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

Rob Lanphier robla at robla.net
Mon Nov 16 00:03:00 PST 2020

```Hi Kevin,

Thanks for the prompt and helpful reply!   I think I know how I want
to go about editing the "Monotonicity" article on electowiki, but that
article needs a lot more work than just this addition.

More inline:

On Sun, Nov 15, 2020 at 6:59 PM Kevin Venzke <stepjak at yahoo.fr> wrote:
> For what people usually mean when discussing monotonicity (such as in
> connection with IRV) this corresponds to Woodall's Mono-raise.

Given that "Monotonicity" is more-or-less equivalent to "mono-raise"
(both by your reckoning, and by my previous understanding), I'd like
to use this as a tool to simplify the "Monotonicity" article on
electowiki, moving the more technical mathematical definitions out of
the summary of the article

> I don't see how Woodall can be wrong, it's his choice to define these
> criteria and characterize them as dealing with monotonicity. But to me,
> if you say a method "fails monotonicity," or "is monotone," you're either
> talking about Mono-raise or else you're being unclear. Inserting these
> into an article called "Monotonicity" could be unhelpful unless it's made
> clear that these are other criteria connected to the idea, and are used
> (as far as I know) primarily by Woodall.

I've seen other folks use at least some of the nine criteria that
Woodall defines, so I'd like to define them somewhere on electowiki.
I'll give it some thought.

One relatively simple restatement comes from the Wikipedia article
<https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem>

Here's the way that the Wikipedia article restates monotonicity:
"If any individual modifies his or her preference order by promoting a
certain option, then the societal preference order should respond only
by promoting that same option or not changing, never by placing it
lower than before. An individual should not be able to hurt an option
by ranking it higher."

More ways of thinking about it....

> Note that (at least in other articles) Woodall is/was largely concerned
> with which sets of properties are compatible with each other, and he
> didn't usually make statements judging the relative value of criteria. This
> leaves the job to other people to explain why we should care about a
> given property.

Thanks for your advice! I'll give all of this more thought before I
make big changes to that electowiki article.

Rob
```