Median constrained bucket order rank aggregation

Abstract

The rank aggregation problem can be summarized as the problem of aggregating individua! preferences expressed by a set of judges to obtain a ranking that represents the best synthesis of their choices. Several approaches for handling this problem have been proposed and are generally linked with either axiomatic frameworks or alternative strategies. In this paper, we present a new definition of median ranking and frame it within the Kemeny's axiomatic framework. Moreover, we show the usefulness of our approach in a practical case about triage prioritization.

How to improve the Triage: A dashboard to assess the quality of nurses’ decision-making

“…The discrimination index measures how well the nurses separate the cases, if they are different, giving a distribution of cases in the n classes (in our case classes correspond to diverse priority codes) coherently with the correct distribution. The discrimination index is a clustering method, usually applied to compare two partitions in order to resolve rank aggregation problems 39,40 and it is a suitable method for comparing the nurse’ s partition of cases into the n classes with the correct one. Let us consider the row vector xi′ (containing for each patient scenario the attribution of the code by the nurse i) as a partition of the m cases into N classes, and the row vector y′ as the correct partition.…”

Rank‐based Bayesian variable selection for genome‐wide transcriptomic analyses

“…Nonetheless, as mentioned in the simulation studies while commenting upon the marginal posterior distribution of obtained when , our method can be seen as an alternative to the constrained median bucket order technique. 35 It would then be interesting to fully compare the respective estimates obtained via lowBMM and the median bucket order, in the light of the relationship between the choice of permutation space (strong vs weak rankings), distance (any distance vs the Kemeny only), and estimation procedure (Bayesian vs frequentist). This comparison is clearly out of the scopes of the present article, but makes up a very interesting future research direction.…”

“…It is also interesting to evaluate how the consensus ranking changes when differs from the true value: the marginal posterior distribution of obtained when is displayed in Figure 6 on the left, and when on the right, with . By inspecting the left panel we see that assuming yields a clustered structure, thus implying that the best lower‐dimensional solution of ranked data in a higher‐dimension is consistent with a partial ordering, also called “bucket solution.” 35 On the other hand, assuming (Figure 6 , right panel) yields a top‐rank solution, as the algorithm seems to be able to indirectly suggest the true by showing a much larger uncertainty around the items ranked with larger values than the true . Overall, when , the posterior distribution of is anyway accurate, since the subset of relevant items has larger marginal posterior probability of being top‐ranked.…”

“…It is also interesting to evaluate how the consensus ranking $$$ \boldsymbol{\rho} $$$ changes when $$$ {n}_{\mathrm{guess}}^{\ast } $$$ differs from the true value: the marginal posterior distribution of $$$ \boldsymbol{\rho} $$$ obtained when $$$ {n}_{\mathrm{guess}}^{\ast }<{n}^{\ast } $$$ is displayed in Figure 6 on the left, and when $$$ {n}_{\mathrm{guess}}^{\ast }>{n}^{\ast } $$$ on the right, with $$$ {n}^{\ast }=8 $$$. By inspecting the left panel we see that assuming $$$ {n}_{\mathrm{guess}}^{\ast }<{n}^{\ast } $$$ yields a clustered structure, thus implying that the best lower‐dimensional solution of ranked data in a higher‐dimension is consistent with a partial ordering, also called “bucket solution.” 35 On the other hand, assuming $$$ {n}_{\mathrm{guess}}^{\ast }>{n}^{\ast } $$$ (Figure 6, right panel) yields a top‐rank solution, as the algorithm seems to be able to indirectly suggest the true $$$ {n}^{\ast } $$$ by showing a much larger uncertainty around the items ranked with larger values than the true $$$ {n}^{\ast } $$$. Overall, when …”

The Bradly-Terry Regression Trunk approach for modelling preference data with small trees

“…In analyzing rank data, the goal is often to find one ranking that best represents all the preferences stated by the individuals. This goal, when dealing with rank vectors, is known as the consensus ranking problem, the Kemeny problem, or the rank aggregation problem (D'Ambrosio, Iorio, Staiano & Siciliano, 2019). When dealing with paired comparison rankings, the goal is to determine the probability that object i is preferred to object j for all the possible pairs of them: the final outcome is thus a probabilistic determination of the central ranking (Kendall & Babington Smith, 1940;Bradley & Terry, 1952;Mallows, 1957).…”