The notion of the existence of a Strict Ostrogorski Paradox presents an interesting phenomenon that could lead to some very unsettling outcomes in group decision-making situations. This phenomenon cannot be observed in two-issue situations, and when three-issue situations are considered, the probability that such an outcome will be observed never reaches a likelihood of as much as two percent for large electorates, regardless of the propensity of voters to align their preferences on issues with the standards of political parties. The probability of observing a Strict Ostrogorski Paradox in four-issue situations is nearly zero when using an assumption that exaggerates the likelihood that such a paradoxical outcome will be observed. We conclude that it is very unlikely that a Strict Ostrogorski Paradox would ever be observed in any real voting situation with a large electorate