[EM] What is the most useful definition of "monotonicity"?

Rob Lanphier robla at robla.net
Tue Nov 17 00:57:52 PST 2020

Thanks Toby!  Given the private and public responses I've gotten to my
question, and the deeper understanding of "the Monotonicity criterion"
that I'm developing, I think that it makes sense to figure out how
"the Woodall nine" (as I'll start calling them) map to "monotonicity"
when talking to people who understand matrix addition.

More below...

On Mon, Nov 16, 2020 at 2:17 AM Toby Pereira <tdp201b at yahoo.co.uk> wrote:
> I think the scenarios where new ballots are added have more in common with
> participation than monotonicity, in terms of how it is normally understood in
> voting theory at least.

Let's use the Woodall Nine to talk about this.  What would you say the
mapping is?  I started coming up with my own version of the list
(which was serious), but this became a self-parody.  The format of
each line is

* woodall-name - robla-named-criterion ("Proposed Wikipedia/electowiki Article")

Here's the mappings as I saw them on my first runthough:

* mono-raise - dont-muck-with-ballots-criterion ("Monotonicity (Classic)")
* mono-raise-delete - participation-criterion ("Monotonicity (Nuke ballots)")
* mono-raise-random - adding-random-ballots-causes-mayhem-criterion
("Monotonicity (Add random)")
* mono-append - fill-in-ballot-bubbles-criterion ("Monotonicity (Add
* mono-sub-plump - replace-ballots-criterion ("Monotonicity (Erase preference)")
* mono-sub-top - replace-with-new-winner-criterion ("Monotonicity ()")
* mono-add-plump -
add-incompletely-ranked-ballots-to-cause-loss-criterion ("Monotonicity
(Add incomplete ballots)")
* mono-add-top - add-top-scored-but-mostly-random-criterion
("Monotonicity (Add mostly random)")
* mono-remove-bottom -
remove-bottom-ranked-Condorcet-loser-ballots-criterion ("Monotonicity
(Remove Condorcet loser haters)")

I think this thing needs to exist in the world, so I'm actually going
to keep working on it here:


Toby, I would love for you and others on this mailing list to come up
with more serious versions.  I spent about an hour trying to be
serious when coming up with my mappings, and I think it was a valuable
exercise.  My fear: there are many electoral reform advocates who will
say  "I understand the monotonicity criterion".  However, most of
those people wouldn't be able to answer this question: "what do YOU
mean when you say 'monotonicity criterion'?"  My guess: they would
deflect, and say "I know someone who knows what it means, and I've
never really understood it, but I THINK it means this: xyz", and then
their "xyz" would be an oversimplified example involving Woodall's
"mono-raise" or perhaps "Participation" or something vaguely related
to Pareto efficiency.  They probably don't understand very well, and
my hunch is that most people on this mailing list are overconfident
with THEIR understanding of "monotonicity".

When someone asks "What is the 'monotonicity criterion'?", it seems
the correct answer is to throw the question back at them: "before I
explain: do you know what 'monotonicity' is?".  If it seems they
aren't very well-versed in advanced mathematics, and they aren't
familiar with what a monotonically-increasing sequence is, then assume
that it's time to back off the math jargon.  I think "monotonicity
criterion" seems to be a terrible name for talking about electoral

That's the reason why I want to talk about the Woodall Nine.  I'd like
to come up with layperson names for each of them, and possibly map
them to various criteria that have Wikipedia articles about them.  If
there's not yet a Wikipedia article, maybe an electowiki article.  If
there's not yet an electowiki article, maybe a section of an
electowiki article.

Responding to one last bit of your email:

> Mono-add-top is just a specific case of participation.

Are there any other mono-woodall methods that are subsets of the
Participation criterion?


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