---
url: "https://questionstar.com/principles-of-survey-research/chapter-2/slide-033.html"
title: "Violations of transitivity when aggregating preferences"
type: "lehrbuch-slide"
chapter: 2
chapterTitle: "Survey: Measurement and Scaling"
slide: 33
---

# Violations of transitivity when aggregating preferences

*Apple ≻ Tomato ≻ Orange ≻ Apple. Apple is simultaneously the most and the least preferred — the group preferences are inconsistent!*

Respondent #1

1 Apple

2 Tomato

3 Orange

Respondent #2

1 Tomato

2 Orange

3 Apple

Respondent #3

1 Orange

2 Apple

3 Tomato

Vote count

Apple ≻ Tomato 2 : 1

Tomato ≻ Orange 2 : 1

Orange ≻ Apple 2 : 1

**Apple ≻ Tomato ≻ Orange ≻ Apple.** Apple is simultaneously the most and the least preferred — the group preferences are inconsistent!

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*Slide 33 of 274 · Chapter 2: Survey: Measurement and Scaling · Principles of Survey Research · Dr. Paul Marx*