Last Updated on 28. April 2023 by Martin Schuster

In this method, a candidate wins the election if he wins every head-to-head election against all other candidates.

Example

Preference	A	A	B	B	C	C
Preference	B	C	A	C	A	B
Preference	C	B	C	A	B	A
Number of persons with this preference order	6	0	5	2	5	3

Here, not only the highest (1.) preference is important but also all other preferences.

• A is preferred over B in 11 cases. B is preferred over A in 10 cases: A wins against B.
• A is preferred over C in 11 cases. C is preferred over A in 10 cases. A wins against C.
• B is preferred over C in 13 cases. C is preferred over B in 8 cases. B wins against C.

Hence, A is preferred to B is preferred to C

Condorcet Paradox

The problem with this method is that if the preferences are cyclic, the result can be ambiguous. The table shows the preferences for three candidates A, B, and C.

Preference	A	B	C
Preference	B	C	A
Preference	C	A	B
Number of persons with this preference order	1	1	1

• A > B: 2:1
• B > C: 2:1
• C > A: 2:1

Hence, A > B > C > A. But this is not possible.

This is called the Condorcet paradox.