Publications in experiments in quantification
Peer-reviewed publications are available from the publications sites provided.
How does one win in a game of life in community? The Sermon on the Mount can be seen as strategies according to Christian tenets. These strategies may appear counter-intuitive for victory. What is victory in the game of life and how do we quantify it? And can the strategies as set out in the Sermon lead to sustainable victory?
Game theory provides a unique perspective as an analysis of the conflict between a human's selfish ego and the desire for social relationships. We quantify the game of the Sermon on the Mount for ego-depletion and prosocial gain, with five tasks identified and quantified accordingly. We view the Sermon as a set of strategies for achieving success in life, and calculate the Nash equilibrium to determine the best strategy for each player. We calculate payoff values for the five tasks by the Analytical Hierarchy Process (AHP), and simulate and rank repeated interactions between two players by their total payoff values as three types of repeated games, namely, natural, faith, and sustainability games.
We show that to live according to the tasks in the Sermon on the Mount is not an intuitive choice, but with faith a player can profit from and be victorious by following these strategies. In scenarios where the opponent mirrors the player's strategies, the best outcome for both players is achieved when both players cooperate to reward their opponent.
Working paperes in experiments in quantification
The working papers, research projects, theses and dissertations listed are being prepared for publication.
A game theoretical study of the pursuit of romantic happiness
2021
Human beings seek happiness in relationship. However, the very definition of happiness must be defined. What is happiness? How can we find in the complexity of human nature a way for everyone to behave so to find happiness? In this research, the use of mathematics and specifically the field of game theory is used to create and implement a romantic game capable of representing as faithfully as possible the interactions between two individuals who may have completely different personalities. A two-player non-zero game is constructed for players choosing one of sixteen strategies. These strategies depend on the personality of the player and the opponent based on their Myers-Briggs Type Indicator result. Romantic happiness is a measure of the happiness a player gains by being authentic to their own personality while being compatible to the personality of their love interest.
The best strategy for each player is shown to be a mixed strategy of four best strategies. These four best strategies show a bias for the player to remain faithful to their own personality while only slightly comprimising for compatibility with the opponent's personality. The maximum expected romantic happiness for all players is a value of 0.56 between the minimum happiness lower bound of 0 and the maximum happiness upperbound of 1.
2021
South Africa is faced with a constitutional crisis as it was suffering from one of the worst performing basic education systems in the world. There was a clear social and educational disparity between the majority of children that attended government schools in low-income communities, compared to the minority of learners who attend elite private schools in wealthy communities.
Educators play an integral role in the development of a leaners academic performance thus it is imperative that one isolates and analyses the factors that influence the effectiveness of a teacher. The system of differential equations describing the TEM consisting of 24 variables in need of weight calibration to improve their relationship to each other. A Tabu Search (TS) algorithm is developed to search for the best weight parameter combination to ensure that the difference between the observed and simulated results were minimised. The best percentage mean square error found from TS algorithm is 2.72.
2021
In an attempt to fulfil the Bill of Rights, education in South Africa is governed by two national departments. The South African education system has been described to still display dysfunctional behaviour despite the national government developing progressive policies that
are in line with international trends. Approximately 25% of learners from wealthier areas attain a higher reading score compared to learners from poorer areas ( approximately 75%) . Undoing said damage is not a simple process and requires continuous assessment and re-evaluation of state and policy makers, academic researchers and educational NGOs depend on quality data for proper management, planning and policy-formulation. For this reason, it is of importance to update inventories of data sets available as well as assess their quality. The goal of this project was to explore the main international and national datasets on the South African basic education system. A critique of the usability and quality of each of the main education datasets compared against the best practice techniques. The main international data sets include the TIMSS, PIRLS and SACMEQ and their contents were summarised. The same was done for the national education data sets and the main sets include the SNAP Survey of ordinary schools, the National Senior Certificate, NIDS-CRAM and the General Household Survey. It was found that the PIRLS and TIMSS are useful for global comparisons and identifying problem areas for learners but are not so useful for accurately representing the South African education system.
The national datasets are useful for assessing the socio-economic influences on education but are not so useful is assessing the performance of learners. It was also found that the international and national datasets were created using best practice techniques. The modelling techniques that could be utilised given the available datasets were presented.
Building a dataset for the Primary School Model
2020
Education systems are by nature complex, interdependent and policy-laden systems, the design of which is by no means an intuitive endeavour. System dynamics is a highly recommended technique with which to study the internal dynamics of education systems. The South African education system is in crisis. On average, South Africa has the worst education system of all middle-income countries and perform worse than many lower-income African countries. The Primary School Model uses system dynamics modelling to simulate the progression of learners in the primary public school system from Grade 1 to Grade 7. There exists a large number of datasets describing these learners, but the datasets are never based on the same sample and often describe very different characteristics. The ideal would be a single, large dataset containing all the necessary characteristics. This dataset can be constructed if care is taken to maintain correlation and causation relationships by using formal statistical techniques.
