An analytical and experimental comparison of maximal lottery schemes

Florian Brandl (), Felix Brandt () and Christian Stricker ()
Additional contact information
Florian Brandl: Princeton University
Felix Brandt: TU München
Christian Stricker: TU München

Social Choice and Welfare, 2022, vol. 58, issue 1, No 2, 5-38

Abstract: Abstract Maximal lottery ( $$ ML $$ ML ) schemes constitute an interesting class of randomized voting rules that were proposed by Peter Fishburn in 1984 and have been repeatedly recommended for practical use. However, the subtle differences between different $$ ML $$ ML schemes are often overlooked. Two canonical subsets of $$ ML $$ ML schemes are schemes (which only depend on unweighted majority comparisons) and schemes (which only depend on weighted majority comparisons). We prove that schemes are the only homogeneous $$ ML $$ ML schemes that satisfy $$ SD $$ SD -efficiency and $$ SD $$ SD -participation, but are also among the most manipulable $$ ML $$ ML schemes. While all $$ ML $$ ML schemes are manipulable and even violate monotonicity, they are never manipulable when a Condorcet winner exists and satisfy a relative notion of monotonicity. We also evaluate the frequency of manipulable preference profiles and the degree of randomization of $$ ML $$ ML schemes via extensive computer simulations. In summary, $$ ML $$ ML schemes are rarely manipulable and often do not randomize at all, especially for few alternatives. The average degree of randomization of schemes is consistently lower than that of schemes.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s00355-021-01326-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sochwe:v:58:y:2022:i:1:d:10.1007_s00355-021-01326-x

Ordering information: This journal article can be ordered from
http://www.springer. ... c+theory/journal/355

DOI: 10.1007/s00355-021-01326-x

Access Statistics for this article

Social Choice and Welfare is currently edited by Bhaskar Dutta, Marc Fleurbaey, Elizabeth Maggie Penn and Clemens Puppe

More articles in Social Choice and Welfare from Springer, The Society for Social Choice and Welfare Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().