Research Article
Implementation of a Voting Method Based on Mean-Deviation Evaluation for a Large-Scale Election
Hadarou Yiogo*
,
Zoïnabo Savadogo
Issue:
Volume 14, Issue 2, April 2025
Pages:
13-23
Received:
7 March 2025
Accepted:
17 March 2025
Published:
10 April 2025
Abstract: Today, many countries around the world, particularly in Africa, are experiencing post-election difficulties due to unexpected election results. This sometimes provokes protests and revolt among the population. To overcome this major problem, several voting systems have been developed in the literature, but some of them are not lacking in shortcomings. It was with this in mind that the voting method based on the evaluation of the mean deviation was born. It's a voting system that seems to be appreciated because it respects a certain number of fundamental properties of a ranking method. On the other hand, we note in the literature that it is only applicable to small-scale data with an insignificant number of candidates and voters. For this reason, we set ourselves the goal of implementing this method in order to extend its use to large-scale problems. Thus, we proposed the computer program using python software, which takes as input the scores assigned to the candidates by each voter and displays as output the best candidate. To do this, we built sub-programs such as median, arithmetic mean and mean-spread functions, each of which plays an effective role in selecting the best candidate. We then studied the algorithmic time complexity theoretically, then graphically, and ended by applying our computer program to several voting examples containing a very large number of candidates and voters. Numerous applications enabled us to observe that, whatever the size of the data, we always obtained a conclusive and satisfactory result with polynomial-type time complexity.
Abstract: Today, many countries around the world, particularly in Africa, are experiencing post-election difficulties due to unexpected election results. This sometimes provokes protests and revolt among the population. To overcome this major problem, several voting systems have been developed in the literature, but some of them are not lacking in shortcomin...
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Research Article
Sharpness of the Segre’s Upper Bound for the Regularity Index of Fat Points
Phan Van Thien*
Issue:
Volume 14, Issue 2, April 2025
Pages:
24-28
Received:
11 March 2025
Accepted:
25 March 2025
Published:
6 May 2025
DOI:
10.11648/j.pamj.20251402.12
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Abstract: In this paper we show some results about estimating the regularity index of fat points and study when the Segre’s upper bound is sharp for arbitrary fat points in 𝕡n. We show that the Segre’s upper bound is sharp for fat points where the points are constrained by geometric conditions in 𝕡n (Corollary 2.1 and Proposition 2.1). We show that if s ≤ 4, the Segre’s upper bound is sharp for s arbitrary fat points in 𝕡n (Theorem 3.1), and the Segre’s upper bound is sharp for 5 equimultiple fat points in 𝕡n (Theorem 3.2). We also show that if s ≥ 6 and n ≥ 2, then there exists always a set of s fat points in 𝕡n whose the Segre’s upper bound is not sharp (Proposition 3.1). We predict that Segre’s upper bound is sharp for 5 non-equimultiple fat points, but we can not prove this prediction nor we can find an example to show that the prediction is incorrect.
Abstract: In this paper we show some results about estimating the regularity index of fat points and study when the Segre’s upper bound is sharp for arbitrary fat points in 𝕡n. We show that the Segre’s upper bound is sharp for fat points where the points are constrained by geometric conditions in 𝕡n (Corollary 2.1 and Proposition 2.1). We sho...
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