[EM] Mono-add-top method suggestion

[Chris Benham]

Kevin,

Interesting. I used to be in some ways quite intelligent.

What keeps getting more and more confirmed to me is that Hare (aka IRV) 
is a very bad mixer and it is very difficult to compete with it on its 
strengths.  The "Benham" method hangs on to Unburiable Mutual Dominant 
Third but beyond that pays a significant price (at least in terms of 
criterion compliances) for meeting Condorcet.

It occurred to me that could have some pretty horrible method that in 
some way just combined the Approval and MMM (minimum additional votes to 
become the CW) scores that would meet Mono-add-Top and probably 
mono-nearly everything else.

Chris

On 22/08/2025 8:45 am, Kevin Venzke wrote:
> Hi Chris,
>
>> Kevin,
>>   
>> Thanks for that demonstration.
>>   
>> A much more simple method (using the same type of ballots) definitely
>> does meet Mono-add-Top:
>>   
>> *Elect whichever of the Hare winner and the most approved candidate
>> pairwise beats the other.*
> Unfortunately this doesn't seem to me to work:
>
> 358: B>C | A
> 305: C | A>B
> 187: A | B>C
> 148: A>C | B
>
> A is the IRV winner, C is the approval winner, and C beats A, so C wins.
>
> Add 35 more of the C-top ballots:
>
> 358: B>C | A
> 340: C | A>B
> 187: A | B>C
> 148: A>C | B
>
> Now B is the IRV winner, C is still approval winner, but B beats C, so B wins.
>
> Kevin
> votingmethods.net