Discrete Mathematics

26 DISCRETE MATHEMATIC..._

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• R is a locally fair ranking for

T.

• QED

(iii) QED

(d) QED

3.

QED

Locally Fair Rankings and Number

of

Wins

Implication

Strong induction

For a while, the customers are happy with just locally fair rankings. But then a game comes up where local

fairness does not work out so well.

'

,E:xti~pl

.

~

8 · A beats B

B beats C

C beats A, D

D beats A, B, E

E beats A, B, C

(draw)

Here, A, B,

C. D, E is a locally fair ranking. However, according to the number

of

wins it is in the

reverse order. This is clearly a problem.

It

now occurs to the company that it would be nice

if

the rankings

could also ...