Institute of Control Sciences seminar "Expert opinion and data analysis"
On Wednesday, June 9, the National Research University Higher School of Economics hosted an Institute of Control Sciences seminar "Expert opinion and data analysis".
Aleksei Kondratev, Egor Ianovski, Alexander Nesterov (HSE University)
Doctor of Technical Sciences, prof. Aleskerov Fuad Tagievich
Doctor of Technical Sciences, prof. Novikov Dmitriy Aleksandrovich
We study how to rank candidates based on individual rankings via positional scoring rules. Our selection principle is consistency: once one of the candidates is removed, we want the aggregate ranking to remain intact. Unfortunately, no scoring rule is completely consistent, but there are weaker notions of consistency we can use. There are scoring rules which are consistent if we add or remove a unanimous winner — such as an athlete with suspiciously strong results. Likewise, consistent for removing or adding a unanimous loser — such as a spoiler candidate in an election. While extremely permissive individually, together these two criteria pin down a one-parameter family with the geometric, arithmetic, or inverse geometric sequence of scores. This family includes Borda count, generalised plurality (medal count), and generalised antiplurality (threshold rule) as edge cases, and we provide elegant new axiomatisations of these rules. Finally, we demonstrate how the one-parameter formulation can simplify the selection of suitable scoring rules for particular scenarios.