# math 103 website - Arrow & Saari

DEMOREP1 at aol.com DEMOREP1 at aol.com
Wed Jan 9 20:58:22 PST 2002

```Mr. Schulze wrote-

There are two kinds of strategical nominations: clones and
irrelevant alternatives.

An election method violates "Independence from Irrelevant
Alternatives" when there are situations where you can
increase the winning probability of a given already running
candidate by introducing an additional candidate.

An election method violates "Independence from Clones"
when there are situations where you can (1) increase or
decrease the probability that a candidate of a given set
of clones is elected by introducing additional clones to
this set of clones or (2) increase or decrease the
probability that a given candidate is elected by introducing
additional clones to a set of clones to which this candidate
doesn't belong.

"Independence from Irrelevant Alternatives" and "Independence
from Clones" describe two different nomination strategies.

Examples: Random Candidate meets "Independence from Irrelevant
Alternatives" and violates "Independence from Clones". Tideman's
Ranked Pairs method meets "Independence from Clones" and violates
"Independence from Irrelevant Alternatives".
---
D-   Again ---- if C is added to A versus B, then C may (head to head) -

beat both A and B
beat A
beat B
be beaten by both A and B

The beatings may, of course, range from 100 percent (*pure* clones) to bare
majority.

```