al. [66, 115] which developed generalised frameworks for the creation of classifications, taxonomies and typologies in the domain of design science for information systems. As the purpose of a taxonomy development is to structure and / or order knowledge or objects within a specific domain, this allows researchers to understand how concepts are interrelated and whether there are anisotropies in the relative incidence of ensembles of characteristics within the group of objects to be classified, if voids or dearths of combinations of characteristics exist within the possibility space and so on.

Using the methodology of Nickerson et al. with terminology as outlined in Section 2.1, we can recall the use of the generalised term taxonomy to refer to conceptual, axiomatic, intuitive, elicited, empirical or hybrid approaches to classification. Phenetics - numerical taxonomy - may be employed to score or weight branches of a taxonomy based on quantitative metrics - such as the number or proportion of fully validating nodes in a network - or to arrive at some initial phenomenological groupings of objects using clustering or other statistical grouping techniques. It is instructive to state explicitly that though classifications may be a step towards ontology as evinced by the periodic table of chemical elements in Section 2.3, the exercise of developing taxonomies themselves is often conducted with a large degree of intuitive reasoning or ad hoc decision making as the process of developing component taxa - and the taxonomies they are constructed from - is typically iterative. Using this approach, Nickerson and coworkers have made a valuable contribution to the systematisation the act of systematising domain information - in a sense, meta-taxonomy [66, 115].

In the binomial classification paradigm of Linneaus - as applied to biology, botany and zoology - there exists a hierarchy of categories that the user of the taxonomy must follow in order to classify a living thing as a member of a taxonomic rank: kingdom, phylum, class, order, family, genus or species [116]. Such approaches may be considered as cladistic as well (Section 2.1), in that they are based on geneaology, provenance or ancestry. Codebase forkonomies - fragmentation maps of OSS codebases, kernels and distributions - are a more modern example of simple cladistic taxonomies [5].

3.2 Construction of the TokenSpace Framework: Components & Methodology

3.2.1 Building Robust Taxonomies based on Information Systems Best Practices

Nickerson and co-authors describe what can be considered a taxonomy with flat dimensions, arrived at by following the process outlined in Figure 13 and approach details in Table 4:

Prat et al. later extended this formal definition to allow hierarchical dimensions, so that characteristics may be grouped into categories, which may themselves be nested in a higher-level category - Nickerson's dimensions - as many times as necessary until the highest (root) category is reached which corresponds to the meta-characteristic in Nickerson's lexicon [117].

<p>Figure 13: Methodology for taxonomy development by Nickerson et al. [115]</p>

Figure 13: Methodology for taxonomy development by Nickerson et al. [115]


Meta-characteristics and characteristics: taxonomy development requires the determination meta-characteristics, to serve as the basis of choice of characteristics within the taxonomy. Choice of meta-chararacteristic should be based on the purpose of the taxonomy, and purpose should be based on use. The choice of meta-characteristic in a taxonomy may be arrived at iteratively, as “themes” of the object characteristics being analysed become apparent or alternatively may be determined via empirical investigation with statistical analysis, intuition or by pre-existing conceptual design. After the meta-characteristic has been selected, the researcher can proceed with either conceptual or empirical approaches to reach the first iteration of their proto-taxonomy. The meta-characteristic should be the most comprehensive characteristic which the taxonomy should differentiate on the basis of. Characteristics should be logical consequences of the meta-characteristic. Each characteristic that objects exhibit should follow from the meta-characteristic but also discriminate among the objects.

Dimensions: groupings of characteristics which branch recursively from the meta-characteristics. Approaching conceptually-to-empirically, dimensions are first conceived intuitively or inductively with meta-characteristic in mind, with characteristics which then follow from the meta-characteristic and are also mutually exclusive and collectively exhaustive amongst themselves. In an approach of empirical-to-conceptual type, dimensions may be conceived a priori and later subjected to methodological scrutiny as to their validity. The optimal approach depends on domain knowledge of researcher and the quality and quantity of empirical data available. Flexibility in the approach adopted is valuable as further empirical data and / or domain objects to classify may become available over time.

Ending conditions: using an iterative method there must be specified conditions for the taxonomy development process to terminate / complete, as seen in Table 5. When the classification system fits the definition of a functioning taxonomy that iteration of the taxonomy is complete, for example: characteristics mutually exclusive and collectively exhaustive, sufficient specificity and dimensionality to adequately characterise and differentiate domain objects of interest. That is to say, the taxonomic process can be considered to have completed satisfactorily when no spurious dimensions or characteristics remain, new objects may be classified without need for amendment, each object is satisfactorily classified and the activity of classification furthers understanding of the properties of the class of objects, rather than simply describing them.

<p>Table 5: Ending conditions for useful taxonomies [115, 118]</p>

Table 5: Ending conditions for useful taxonomies [115, 118]


3.2.2 Three Conceptual-to-Empirical Approaches to Short-Listing Taxonomy Dimensions & Characteristics

Selected dimensions and characteristics for this instantiation of a TokenSpace based on the legacy asset classes discussed in Section 1.3 follow. Individual taxonomies have been iteratively constructed using a conceptual-to-empirical approach for each meta-characteristic. Taxonomy examples, scores and visual representations are detailed in Section 4.

Securityness: The extent to which an asset or instrument exhibits characteristics of a security.

Proposed contributing factors to an asset's Securityness score which are candidate attributes for taxonomy dimensions and characteristics are listed in Table 6.

<p>Table 6: Candidate attributes for Securityness</p>

Table 6: Candidate attributes for Securityness


Moneyness: The extent to which an asset or instrument exhibits characteristics of a monetary good.

Proposed contributing factors to an asset's Moneyness score which are candidate attributes for taxonomy dimensions and characteristics are listed in Table 7.

<p>Table 7: Candidate attributes for Moneyness</p>

Table 7: Candidate attributes for Moneyness


Commodityness: The extent to which an asset or instrument exhibits characteristics of a commodity good.

Proposed contributing factors to an asset's Commodityness score which are candidate attributes for taxonomy dimensions and characteristics are listed in Table 8.

<p>Table 8: Candidate Attributes for Commodityness</p>

Table 8: Candidate Attributes for Commodityness


3.3 Design Choices & Justifications for TokenSpace

3.3.1 TokenSpace as a Conceptual Representation of Spatio-Temporal Reality

The instantiation of a TokenSpace presented in Section 4 is best thought of as an idealised three-dimensional space within which assets are placed according to taxonomy-derived “scores”. Each axis maps to a particular meta-characteristic as outlined in Section 3.2, “Securityness”, “Moneyness” and “Commodityness”. The TokenSpace presented here may be considered by analogy with our own spatio-temporal conception of reality, consisting of a three-dimensional space delineated (for convenience and visual clarity) by orthogonal axes

S{\mathcal S}
bar,
M{\mathcal M}
bar and
C{\mathcal C}
bar, with a fourth temporal dimension able to be incorporated through the “movement” of assets through the space as characteristics evolve over time.

<p>Figure 14: <em>TokenSpace</em> visual impression</p>

Figure 14: TokenSpace visual impression


Other constructions with different meta-characteristics, boundaries, scoring methods or dimensionality are possible. TokenSpace is intended to be a flexible conceptual framework designed to output visually comparable results. Assets may possess a score or range on each axis between 0 and 1 inclusive giving rise to an object inhabiting a region of TokenSpace described by the (x, y, z) coordinates which in this case map to the meta-characteristics

S{\mathcal S}
bar,
M{\mathcal M}
bar and
C{\mathcal C}
bar. Each asset's location in TokenSpace is intended to be derived from a weighted scoring system based upon combinations of taxonomy, typology, intuitive, elicited and / or quantitative methods depending on the choices and assertions of the user - which may or may not be identical to those proposed in this work.


3.3.2 Defining Boundaries

For the purposes of facile comprehension, each axis is bounded between the values of zero and one. An asset that is determined - using whichever scoring method is chosen by the researcher - to exhibit none of the properties that are taken to constitute the meta-characteristic would possess a score of zero. Conversely an asset constituting an ideal or canonical example in the context of Bailey's definitions (see Section 2.1) of the meta-characteristic in question would possess a score of one. Assets may possess any value between zero and one, although this somewhat coarse approach does not distinguish between “good” or “bad” assets - for example a 2017 ICO may constitute a very poor investment analogue of a security, and at present TokenSpace does not distinguish between this asset's Securityness from a bona fide security such as a legitimately issued stock or bond. TokenSpace could be extended to occupy a space between negative one and positive one to reflect the difference in quality of assets in the future.


3.3.3 Dimensionality & Clarity

The choice of three meta-characteristics and hence spatial dimensions in the example instantiation of a TokenSpace constructed in Section 4 is partially justified by the analysis of traditional asset classes in Section 1.3.3 and the apparent link between securities, commodities and moneys with characteristics of various cryptographic assets. Depending on the needs of the user, a custom TokenSpace could be created with any number of dimensions but beyond 3 or 4 the visual clarity afforded by the framework diminishes. Conversely fewer dimensions could be used, or a bespoke TokenSpace could be constructed by iteratively adding dimensions with scores derived from the usual menu of options with judgement applied as to the dimensionality which provides the greatest explanatory power. Alternative graphical approaches such as a “radar” diagram may be helpful in visually comparing higher dimension TokenSpaces, as seen in Figure 15, though awareness of the so-called Curse of Dimensionality and in particular implications to statistical analysis of populations in sparsely populated high-dimensional Euclidean space [119]. In particular analytical techniques such as k-means clustering may produce unreliable results in such scenarios.

<p>Figure 15: A radar graphical approach for a hypothetical <em>TokenSpace</em></p>

Figure 15: A radar graphical approach for a hypothetical TokenSpace


Some discussion of the true “orthogonality” of the meta-characteristics employed here is worthwhile. It is not the belief of the author that these overarching attributes are completely independent from one another, instead the utilisation of orthogonal axes is a conceptual simplification considered acceptable in order to produce output which can be easily visually discerned by humans. This is in accordance with the aims of producing a useful classification framework for the subjective comparison of cryptographic asset properties. For instance Commodityness could be seen as an analogue of utilityness, but so-called utility tokens also frequently exhibit security-like characteristics. Likewise, commodity-like assets such as Bitcoin and Ethereum are also partially usable as pseudo-monetary goods. The taxonomies displayed in Tables 10 and 11 show a great deal of commonality in the dimensions between Moneyness and Commodityness, with significant differences in the weightings of scores.


3.3.4 Categorical & Numerical Characteristics

For an ideal instantiation of TokenSpace with maximum explanatory power, a balance should be struck between thorough utilisation of discriminatory attributes whilst not encumbering the researcher with a classification which is overly burdensome to apply. For the instantiation of TokenSpace in Section 4 the optimal balance was found with hybrids of categorical and phenetic taxonomy types. This design choice - preferring hybrid supra-taxonomies to simpler categorical taxonomies - is justified by the desired outcome of numerical scores as the output of the classification execution in order to populate asset locations in the Euclidean 3D space that TokenSpace creates. A particularly useful tool, made use of widely in the taxonomy examples in Section 4 is the indexed dimension. Taking the notion of a range-bound score - determined in any manner deemed acceptable as part of the experiment design process - as a proxy for one or more categorical discriminants allows significant simplification of the application of taxonomic systems to objects. A pertinent example of this in the TS10 TokenSpace example illustrated in Section 4 is the consolidation of seven multi-layered dimensions addressing the balance of power and influence between network stakeholders into a single “alignment index”.

It is important to consider Goodhart's Law when developing quantitative metrics, as the decentralisation theatre discussed in Section 1.3.3 or susceptibility of metrics to Sybil nodes or automated agents mean that many quantitative metrics cannot be relied upon in an absolute sense. That which can be measured, becomes an optimisation target and as a result is susceptible to manipulation [120]. Comparative analytical approaches may be still be valuable, and judgement should be exercised by the researcher with respect to this. Taking this one step further, the researcher should keep in mind that their classification approach may require constant appraisal and optimisation. Due to strong incentives for ecosystem participants to portray some assets favourably with respect to others for a variety of motivations, the very act of publishing a classification approach renders it vulnerable to perversion through relatively facile means of manipulation. In this respect, though making use of indexed dimensions increases the relative subjectivity of a classification system it also somewhat mitigates the effects of Goodhart's Law providing the researcher is sufficiently cautious in the development of their taxonomic system and its application to populations of objects.


3.3.5 Score Modifiers & Weightings for Taxonomy Characteristics & Dimensions

The purpose of assigning weightings to each dimension and/or characteristic in a meta-characteristic's taxonomy is to provide a rational basis from which to derive a quantitative but subjective score for each axis that a TokenSpace is constructed from. In the instantiation of TokenSpace presented in Section 4, with three meta-characteristics and indexed or categorical discrimination the weightings attached to dimensions may be conceived intuitively or by employing optimisation approaches. So for a dimension with three (mutually-exclusive) characteristics, characteristic A may increase the overall score by 0.05, characteristic B may increase it by 0.025 and characteristic C leads to no change. In the instantiation of TokenSpace presented in Section 4, weightings have been applied in an ad hoc manner for each meta-characteristic's taxonomy. In doing so, even when different taxonomies contain significant overlap of dimensions, categories and characteristics their weightings and overall scores may vary depending on how important those factors are judged to be in contributing to the meta-characteristic.

Approximate “target” scores for a selection of assets were intuitively reasoned and score modifiers for characteristics adjusted to facilitate loose convergence of conceptual and empirical methods. This approach could be refined by using statistical and operational research techniques such as cluster analysis of results, algorithmic optimisation or methods such as Delphi elicited judgement [121].

The approach employed in Section 4 with TS10 was to assign weightings to the dimensions themselves, so that the characteristic scores are themselves scored for importance in their overall contribution to each meta-characteristic score.

The definition of one or more category would be the selection of the dimensions: {a i , i = 1, ..., n}, which together would constitute the taxonomy for a particular meta-characteristic, and the relative weighting of these attributes:

3.3.6 Time-Dependence

Time-dependence of asset characteristics and hence their location in TokenSpace may be significant in certain instances due to temporal phenomena such as the putative Lindy effect, increased functionality of a network and hence a token that is required to access its services, and more generally the dynamic nature of cryptocurrency protocol networks and their native assets, tokens issued atop them and network fragmentations such as ledger forks. Time-dependent phenomena can be coarsely incorporated into this framework by evaluating an asset's location in TokenSpace at different points in time and charting asset trajectories. A more advanced approach could be to calculate a coordinate at time t based upon functions mapping expected or judged variation. Care should be taken to distinguish between temporal interpolation between past and present, and extrapolation beyond the present as future characteristics of an asset may not necessarily be easily predicted with a high degree of confidence.

A pertinent example of time-dependence of the Securityness meta-characteristic is the ostensible judgement of senior SEC official William Hinman to heavily imply in public comments made in summer 2018 that he deemed the Ethereum network to have become “sufficiently decentralised” for its native token ETH to not be considered a security, although the token crowdfunding event in 2014 most likely was a securities offering (see Section 1.3.3). These comments give rise to the necessity of a time-dependent scoring aspect to allow for changes as the network and / or asset matures. This may be justified as follows: the evolving characteristics of proliferating tokenised P2P networks appear to have a significant bearing on the opinions of senior regulators with respect to the security status of particular assets, and no objective boundary (or “Securityness threshold”) to separate objects on either side of exists a priori. Another consideration is the prospect of a “grace period” for distributed networks bearing cryptographic assets and tokens, as invariably these will commence operation as much more concentrated / centralised systems than the would eventually be envisaged to become.

Whilst these types of comments are indicative of an open-minded approach from legislative officials, some open questions remain. If future claims of ether on the as-yet-unfunctional Ethereum Frontier mainnet were a security at time of the crowdfunding, but ETH no longer carries that designation due to an “increase in decentralisation” then - making the assumption that regulators are rational and logical actors - we can propose that some regulatory boundary surface / zone in TokenSpace has been advanced through, from is security to is not security and the primarily underlying reason for this according to Hinman is “sufficient decentralisation” without making clear what the justification for this opinion was, or indeed decentralistion at which layer of the network meta-stack and ecosystem Section 1.2.

A more general regulatory policy question arises, which has significant implications for assets which were issued in a state of high Securityness with properties such as pre-network functionality and / or tightly held supply by insiders. Indeed the long-running cryptoasset exchange Poloniex announced in late 2018 that it was delisting three assets Gnosis (GNO), Expanse (EXP) and Synereo (AMP) without reasons proffered. However these assets share to some extent both of the above Securityness increasing properties, lending credence to the notion that the new owner of the business - Goldman Sachs-backed Circle - intends to follow a compliance-first strategy and are assessing the possible declaration of particular cryptoassets as securities by the SEC at some point in the future [46].


3.3.7 Boundary Functions

Following on from the complexities raised in Section 3.3.6 regarding the time-dependence of the location of assets inhabiting TokenSpace, the notion of a regulatory boundary function has been developed to delineate the change in ETH's status from is security to is not security based upon Hinman's summer 2018 comments (see Section 1.3.3). Naturally this is a subjective assignment and may be affected by factors both endogenous and exogenous to the networks and assets in question. An example of such a regulatory boundary visualised in TokenSpace is presented in Figure 16.

This binary approach may be extended to account for edge cases and regulatory grey zones by instead making a “safe”, “marginal” or “dangerous” distinction with regard to the likely compliance of assets with respect to particular regulatory regimes. Careful review of territory-specific regulatory guidance and judicious consideration of boundary functions is a necessity for this approach to have utility beyond the hypothetical.

<p>Figure 16: Regulatory / compliance boundary visualised in <em>TokenSpace</em>. Arbitrary polynomial for illustrative purposes</p>

Figure 16: Regulatory / compliance boundary visualised in TokenSpace. Arbitrary polynomial for illustrative purposes



3.3.8 Non-point & Anisotropic Asset Locations

When there is uncertainty or disagreement regarding the optimal weighting of a taxonomy characteristic or the categorical assignment of an asset, it may be helpful to employ a range, error bars or probability density functions (PDFs) to represent the likelihood of the meta-characteristic instead of precise loci [122]. The space-filling representations of quantum mechanical electron orbitals displayed in Figure 17 provide a set of well-understood and characterised functions from which to develop such an extension to TokenSpace and this is the subject of ongoing research.

<p>Figure 17: Single electron orbital probability density functions represented in 3D space [122]</p>

Figure 17: Single electron orbital probability density functions represented in 3D space [122]


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