Aleksei Y. Kondratev (National Research University Higher School of Economics, Saint Petersburg, Russia): How should we score athletes and candidates: geometric scoring rules
Aleksei Y. Kondratev (National Research University Higher School of Economics, Saint Petersburg, Russia) How should we score athletes and candidates: geometric scoring rules című előadása a Corvinus Játékelmélet SzemináriumonSzervezők elérhetősége
C épület, 708
We
study how to rank candidates based on individual rankings via positional
scoring rules. Each position in each individual ranking is worth a
certain number of points; the total sum of points
determines the aggregate ranking. Our selection principle is
consistency: once one of the candidates is removed, we want the
aggregate ranking to remain intact. This principle is crucial whenever
the set of the candidates might change and the remaining ranking
guides our actions: whom should we interview if our first choice got a
better offer? Who gets the cup once the previous winner is convicted of
doping? Which movie should a group watch if everyone already saw the
recommender system’s first choice? Will adding
a spoiler candidate rig the election?
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 sequence of scores. These geometric scoring
rules include 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.
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