[EM] Mono-add-top method suggestion

[Kevin Venzke]

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
>