Distributional Rank Aggregation, and an Axiomatic Analysis

Adarsh Prasad, Harsh Pareek, Pradeep Ravikumar
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:2104-2112, 2015.

Abstract

The rank aggregation problem has been studied with varying desiderata in varied communities such as Theoretical Computer Science, Statistics, Information Retrieval and Social Welfare Theory. We introduce a variant of this problem we call distributional rank aggregation, where the ranking data is only available via the induced distribution over the set of all permutations. We provide a novel translation of the usual social welfare theory axioms to this setting. As we show this allows for a more quantitative characterization of these axioms: which then are not only less prone to misinterpretation, but also allow simpler proofs for some key impossibility theorems. Most importantly, these quantitative characterizations lead to natural and novel relaxations of these axioms, which as we show, allow us to get around celebrated impossibility results in social choice theory. We are able to completely characterize the class of positional scoring rules with respect to our axioms and show that Borda Count is optimal in a certain sense.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-prasad15, title = {Distributional Rank Aggregation, and an Axiomatic Analysis}, author = {Prasad, Adarsh and Pareek, Harsh and Ravikumar, Pradeep}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {2104--2112}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/prasad15.pdf}, url = {https://proceedings.mlr.press/v37/prasad15.html}, abstract = {The rank aggregation problem has been studied with varying desiderata in varied communities such as Theoretical Computer Science, Statistics, Information Retrieval and Social Welfare Theory. We introduce a variant of this problem we call distributional rank aggregation, where the ranking data is only available via the induced distribution over the set of all permutations. We provide a novel translation of the usual social welfare theory axioms to this setting. As we show this allows for a more quantitative characterization of these axioms: which then are not only less prone to misinterpretation, but also allow simpler proofs for some key impossibility theorems. Most importantly, these quantitative characterizations lead to natural and novel relaxations of these axioms, which as we show, allow us to get around celebrated impossibility results in social choice theory. We are able to completely characterize the class of positional scoring rules with respect to our axioms and show that Borda Count is optimal in a certain sense.} }
Endnote
%0 Conference Paper %T Distributional Rank Aggregation, and an Axiomatic Analysis %A Adarsh Prasad %A Harsh Pareek %A Pradeep Ravikumar %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-prasad15 %I PMLR %P 2104--2112 %U https://proceedings.mlr.press/v37/prasad15.html %V 37 %X The rank aggregation problem has been studied with varying desiderata in varied communities such as Theoretical Computer Science, Statistics, Information Retrieval and Social Welfare Theory. We introduce a variant of this problem we call distributional rank aggregation, where the ranking data is only available via the induced distribution over the set of all permutations. We provide a novel translation of the usual social welfare theory axioms to this setting. As we show this allows for a more quantitative characterization of these axioms: which then are not only less prone to misinterpretation, but also allow simpler proofs for some key impossibility theorems. Most importantly, these quantitative characterizations lead to natural and novel relaxations of these axioms, which as we show, allow us to get around celebrated impossibility results in social choice theory. We are able to completely characterize the class of positional scoring rules with respect to our axioms and show that Borda Count is optimal in a certain sense.
RIS
TY - CPAPER TI - Distributional Rank Aggregation, and an Axiomatic Analysis AU - Adarsh Prasad AU - Harsh Pareek AU - Pradeep Ravikumar BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-prasad15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 2104 EP - 2112 L1 - http://proceedings.mlr.press/v37/prasad15.pdf UR - https://proceedings.mlr.press/v37/prasad15.html AB - The rank aggregation problem has been studied with varying desiderata in varied communities such as Theoretical Computer Science, Statistics, Information Retrieval and Social Welfare Theory. We introduce a variant of this problem we call distributional rank aggregation, where the ranking data is only available via the induced distribution over the set of all permutations. We provide a novel translation of the usual social welfare theory axioms to this setting. As we show this allows for a more quantitative characterization of these axioms: which then are not only less prone to misinterpretation, but also allow simpler proofs for some key impossibility theorems. Most importantly, these quantitative characterizations lead to natural and novel relaxations of these axioms, which as we show, allow us to get around celebrated impossibility results in social choice theory. We are able to completely characterize the class of positional scoring rules with respect to our axioms and show that Borda Count is optimal in a certain sense. ER -
APA
Prasad, A., Pareek, H. & Ravikumar, P.. (2015). Distributional Rank Aggregation, and an Axiomatic Analysis. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:2104-2112 Available from https://proceedings.mlr.press/v37/prasad15.html.

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