Violation of the transitivity axiom

Asked Sep 25 '20 at 22:30

Active Sep 25 '20 at 22:30

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I'm struggling to think of a way to violate the transitivity axiom. I was thinking about the following scenario:

Let's say that you're voting on three different choices, A, B and C.

If you pit A vs. B, A wins 3 - 1 so A > B

However, if you pit A vs. C, they're indifferent and neither wins

But just because A = C, does that necessarily mean that pitting C vs. B would either yield C > B or B > C since we do not know the relationship between B and C?

This is the question I'm trying to answer: How can tie votes violate transitivity? Does this violate WARP or SARP?

I'm thinking this violates SARP this the preferences are strict preferences.

asked Sep 25 '20 at 22:30

salitherin

Does https://economics.stackexchange.com/q/32505/42 answer your question? – Herr K. Sep 25 '20 at 22:40
Not exactly. Its close but I'm not relying on completeness for this. Just strictly looking at how transitivity can be violated. Would I need to consider completeness? – salitherin Sep 25 '20 at 23:01
1

Completeness is irrelevant for your question. The accepted answer in that linked question (on rock, paper, scissors) is one that violates transitivity. – Herr K. Sep 25 '20 at 23:27
Got it. Thanks for the help! – salitherin Sep 26 '20 at 18:27
Okay, I'll vote to close your question as a duplicate then. – Herr K. Sep 26 '20 at 18:28

Violation of the transitivity axiom

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