The complexity of individual graphemes is measured by means of the following method. Scanned versions of original Vai writing (from Appendix I) are first vectorised to ensure consistency of scale. From the vector images, two forms of complexity are calculated: perimetric complexity is the squared length of the inside plus outside perimeters of the grapheme divided by the ink area contained within those perimeters, while algorithmic complexity is derived by compressing the vectorised image and measuring the file size. 

Vai graphemes

It might be reasonable to assume that higher-frequency graphemes are likely to experience greater compression since they have undergone more reproductions. We are not, however, predicting a correlation between frequency and complexity-compressibility. Rovenchak, Riley and Tombekai \cite{RN1492} have found that complexity is unevenly distributed in the contemporary Vai script. This fact does not rule out the possibility that individual high-frequency items become more compressed than low-frequency items across multiple generations but it does suggest that Vai is not optimally compressed in terms of frequency across the whole system. Further, as Bodo Winter has argued,  contextual variability is a better predictor than frequency when it comes to the evolution of language. In other words, items that appear in a diverse array of unique contexts are more likely to change than those that appear frequently but in the same environments.  

Part I: Analysis of historical data set

We assign a complexity-compressibility quotient to each of the vectorised graphemes. These scores are plotted against two variables: time in history and the relative frequency of the character.

Part II: Experiments

A few experiments are proposed with varying conditions. In one of these we ask participants to simply learn and then write out individual high-frequency Vai symbols and use the output as the input for the next generation. In an alternative version we ask them to learn and reproduce whole words to test whether compositional effects of linear writing come into play. A variant experiment starts participants at different points in the history of the script. One group is trained on high-frequency characters as they were attested in 1834 and another group on the same set of characters as recorded in 2005.

Predictions

For both parts of the study, our general predictions are the same:
1. Graphemes within the Vai character set will become more compressed over successive generations in both the graphic form of individual items (item-level compression) as well as in the relationships between items (system-level compression).
This will be indicated by the following:
2. The Vai character set will exhibit greater speed of change in earlier generations than in later generations. In other words, as compression sets in, the increasing optimality of the system reduces the pressure for change. The speed of change is measured by comparing time distance with complexity measures. 
In summary we expect to find that repeated transmissions of the script will amplify the compression bias, resulting in graphemes that are more compressed in later generations. For individual graphemes this can be described in terms of a principle of least effort, whereby the maximal amount of information is communicated by means of minimal graphic complexity. Likewise we expect system-wide compression, which will be observed when individual items act on one another systematically within the set, increasing the overall interdependence of the inventory.
If our predictions hold true, our study will represent the first validation that semiotic transmission experiments have explanatory relevance to the real-time evolution of a natural writing system.
[This part is suggested by OM, feel free to amend or drop it:
3. Zipf's law of abbreviation.
This prediction only applies to Study II. Some authors have suggested that Zipf's law of abbreviation might apply to graphic codes in addition to spoken languages (Ferrer i Cancho et al. 2013). Zipf's law of abbreviation is the observation that more frequent words tend to be shorter than longer ones (Zipf 1949, Bentz xxxx). Complexity of written signs is a plausible equivalent of word length, since both longer words and more frequent letters contain more information and require more processing effort (Pelli et al.). Rovenchak et al. (Issues in Quant. Ling. paper + 2008 paper) already attempted to find evidence for show Zipf's law of abbreviation on the Vai script (whose length make it quite suitable for such an analysis). They did not succeed, but the measured letter complexity in an idiosyncratic way, based on manual coding, which we think the present study could improve upon. 
We will assess the correlation between character complexity and character frequency, using the frequency measures provided by Rovenchak et al. Given these previous negative findings, we make no particular prediction regarding the existence or direction of this correlation.]

Why we might be wrong (and why being wrong is also interesting)

If no compression effects are found this may well be due to the fact that the Vai writing system may have already been optimally compressed at the time of its creation. Conventionalised but non-linguistic graphic systems were in use by the Vai people prior to their invention of writing (see Kelly [micenei]) and it is argued by literate Vai that elements of these systems have informed the design of the script (Massaquoi). If this was the case then the transition from a semasiographic system to a phonographic one was in itself a substantial "compression event" in which previously multi-valent signs were affixed to single syllables. Such a radical narrowing of interpretation, brought about through a conscious process of group deliberation, would already account for most of the compression to the system: subsequent transmissions would amount to only minor tweaking. A recent investigation has shown a distinct yet analogous finding with regards to a cardinality bias in the world's writing systems. Morin demonstrated that scripts do not tend to become more cardinal over multiple transmissions in historical time, but that cardinality is "baked in" from the beginning (Morin under review). Thus, we may discover that the near-optimal compression of Vai and other non-laboratory generated graphic systems was an outcome of upstream cognitive processes. 
This is not to invalidate semiotic transmission experiments generally, however a a negative finding may suggest that not all cultural items will change in the process of transmission. This would speak to the trade-off between the set and the individual items within the set: as the set itself becomes compressed it relieves the compression pressure on individual items.
By contrast, it may also suggest that the system is not optimally compressed but that outside sources of inertia are acting on it and preventing compression effects from arising. As previously mentioned, attempts to standardise the Vai script have been rare while the script has not been taught in an institutional setting since 1850. As such, a major source of inertia in the form of institutional pressure has been removed. If, therefore, we detect resistance to compression then we would be unable to argue that such conservatism was a result of top-down institutional pressures unless such institutions escaped notice in the documentary historical record.
A major limitation of asynchronous graphic communication is that misunderstandings can never be repaired in real time (REF Topics paper). Thus, it could be the case that specific coordination demands of successful asynchronous communication already exert too much inertia on the system. We know from other historical contexts that apparently non-optimal writing systems still manage to be transmitted with high fidelity. Eg, writing systems that have enormous redundancy and graphic complexity (eg, xxx) or those that are borrowed from elsewhere and whose typologies are ill-suited to the phonology of the new language. 
All experimental participants will already be literate in the Roman script and perhaps others. This means that the experiments and the historical data are not directly comparable on the dimension of literacy. Consequently, changes to the Vai input across experimental generations may be conditioned by prior literacy in another linear script, thus items may become more Romanised over time. In itself, this does not undermine the premise since our study is interested in detecting compression regardless how that compression is actualised. 

Acknowledgments

The following institutions and individuals helped us secure rare manuscripts for our dataset: Asien-Afrika-Institut (University of Hamburg), Hella Bruns (Max Planck Institute for the Science of Human History, Jena), Valerie Haeder (Library of Congress, Washington). The primary Vai data was tabulated by Olena Tykhostup (Freidrich Schiller University, Jena).