[EM] Mono-add-top method suggestion

[Chris Benham]

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.*

James Green-Armytage mentioned a while ago that he thought that would be 
a good method. At the time I had different priorities and dismissed it 
as something clunky that fails Condorcet and Mono-raise, but now I 
agree. As a practical proposition it is probably doubtful that the extra 
complication versus plain Hare gives enough bang for buck, and I suppose 
as well as failing Condorcet it fails Double Defeat.  But nonetheless it 
must be quite a bit more Condorcet efficient than Hare, while hanging on 
to Mono-add-Top compliance.

Chris

On 10/08/2025 8:10 pm, Kevin Venzke wrote:
> Hi Chris,
>
> Although all three methods satisfy Mono-add-top, the combined method doesn't:
>
> 330: D>A | C>B
> 302: C>A | D>B
> 163: B>C | A>D
> 126: A>B>D | C
> 77: B>D | C>A
>
> A is the approval winner, but MinMax elects C (no CW present) and IRV elects D
> (eliminating A right away). D has more approval than C and so D wins.
>
> But if we add 10 more D>A|C>B ballots:
>
> 340: D>A | C>B
> 302: C>A | D>B
> 163: B>C | A>D
> 126: A>B>D | C
> 77: B>D | C>A
>
> By Mono-add-top, this should not be able to take the win away from D, since we
> added D-top ballots. But with the new ballots, now MinMax is willing to elect A
> instead of C. A has more approval than IRV's D winner (unchanged) and so A wins.
>
> Kevin
> votingmethods.net
>
>
>> Le dimanche 10 août 2025 à 00:44:29 UTC−5, Chris Benham <cbenhamau at yahoo.com.au> a écrit :
>>   
>> I think if there was an informed honest debate on the relative merits
>> (for public political elections) of Hare versus one of the best
>> Condorcet methods I think Hare's compliance with Mono-add-Top would be a
>> big point for it.
>>   
>> MinMax Margins is a Condorcet method that meets Mono-add-Top, but pays
>> too heavy a price for that to qualify as a good Condorcet method.   Hare
>> meets Mono-add-Top and so does Approval.
>>   
>> This is my (not too fanciful thought experiment) idea for a method that
>> meets Mono-add-Top and is more Condorcet efficient than Hare (but more
>> complicated) using ranked ballots with explicit approval cutoffs:
>>   
>> *Elect whichever of the Hare winner and the MinMax Margins winner is
>> more approved.*
>>   
>> Unfortunately as well as failing Condorcet I am sure it also fails
>> Double Defeat (meaning a candidate pairwise beaten by a more approved
>> candidate might win), but a candidate that is both the CW and the AW
>> always wins.
>>   
>> There is no zero-info voter incentive to truncate or to do anything
>> (aside from the approval cutoff) other than give a full sincere
>> ranking.  If MMM tries to flout the Plurality criterion I can't see any
>> way that the Hare winner won't be more approved.
>>   
>> Chris
>>