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Decisions with a continuum of options

Title data

Kurz, Sascha ; Moyouwou, Issofa ; Touyem, Hilaire:
Decisions with a continuum of options.
Event: Application-Oriented Computational Social Choice , 15.-20.09.2019 , Wadern, Deutschland.
(Conference item: Workshop , Speech )

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Abstract in another language

The Shapley-Shubik index was designed to evaluate the power distribution in committee systems drawing binary decisions and is one of the most established power indices. It was generalized to decisions with more than two levels of approval in the input and output. In the limit we have a continuum of options. You may think of e.g. tax rates. For these games with interval decisions we prove an axiomatization of a power measure and show that the Shapley-Shubik index for simple games, as well as for (j,k) simple games, occurs as a special discretization. This relation and the closeness of the stated axiomatization to the classical case suggests to speak of the Shapley-Shubik index for games with interval decisions, that can also be generalized to a value. Also for the Penrose-Banzhaf index there exists a variant for games with interval decisions in the literature on aggregation function. The general framework of games with a continuum of options deserves to be explored more. We collect a list of some open problems in that direction.

Further data

Item Type: Conference item (Speech)
Refereed: No
Additional notes: speaker: Sascha Kurz
Keywords: simple games; decisions with a continuum of options; aggregation functions; power indices; Shapley-Shubik index
Subject classification: Mathematics Subject Classification Code: 91A40 91A80 91B12
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Profile Fields > Emerging Fields > Governance and Responsibility
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Emerging Fields
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
300 Social sciences > 320 Political science
300 Social sciences > 330 Economics
500 Science > 510 Mathematics
Date Deposited: 16 Sep 2019 08:44
Last Modified: 16 Sep 2019 08:44