### Abstract

Rank sum scoring is a popular manner by which to obtain group rankings from events that are individual in nature. For example, rank sum scoring is employed in cross country team competition, the Putnam Mathematics Team Competition, snowboard cross team competition, snowboard half-pipe team competition, and snowboard slopestyle team competition. It also forms the basis for non-parametric statistical tests (the Wilcoxon rank-sum test and the related Mann-Whitney U test) that serve as an ordinal substitute for the two-sample t-test. Moreover, a close variant of rank sum scoring is used in team rowing competitions, alpine ski competitions, as well as in multiple event cross-fit contests. Given its applicability, we formally define rank sum scoring, derive conditions under which the methodology leads to violations of major social choice principles (ranking cycles and violations of "independence from irrelevant groups"), and calculate the probability that an "outcome sequence" leads to a given social choice violation. These probability calculations provide sizable corrections to prior calculations on the topic and alter our view as to the social choice properties of rank sum scoring. Contrary to prior results on the topic, we find that the two violations considered are not mutually inclusive under rank sum scoring.

Original language | English (US) |
---|---|

Pages (from-to) | 20-29 |

Number of pages | 10 |

Journal | Mathematical Social Sciences |

Volume | 71 |

DOIs | |

State | Published - Jan 1 2014 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Sociology and Political Science
- Social Sciences(all)
- Psychology(all)
- Statistics, Probability and Uncertainty

### Cite this

**Social choice violations in rank sum scoring : A formalization of conditions and corrective probability computations.** / Boudreau, James; Ehrlich, Justin; Sanders, Shane; Winn, Adam.

Research output: Contribution to journal › Article

*Mathematical Social Sciences*, vol. 71, pp. 20-29. https://doi.org/10.1016/j.mathsocsci.2014.03.004

}

TY - JOUR

T1 - Social choice violations in rank sum scoring

T2 - A formalization of conditions and corrective probability computations

AU - Boudreau, James

AU - Ehrlich, Justin

AU - Sanders, Shane

AU - Winn, Adam

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Rank sum scoring is a popular manner by which to obtain group rankings from events that are individual in nature. For example, rank sum scoring is employed in cross country team competition, the Putnam Mathematics Team Competition, snowboard cross team competition, snowboard half-pipe team competition, and snowboard slopestyle team competition. It also forms the basis for non-parametric statistical tests (the Wilcoxon rank-sum test and the related Mann-Whitney U test) that serve as an ordinal substitute for the two-sample t-test. Moreover, a close variant of rank sum scoring is used in team rowing competitions, alpine ski competitions, as well as in multiple event cross-fit contests. Given its applicability, we formally define rank sum scoring, derive conditions under which the methodology leads to violations of major social choice principles (ranking cycles and violations of "independence from irrelevant groups"), and calculate the probability that an "outcome sequence" leads to a given social choice violation. These probability calculations provide sizable corrections to prior calculations on the topic and alter our view as to the social choice properties of rank sum scoring. Contrary to prior results on the topic, we find that the two violations considered are not mutually inclusive under rank sum scoring.

AB - Rank sum scoring is a popular manner by which to obtain group rankings from events that are individual in nature. For example, rank sum scoring is employed in cross country team competition, the Putnam Mathematics Team Competition, snowboard cross team competition, snowboard half-pipe team competition, and snowboard slopestyle team competition. It also forms the basis for non-parametric statistical tests (the Wilcoxon rank-sum test and the related Mann-Whitney U test) that serve as an ordinal substitute for the two-sample t-test. Moreover, a close variant of rank sum scoring is used in team rowing competitions, alpine ski competitions, as well as in multiple event cross-fit contests. Given its applicability, we formally define rank sum scoring, derive conditions under which the methodology leads to violations of major social choice principles (ranking cycles and violations of "independence from irrelevant groups"), and calculate the probability that an "outcome sequence" leads to a given social choice violation. These probability calculations provide sizable corrections to prior calculations on the topic and alter our view as to the social choice properties of rank sum scoring. Contrary to prior results on the topic, we find that the two violations considered are not mutually inclusive under rank sum scoring.

UR - http://www.scopus.com/inward/record.url?scp=84899802664&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899802664&partnerID=8YFLogxK

U2 - 10.1016/j.mathsocsci.2014.03.004

DO - 10.1016/j.mathsocsci.2014.03.004

M3 - Article

AN - SCOPUS:84899802664

VL - 71

SP - 20

EP - 29

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

ER -