[EM] Short definition. Long definition fixed.

[MIKE OSSIPOFF]

Here's a short definition of Monotonicity, followed by supporting
definitions, followed by the long definition, with one fix added:


Short Monotonicity definition:

If, by a certain set of ballots, Smith wins, then, if we modify
some of the ballots so that they vote Smith higher, that shouldn't
cause Smith to not win.

[end of short Monotonicity definition]

A ballot votes Smith over Jones if it marks them in such a way
that it's possible to contrive a configuration of other people's
votes such that, if we delete everyone but Smith & Jones from the
ballots, Smith is the unique winner if & only if we count that
ballot.

A voter votes Smith higher if he changes how he marks Smith on
his ballot in such a way that it's possible to contrive
an initial way for that voter to mark the other candidates such
that his change in how he marks Smith causes Smith to be voted over
someone over whom Smith wasn't voted before the change.

How a voter marks Smith on a ballot means how he votes Smith,
determined without regard or comparison to how he votes other
candidates.

[end of supporting definitions]


Monotonicity Criterion, long version:

If, by a certain set of ballots, Smith wins, then if we modify
some of those ballots so that they vote Smith higher, doing so,
if possible, without changing the order in which other candidates
are voted on those ballots, and, if possible, without changing how
other candidates are marked on those ballots, and they don't vote
anyone over Smith who wasn't voted over him before the change,
then, after that change, Smith should still win.

[end of long Monotonicity definition]


Of course the order in which candidates are voted is the matter
of who is or isn't voted over whom.

I think the short definition is airtight, and so the long one
isn't needed.

Mike Ossipoff


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