Talk:Monotonicity

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Merging with mono-raise

From what I understand, the mono-raise criterion and the "monotonicity criterion" are the same thing. Moreover, when I brought this up on EM list, folks there agreed.. So, any problem with merging these? Can anyone help make it happen? -- RobLa (talk) 07:52, 30 November 2020 (UTC)

There are montonicity criteria (of which mono-raise is one), but when EM members refer to "the" monotonicity criterion (or just monotonicity), it's mono-raise. So "a monotonicity criterion" could be any of them, while "the monotonicity criterion" is mono-raise. Kristomun (talk) 18:37, 27 November 2021 (UTC)

We need a better example

I have an improved version of IRV that is monotonic in the example given. I would elect Center (the Condorcet winner). Can I claim that it is monotonic or just more often monotonic? (Is it still considered IRV? See the link on my user page). RalphInOttawa (talk) 14:54, 13 December 2023 (UTC)

For a method to be monotone, there must be no monotonicity failures anywhere. Checking against an example only shows that there's no monotonicity failure there; there might still be others elsewhere. The only way to know would be by checking a large number of elections, e.g. by simulations, or being entirely certain by mathematical proof. Kristomun (talk) 14:50, 18 December 2023 (UTC)

Thanks. I should have indicated that the current example has Left winning, then Right winning. My version of IRV elects Center both times, which is not the point. I need to find an example where my version does what IRV does. Of course, that's what my version is trying to fix. I have spent a little time not hoping to make it happen. So far, I haven't figured out how to not be monotonic. But it's on my list of things to do. RalphInOttawa (talk) 19:00, 19 December 2023 (UTC)

My version is not monotonic, just better than IRV. In the following example, B is elected.

8 A

5 B>A

4 C>B

When 2 of the voters for A change (lowering) their opinion by casting votes for C>A

6 A

5 B>A

4 C>B

2 C>A

The result is three way tie to be decided by random draw. Not the guaranteed win by A that IRV would do.

The same result can be achieved, and is monotonic, by those 2 voters casting A>C.

RalphInOttawa (talk) 23:51, 31 December 2023 (UTC)