# Lesser of two evils

Rob Lanphier robla at eskimo.com
Tue Jul 30 23:04:11 PDT 1996

```I want to resurrect an earlier thread about a formal mathematical
definition of Lesser of Two Evils.  Mike, please correct me if I'm
wrong, but your earlier definitions were designed more as political
principles than mathematical axioms.  Correct?

Here's an axiom that I think best describes Lesser of Two Evils:

Within a given set of preference ballots P, there exists a
majority subset M such that candidate x is always ranked above
candidate y.  Where a voting system declares x the winner using P,
it is impossible to change the winner to y by ranking a separate
candidate z higher than x on ballots in M, all else unchanged.

What this says in English:

If Candidate X would win an election against Y using a given
election method, those that supported X over Y should not be afraid
of Y winning merely because they (X supporters) vote their
preference of a separate Candidate Z over X, still ranking Y below
X.

This I think states Lesser of Two Evils concisely, without overreaching.

Thanks
Rob Lanphier
robla at eskimo.com
http://www.eskimo.com/~robla

```

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