A stochastic dominance analysis of ranked voting systems with scoring

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

“…Another relevant subfamily of scoring ranking rules, known as convex scoring ranking rules [154], contains all scoring ranking rules such that α − α +1 ≥ α +1 − α +2 for any ∈ {1, . .…”

“…The notion of a scorix is well known [52,53,57,58,92,93,144,154,169] in social choice theory, usually considered either in the form of a matrix or in the form of an ensemble of vectors corresponding to the different rows of the scorix.…”

“…It has been shown to have applications in decision theory [89], economics [10,72], machine learning [132,163,164] and social choice theory [124,154]. Stochastic dominance establishes a relation between probability distributions that is based on the pairwise comparison of the corresponding cumulative probability distributions.…”

A data envelopment analysis model for rank ordering suppliers in the oil industry

“…Nevertheless, the arbitrary choice of weighting can lead to different final placings and logically to different awards. We can achieve a partial ordering using only the concept of stochastic dominance (Stein, Mizzi & Pfaffenberger, 1994), without specifying the weighting beforehand, considering them only decreasing and convex and adding two restrictions to the model established earlier: However, this model is also arbitrary, because the choice of the function d(r,ε) influences the result of the ranking, which brings back the original problem, according to Green, Doyle & Cook (1996). The authors warn that the use of the function d(r,ε) = c coincides with the actual Borda method and they also recommend, for the intended ranking, the use of d(r,ε) = 0, and the technique called cross evaluation.…”

“…This arbitration is already commonly adopted in ranking processes (Stein, Mizzi & Pfaffenberger, 1994), leaving only the ties between efficient DMUs as an inconvenience still to be solved. We can break these ties through the use of the concept of superefficiency (Andersen & Petersen, 1993), in which there is no limit to the efficiency of the DMU which is being evaluated, leading to evaluation score greater than 100%.…”