Journal Pre-proof 1 such as ventilators in limited supply, preparations should be made ahead of time on how to allocate these finite resources. More information about COVID-19 can be found in [2], [3], and [7]. The best course of action to "flatten the curve" is to follow WHO guidelines. The best way to keep hospitals under capacity is social distancing: limiting or cancelling large gatherings, only travelling when necessary, and keeping a distance from others all help to prevent the spread. Heuristic predictionThe presented heuristic is based on the exponential growth of the data collected Journal Pre-proof J o u r n a l P r e -p r o o f 4 WWK, MAM, WP, AW-D, PFZ, DS, TA, AHZ, MD, AND JM by WHO situation reports for days 31 to 57. As pointed out in [4] the predictability could be improved by pairwise comparisons based on abductive reasoning [5]. Abduction is frequently used in diagnostic expert systems. The abductive reasoning (or inference) process was used for this study. It is a type of logical inference which starts with a set of observations and then searches for Journal Pre-proof J o u r n a l P r e -p r o o f 1,000,000 COVID-19 CASES

In this study, we provide mathematical and practice-driven justification for using [0, 1] normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization, are presented. A new type of paradox of infinity is described.

This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elements of pairwise comparisons matrix are derived. A numerical example is presented.

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Pairwise comparisons constitute a popular and important tool for multiple-criteria decision making. Consistency is one particular aspect of pairwise comparisons that has been studied thoroughly in recent decades since human judgements are seldom fully consistent. The aim of this paper is to propose a new simple and intuitive iterative Step-by-Step (SBS) algorithm for inconsistency reduction of a (multiplicative) pairwise comparison matrix based on step-by-step changes of the most inconsistent matrix element, where the inconsistency is measured by a modified Koczkodaj's inconsistency index. A comparison of the proposed SBS algorithm with other algorithms for inconsistency reduction is provided as well.