# A New Way to Analyze Paired Comparison Rules

@article{Saari2014ANW, title={A New Way to Analyze Paired Comparison Rules}, author={Donald G. Saari}, journal={Math. Oper. Res.}, year={2014}, volume={39}, pages={647-655} }

The importance of “paired comparisons” has led to the development of several approaches. Missing is a common analytical way to compare techniques and explain properties. To do so, the approach developed here creates a “data space” coordinate system where data aspects that satisfy a strong transitivity condition are separated from those that represent “noise” as characterized by cyclic effects. With this system, paired comparison rules can be compared and paradoxical behavior explained.

## 15 Citations

### Explaining All Possible Paired Comparison Problems

- Economics
- 2013

For centuries, cycles and other anomalies have hindered the use of paired comparisons, whether it be in decision theory, voting, economics, engineering, statistics, and on and on. It is shown here…

### Seeking consistency with paired comparisons: a systems approach

- MathematicsTheory and Decision
- 2021

It is well known that decision methods based on pairwise rankings can suffer from a wide range of difficulties. These problems are addressed here by treating the methods as systems, where each pair…

### Arrow, and unexpected consequences of his theorem

- PhysicsPublic Choice
- 2018

A new way to interpret Arrow’s impossibility theorem leads to valued insights that extend beyond voting and social choice to address other mysteries ranging from the social sciences to even the “dark…

### Arrow, and unexpected consequences of his theorem

- Physics
- 2019

A new way to interpret Arrow’s impossibility theorem leads to valued insights that extend beyond voting and social choice to address other mysteries ranging from the social sciences to even the “dark…

### The PerronRank family: a brief review

- Computer Science
- 2015

It is shown that HodgeRank and TropicalRank are limits of PerronRank, hence the methods belong to the same family, and their implications in practice are discussed, and some open problems are states.

### From Arrow’s Theorem to ‘Dark Matter’

- EconomicsBritish Journal of Political Science
- 2015

Arrow’s Impossibility Theorem and Sen’s Minimal Liberalism example impose ‘impossibility’ roadblocks on progress. A reinterpretation explained in this article exposes what causes these negative…

### HodgeRank Is the Limit of Perron Rank

- Mathematics, Computer ScienceMath. Oper. Res.
- 2016

It is shown that HodgeRank (row geometric mean), is the limit of Perron Rank (ranking with principal eigenvector) as a certain parameter k goes to 0.

## References

SHOWING 1-10 OF 17 REFERENCES

### Symmetry of Nonparametric Statistical Tests on Three Samples

- Economics
- 2007

Problem statement: Many different nonparametric statistical procedures can be used to
analyze ranked data. Inconsistencies among the outcomes of such procedures can occur when
analyzing the same…

### Mathematical structure of voting paradoxes

- Economics
- 2000

P pairwise voting is described where new results include explanations for all paradoxes, cycles, conflict between Borda and Condorcet rankings, differences among procedures using pairwise votes, and discrepancies among the societal rankings as candidates are dropped or added.

### ARE PART WISE COMPARISONS RELIABLE ?

- Computer Science
- 2003

This work identifies an alternative, closely related decision approach that eliminates problems caused by the nature of the lost information, and shows how to compute the likelihood that an incorrect outcome will occur.

### Dictionaries of Paradoxes for Statistical Tests on k Samples

- Mathematics
- 1992

Abstract A relationship between the Kruskal–Wallis nonparametric statistical test on k samples and the Borda positional method for voting is established and then exploited to gain a complete analysis…

### Matrix analysis

- MathematicsStatistical Inference for Engineers and Data Scientists
- 2018

This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.

### Essai Sur L'Application de L'Analyse a la Probabilite Des Decisions Rendues a la Pluralite Des Voix

- Computer Science
- 2009

### Mathematical Structure of Voting Paradoxes: I. Pairwise Votes

- Economics
- 1999

A theory is developed to identify, characterize, and explain all possible positional and pairwise voting outcomes that can occur for any number of alternatives and any profile. This paper describes…

### Are partwise comparisons reliable?

- Computer Science
- 2004

This work identifies an alternative, closely related decision approach that eliminates problems caused by the nature of the lost information, and shows how to compute the likelihood that an incorrect outcome will occur.