Mark Twain's Social Choice Theory

Introduction
The phrase “public interest” is a mysterious one, often used, but never completely understood. It seems to justify political actions as well as controversial policies and serves the common good by aggregating all preferences of the individuals within the society. Mark Twain, an appreciated and highly respected American writer, even realized: “No public interest is anything other or nobler than a massive accumulation of private interests.” (Twain, Smith and Griffin, 210, 275).
Kenneth Arrow, undoubtedly one of the most influential thinkers and economists, expressed his very own point of view by introducing the Impossibility Theorem (Arrow, 1983) and therefore contributing to the field Social Choice Theory.
In the following paper,

In our case specifically, majority rule even reveals a cycle (as and is not only intransitive), as A is preferred to B, B to C and C to A, which is known as Condorcet Paradox and named after M. J. A. Nicolas Caritat, Marquis de Condorcet, who first described this paradox in his essay Essai sur l 'application de l 'analyse à la probabilité des décisions rendues à la pluralité des voix (Condorcet, 1785). It is worth mentioning that not all intransitive orders are cyclic and that Arrow’s Theorem does not focus on cycles, but on intransitive social preference orders. For a closer focus on cycles, see Thomas Schwartz (1986) who modified Arrow’s Theorem in order to formulate a reviewed Impossibility

Ordeshook (1986) tried to cover both of them in Game theory and political theory and reminds us in particular to prove the general possibility of an appearance of the Condorcet Paradox , which is defined as the “frequency with which the paradox occurs” (Ordeshook, 1986: 58). By computing the likelihood of a revealed cycle, he tried to draw several conclusions about the importance of the problem of the Condorcet Paradox.
Ordeshook assumed all individual preference rankings to be equally likely and found that the probability of the Condorcet Paradox is never zero, but 0.056 when taking three alternatives and three individuals into consideration. By increasing either the numbers of voters or the number of alternatives, the likelihood is bound to increase (Ordeshook,