[EM] Later-no-harm definition

Kevin Venzke stepjak at yahoo.fr
Sat Dec 27 12:10:02 PST 2003


 --- Bart Ingles <bartman at netgate.net> a écrit : > 
> This paper must be part of a series, as Woodall never explains his
> assertion that "Of these three properties, Majority is far and away the
> most important."  He seems to have his own definitions for monotonicity;
> I hadn't seen these anywhere else.

(He comments on Majority as above, says Plurality is "also important, but
it is much less likely to be violated: every reasonable electoral system
seems to satisfy it, whereas many systems proposed or actually used ...
fail majority."  Condorcet is "a very attractive property" but it "leads
to problems with monotonicity.")

I think Woodall may consider Participation to be part of Monotonicity.  In
any case, another paper of his makes these claims:

A method that always elects a candidate with a majority-strength defeat
over every other candidate, cannot meet "Mono-raise-random" or 
"Mono-sub-top."  They say that X can't be harmed (made to lose, in
most cases) if X is raised on some ballots with the lower preferences
on those ballots replaced with anything valid; or (respectively) if
"some ballots that do not have X top are replaced by ballots that have
X top (and are otherwise arbitrary)".

A method that always elects a candidate with a defeat (of any strength)
over every other cannot, additionally can't meet "Mono-raise-delete"
and "Mono-sub-plump."  The former means X is raised, and the ranking
is truncated after him.  The latter means ballots which don't place X
first are replaced with ballots which bullet vote for X.

Also, a method cannot do all three of:
1. always elect a CW (defeats of any strength);
2. meet Plurality; and
3. Meet "Mono-add-top," meaning that random ballots may be added
with X ranked first, without causing X to lose.

And, a method can't do all four of:
1. always elect a CW with all majority-strength pairwise defeats;
2. meet Plurality;
3. meet "Symmetric-Completion"; and
4. meet "Mono-remove-bottom," meaning X can't be harmed if ballots
are removed which placed X (and only X) last.

Make what you will of all that...  I'm pretty sure I've reproduced
it accurately.

Kevin Venzke
stepjak at yahoo.fr

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