International Journal of Mathematical Research

Published by: Conscientia Beam
Online ISSN: 2306-2223
Print ISSN: 2311-7427
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No. 5

On Statistical Definition of Free and Fair Election: Bivariate Normal Distribution Model

Pages: 49-62
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On Statistical Definition of Free and Fair Election: Bivariate Normal Distribution Model

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Ronald Wesonga , Fabian Nabugoomu , Abraham Owino , Leonard Atuhaire , Agnes Ssekiboobo , Xavier Mugisha , James Ntozi , Tom Makumbi , Peter Jehopio , Bruno Ocaya

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  1. Government of Uganda, The constitution of the Republic of Uganda 1995, Government of Uganda, Kampala, 1995.
  2. J. Gerring, S. C. Thacker, and R. Alfaro, "Democracy and human development," The Journal of Politics, vol. 74, pp. 1-17, 2012.
  3. G. World Bank, World development indicators 2012: World Bank Publications, 2012.
  4. D. G. Beco, "Human rights indicators: From theoretical debate to practical application," Journal of Human Rights Practice, vol. 5, pp. 380-397 2013.
  5. J. Donnelly, Universal human rights in theory and practice: Cornell University Press, 2013.
  6. M. Goodhart, Democracy as human rights: Freedom and equality in the age of globalization: Routledge, 2013.
  7. D. A. Marker, "The statistical role in voter identification (ID) laws," Statistics and Public Policy, pp. 46-50, 2014.
  8. C. Darch, "Statistics, indicators and access to information in African countries," Access to Information in Africa: Law, Culture and Practice, vol. 1, p. 109, 2013.
  9. K. N. Kotsoglou, "How to become an epistemic engineer: What shifts when we change the standard of proof?," Law, Probability and Risk, vol. 12, pp. 275-298, 2013.
  10. D. L. Cingranelli and D. L. Richards, "The cingranelli and richards (CIRI) human rights data project," Human Rights Quarterly, vol. 32, pp. 401-424, 2010.
  11. A. Mascarenhas, P. Coelho, E. Subtil, and T. B. Ramos, "The role of common local indicators in regional sustainability assessment," Ecological Indicators, vol. 10, pp. 646-656, 2010.
  12. R. Wesonga, F. Nabugoomu, and P. Jehopio, "Parameterized framework for the analysis of probabilities of aircraft delay at an airport," Journal of Air Transport Management, vol. 23, pp. 1-4, 2012.
  13. A. DasGupta, Probability for statistics and machine learning: Fundamentals and advanced topics: Springer, 2011.
  14. G. E. P. Box and G. C. Tiao, Bayesian inference in statistical analysis vol. 40: John Wiley & Sons, 2011.
  15. R. Y. Rubinstein and D. P. Kroese, Simulation and the monte Carlo method vol. 707: John Wiley & Sons, 2011.
  16. E. J. Gumbel, Statistics of extremes: Courier Dover Publications, 2012.
  17. G. Rajesh, E. I. Abdul-Sathar, K. V. Reshmi, and K. R. Muraleedharan Nair, "Bivariate generalized cumulative residual entropy," Sankhya A, vol. 76, pp. 101-122, 2014.
  18. J. D. Hadfield, "MCMC methods for multi-response generalized linear mixed models: The MCMCglmm R package," Journal of Statistical Software, vol. 33, pp. 1-22, 2010.
  19. A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian data analysis: CRC Press, 2011.
  20. B. Everitt and T. Hothorn, An introduction to applied multivariate analysis with R: Springer, 2011.
  21. R. M. Feldman and C. Valdez-Flores, Applied probability and stochastic processes: Springer, 2012.
  22. K. J. Preacher and J. P. Selig, "Advantages of Monte Carlo confidence intervals for indirect effects," Communication Methods and Measures, vol. 6, pp. 77-98, 2012.
  23. R. Wesonga and F. Nabugoomu, "Bayesian model averaging: An application to the determinants of airport departure delay in Uganda," American Journal of Theoretical and Applied Statistics, vol. 3, pp. 1-5, 2014.
  24. D. Stegmueller, "Bayesian hierarchical age-period-cohort models with time-structured effects: An application to religious voting in the US, 1972-2008," Electoral Studies, vol. 33, pp. 52-62, 2014.
  25. P. S. Jensen and M. K. Justesen, "Poverty and vote buying: Survey-based evidence from Africa," Electoral Studies, vol. 33, pp. 220-232, 2014.
  26. F. M. Sjoberg, "Autocratic adaptation: The strategic use of transparency and the persistence of election fraud," Electoral Studies, vol. 33, pp. 233-245, 2014.
  27. B. M. Ayyub and R. H. McCuen, Probability, statistics, and reliability for engineers and scientists: CRC Press, 2011.
  28. M. Pellicer and E. Wegner, "The mechanical and psychological effects of legal thresholds," Electoral Studies, vol. 33, pp. 258-266, 2014.
  29. A. Adam, "Do elections bring optimism?," Electoral Studies, vol. 33, pp. 137-143, 2014.
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Ronald Wesonga , Fabian Nabugoomu , Abraham Owino , Leonard Atuhaire , Agnes Ssekiboobo , Xavier Mugisha , James Ntozi , Tom Makumbi , Peter Jehopio , Bruno Ocaya (2014). On Statistical Definition of Free and Fair Election: Bivariate Normal Distribution Model. International Journal of Mathematical Research, 3(5): 49-62. DOI:
The coining of the expression free and fair was a good way towards evaluating elections, but fell short of qualifying its real quantification to guide an informed judgment; this paper provides guidance for such a definition.
Data from the Uganda National Baseline Survey were used to assess the dynamics of the determinants for a free and fair election. All determinants were statistically significant (p<0.01) for the two multinomial models (free and fair election models). The predicted probabilities for free and fair were each used as inputs to form probability distribution function could  jointly define the expression free and fair using a bivariate normal distribution. A strong positive correlation was identified between an election being free and fair (ρ=0.9693,p<0.01) implying the reliability of the statistical models in jointly considering free and fair.  
The study recommends development of central statistical computational system to inform electoral bodies and judges in passing scientifically backed ruling on whether an election is free and fair. A threshold percentage for any election to be referred to as free and fair could be developed either deterministically or stochastically and provisions of which passed under electoral law.

Contribution/ Originality
The paper contributes the first logical analysis of a national governance household baseline survey data and consequently proposes a framework for defining free and fair election. Given that free and fair is considered jointly, the paper recommends a definition based on joint bivariate probability distribution function.