Speaker: Arkadii Slinko
Affiliation: University of Auckland
Title: Clone Structures
Date: Tuesday, 4 Jun 2013
In Economics, a set of linear orders is normally interpreted as a set of opinions of agents about objects in C. Cloning candidates (products) is one of the most sophisticated tools of manipulation of elections (consumer surveys). Unfortunately most common voting rules are vulnerable to this method of manipulation. So clones do matter.
Mathematically, a subset of C which is ranked consecutively (though possibly in different order) in all linear orders is called a clone set. All clone sets for a given family of linear orders form the clone structure. In this talk I will formalise and study properties of clone structures. In particular, I will give an axiomatic characterisation of clone structures, define the composition of those, classify irreducible ones, and show that it is sufficient to have only three linear orders to realise any clone structure.
This is a joint work with Piotr Faliszewski (Krakow) and Edith Elkind (Oxford).