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The possible existence of various voting paradoxes has been the focus of numerous investigations. This research has largely been dominated by studies that are associated with Condorcet’s Paradox. There is widespread, but not universal, acceptance of the notion that the PMRW is the best candidate for selection in an election process, when such a candidate exists. When Condorcet’s Paradox occurs, there is no PMRW in three-candidate elections, and there is a need to find some other voting mechanism to determine a winner in such cases.

There is a resulting interest in determining estimates of the likelihood that a PMRW exists in various situations. This observation is intensified by the fact that we have seen that the conditions that are necessary for Condorcet’s Paradox to exist are the same as the conditions that are required for the existence a number of other paradoxes, like the Paradox of Multiple Elections and the Vote Trading Paradox. In some cases there are links between the conditions that are necessary for other paradoxes to exist and the conditions for Condorcet’s Paradox, as with the No Show Paradox. Researchers even feel obligated to show that the conditions that are necessary for other paradoxes, like Ostrogorski’s Paradox, to exist are not the same as the conditions that are required for Condorcet’s Paradox to exist.

Numerous empirical studies have been conducted to determine if Condorcet’s Paradox is ever observed in actual elections. After surveying these studies, we must conclude that the evidence does not suggest that the phenomenon is widespread in voting situations. However, there clearly are cases in which the evidence shows that Condorcet’s Paradox has occurred in actual elections. The most typical observations of the phenomenon occur when there are a large number of candidates in an election, but there are cases in which it has been observed in three-candidate elections. Following notions that are suggested in some theoretical studies, examples have also been found to show that various means occasionally have intentionally been used to create PMR cycles in election settings to gain a political advantage. It is clearly of interest to determine what the characteristics of voting situations are that make the possible existence of Condorcet’s Paradox most likely to occur.

Bone marrow (BM) adipose tissue should no longer be considered simply as a filling material for bone cavities that is not needed for hematopoietic activity. In addition to its potential role as an energy store, BM adipose tissue exhibits a considerable adaptive plasticity and secretes a broad spectrum of hormones, cytokines and growth factors whose receptors are present on different cells of the stromal microenvironment. BM adipocytes, originating like osteoblasts from mesenchymal stem cells, display a marked metabolic and secretory activity. Among the various secreted adipokines, leptin, and adiponectin have opposite effects on hematopoiesis, immunity, inflammation, and bone remodeling. As a whole, a counterbalance exists between adipogenesis and erythropoiesis, and between adipose and bone formation. The better knowledge of the different paracrine and endocrine agents involved in the subtle and complex regulation of hematopoiesis and its osseous environment suggests that BM adipose tissue may represent a target for drugs in situations such as blood diseases or osteoporosis.

Bone marrow (BM) adipose tissue should no longer be considered simply as a filling material for bone cavities that is not needed for hematopoietic activity. In addition to its potential role as an energy store, BM adipose tissue exhibits a considerable adaptive plasticity and secretes a broad spectrum of hormones, cytokines and growth factors whose receptors are present on different cells of the stromal microenvironment. BM adipocytes, originating like osteoblasts from mesenchymal stem cells, display a marked metabolic and secretory activity. Among the various secreted adipokines, leptin, and adiponectin have opposite effects on hematopoiesis, immunity, inflammation, and bone remodeling. As a whole, a counterbalance exists between adipogenesis and erythropoiesis, and between adipose and bone formation. The better knowledge of the different paracrine and endocrine agents involved in the subtle and complex regulation of hematopoiesis and its osseous environment suggests that BM adipose tissue may represent a target for drugs in situations such as blood diseases or osteoporosis.

A number of societal factors have been found to have an impact on the probability that a PMRW exists. The factor that has been most thoroughly examined in this context is the degree of coherence or consistency of voters’ preferences, as measured according to some definition of social homogeneity. Numerous studies have sought to find general relationships between these measures of social homogeneity and the probability that a PMRW exists. Some theoretical studies have successfully shown that such relationships can exist on an expected value basis, without measuring the overall strength of the relationships. Strong evidence has also been provided to indicate that simple measures of social homogeneity are very ineffective at showing such a relationship at all. In particular, the connection between some of these measures of social homogeneity and the probability that a PMRW exists is found to be reversed, based on whether the number of voters is restricted to be odd or even. If such a general relationship is to be found with a significant degree of strength, the measure of homogeneity has to be based on an understanding of the mechanism by which voters preferences are formed. The proximity of the voters’ preferences to single-peaked preferences is an example of such a measure of social homogeneity.

Other significant societal factors that have an impact on the probability that a PMRW exists include: the propensity of voters to abstain from the election, the degree of voter indifference between candidates, the propensity of voters to have intransitive preferences, and the presence of uncertainty regarding the exact position that candidates represent on issues.

When voters’ preferences in a three-candidate voting situation reflect any significant degree of proximity to perfect single-peakedness, perfect single-troughedness, or perfect polarization, the probability that a PMRW exists is quite high. When voters’ preferences are at all close to reflecting a situation in which a unifying candidate exists, the probability that a PMRW exists is very high. It is very important to note that the associated underlying models that lead to single-peaked, single-troughed, or polarized preferences do not actually have to be the basis of the mechanism by which the voters’ preference rankings on candidates are actually formed. It is only required that the preferences in a given voting situation could have been obtained by one of these models. As a result, Condorcet’s Paradox should rarely be observed in any real elections on a small number of candidates with large electorates, as long as voters’ preferences reflect any significant degree of group coherence or consistency.

Bone marrow (BM) adipose tissue should no longer be considered simply as a filling material for bone cavities that is not needed for hematopoietic activity. In addition to its potential role as an energy store, BM adipose tissue exhibits a considerable adaptive plasticity and secretes a broad spectrum of hormones, cytokines and growth factors whose receptors are present on different cells of the stromal microenvironment. BM adipocytes, originating like osteoblasts from mesenchymal stem cells, display a marked metabolic and secretory activity. Among the various secreted adipokines, leptin, and adiponectin have opposite effects on hematopoiesis, immunity, inflammation, and bone remodeling. As a whole, a counterbalance exists between adipogenesis and erythropoiesis, and between adipose and bone formation. The better knowledge of the different paracrine and endocrine agents involved in the subtle and complex regulation of hematopoiesis and its osseous environment suggests that BM adipose tissue may represent a target for drugs in situations such as blood diseases or osteoporosis.