# 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.

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## 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 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.

### 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.

### Social Choice and Individual Values

- Economics
- 1951

Originally published in 1951, Social Choice and Individual Values introduced "Arrow's Impossibility Theorem" and founded the field of social choice theory in economics and political science. This new…