We provide simple interpretations of probability with a view towards its potential for real world (i.e., practical) applications. Our discussion is along the lines initiated by David Ramsey and Bruno de Finetti, though we do not provide a theory of probability but merely use their axioms and results to interpret mathematical probability. Subsequently, we provide a critique as well as a resolution of the well-known St. Petersburg paradox that is consistent with expected utility theory.

The paper attempts to rectify what appear to be popular but elementary misconceptions about the concept of consumer surplus in the context of Marshallian demand curves. It is primarily addressed to teachers of microeconomics at the undergraduate level or in MBA programs of business schools. The main text informs the reader about the model/context and the results we are concerned with, all of the latter being a comprehensive teaching note, relegated to an appendix of the paper. Thus, the potential instructor may use the main text to motivate himself/herself and at the same time inform his/her students as to the topic i.e. the rehabilitation of consumer surplus as an exact measure of welfare from the stand-point of cost benefit analysis. Thereafter the appendix can be referred to for a more formal presentation. The technical results contained in the appendix begin by showing that willingness to pay is the area under the demand curve if and only if consumers are surplus maximizers. The last result in the appendix is a theoretically ‘happy ending’ since it shows that for purposes of applied economics, budget constrained preference maximization implies surplus maximization and hence for such consumers, willingness to pay is indeed the area under the demand curve up to the quantity consumed.

In this paper we obtain conditions on weak tournaments, which guarantee that every non-empty subset of alternatives admits a stable set. We also show that there exists a unique stable set for each non-empty subset of alternatives which coincides with its set of best elements, if and only if, the weak tournament is quasi-transitive. A somewhat weaker version of this result, which is also established in this paper, is that there exists a unique stable set for each non-empty subset of alternatives (: which may or may not coincide with its set of best elements), if and only if the weak tournament is acyclic.

We show that three conditions due to Pattanaik, when satisfied by a given profile of state-dependent preferences (linear orders) on a given and fixed set of alternatives and a probability distribution with which the various states of nature occur, are individually sufficient, for the non-emptiness of the set of alternative(s) which are individually preferred to all alternatives other than itself with probability at least half. Before this, we show that since each axiom individually implies Sen-coherence, then, as a consequence of a result obtained earlier, each axiom along with asymmetry of the preferred with at probability at least half relation implies the transitivity of the relation. All the sufficient conditions discussed here are required to apply at least to all those otherwise relevant events that have positive probability. This observation also applies to a sufficient condition for the non-emptiness of the set of alternative(s) which are individually preferred to all alternatives other than itself with probability at least half, called generalised Sen coherence introduced and discussed in earlier research.