Abstract
Ecological models are useful in modeling organizations and their competition over resources. However, the traditional approaches, particularly Blau space models, are restrictive in their dependence on a continuous space. In addition, these models are susceptible to indicating competition in sparsely populated areas of an ecology, resulting in competition being indicated where there are no resources to compete over. To deal with these problems we reconceptualize Blau space into the Hybrid Blau space model, using both a cellular structure to model a wider number of variable types, and probabilistic urn models to simulate competition between organizations. We briefly review the basic concepts of Blau space, demonstrate the issues with traditional Blau space modeling, present a new model referred to as the Hybrid model, and propose several new metrics to describe the behavior of organizations in this new model. A novel data source, attribute data from Parliament Members of the Ukrainian Parliament, are used to illustrate the Hybrid Blau space model.
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The data available are for Convocations 3–8 of the Ukrainian Parliament and were obtained from the parliament’s official website. Most of these data are in Ukrainian, so we have collaborated with native Ukrainian speakers to translate these materials. Convocation 8 is used because it is the most recent Convocation of the Ukrainian parliament, as well as it provides the most detailed, complete, and clearly translated data at this time.
In Ukraine the Parliament does not have regular elections. Instead they are called by the government and the rules that govern an election are voted on by the exiting members of the parliament. The governments that form after these elections are called Convocations. At the time of analysis, the 8th Convocation was the current convocation of the Ukrainian Parliament.
Because of the annexation of the Crimean Peninsula by Russia and the war in the Donbass, up to 27 seats in the parliament are presently unoccupied (IFES 2019). It is also common for seats in the parliament to go unfilled for some time for other reasons, such as the death of a parliament member or charges of corruption. As a result, the total number of filled seats is frequently less than the number that could be filled.
These individuals are referred to as non-factional and are not included in the analysis and examples unless need to illustrate unclaimed individuals within the ecology. This is done to simplify understanding of the Ukrainian Parliament for the reader.
Because of the nature of the Ukrainian Parliament as a changing and evolving Parliament, and the fact that the most recent and up to date information on its functions is not available in English, we rely heavily on correspondence with a Ukrainian colleague to provide background information.
Image produced using Blaunet Version 2.0.8. For more information on Blaunet see: Genkin et al. (2018). Download link: https://CRAN.R-project.org/package=Blaunet.
Number of assistants is used as a proxy for income because the exact income and monetary holdings of MPs are not publicly reported. However, members of parliament that have more than a single assistant likely are funding the assistants themselves and therefore have the financial resources to make this practical. In practice, this is somewhat difficult to measure directly because additional assistants are reported as volunteers, and no evidence of payment to volunteers is required (Brik 2020).
This scaling might rely on MDS techniques or a Goodman RC-II model, but these details are beyond the focus of this paper.
The limitation to adjacent cells being within the maximum and minimum values of a dimension also implies that there are limit cases where no adjacent cell can be considered for the recruitment space because they exist outside the limits of Blau space as it is utilized for the Hybrid Blau space model.
An organization’s niche is calculated as range which extends out a fixed amount above and below the mean value on each dimension. The niche width is often fixed at 1.5 Std. Dev. in traditional Blau space analysis, but this parameter is tunable. In traditional Blau space analysis the recruitment range is seen as the entire space. See also: McPherson (1983), McPherson and Ranger-Moore (1991), and Popielarz and McPherson (1995).
An example of this would be a cell neighborhood that includes cells two units out from the focal cell on all sociodemographics.
We use the sampling with replacement implementation of an urn model because the recruitment of one individual into an organization does not instantaneously make recruitment of another into the same organization less likely.
The fraction of the focal cell that is updated in a given iteration is a tunable parameter. In other words, it is possible to only update half of the memberships, a quarter of the memberships, or even a single membership, during an iteration.
We are evaluating a criterion that identifies convergence using the amount of change in the last several iterations of the model. This simple criterion typically stops the models around the 5000 to 6000 iteration step range, providing more support for our claim of overpermutation. Although the simple convergence criterion is not discussed in depth in this paper, more information is available by request, and we are actively working to develop an appropriate strategy.
For the purpose of generating scores for the Extensiveness metric, this is also total recruitment area of the space.
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Funding was provided by Office of Naval Research Multidisplinary University Research Initiative (MURI) under Grant Number N00014-17-1-2675.
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Appendices
Appendix 1: Model performance at different iterations
See Table 7.
Appendix 2: Comparison between initial election results and session 1
Below is a comparison of the differences between the intital session of the 8th convocation of the Ukrainian Parliament and session 1. Overall, these results point to gradual changes between sessions in a convocation, that the relative size of the factions in the parliament stays similar between sessions, and that most of the changes in membership are changes of members affiliation with a faction. No faction affiliation individuals are not included in this comparison, but do contribute to the total number of individuals available for memberships. These results reinforce conclusions drawn in the section on results and model interpretation.
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Harder, N.L., Brashears, M.E. Predicting organizational recruitment using a hybrid cellular model: new directions in Blau space analysis. Comput Math Organ Theory 26, 320–349 (2020). https://doi.org/10.1007/s10588-020-09306-9
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DOI: https://doi.org/10.1007/s10588-020-09306-9