[EM] MinMax Opposition

[John Karr]

The other Later Harm (IRV/Hare) safe method is also highly flawed.

Ultimately I think the best method is gong to have to be a compromise 
between Later Harm and better results. Extending Arrows Theorem: to get 
sincere ballots the voters must not be concerned by Later Harm Risk, the 
Condorcet and Smith criteria cannot be met while guaranteeing Later Harm 
protection.

My query was hoping to find more discussion of this problem. Since MMPO 
appears to produce outcomes closer to Condorcet than IRV, is there a fix 
to MMPO that protects against its two flaws with only a minimal amount 
of Later Harm impact.

On 11/2/20 5:38 AM, Kristofer Munsterhjelm wrote:
> On 02/11/2020 06.51, John Karr wrote:
>> I've seen very little written about the MinMax Pairwise Opposition
>> Method. Which is surprising, given that it is the only Later Harm Safe
>> RCV method other than IRV (that I'm aware of).
>>
>> It counts the votes against each choice and elects the choice that had
>> the lowest opposition in its worst pairing.
>>
>> It appears to agree with Condorcet more often than IRV does and handle
>> Clones much better than IRV. Its' weakness is that it fails the
>> Plurality and Condorcet Loser Criterion.
>>
>> The obvious fixes involve pairing it with other methods such as
>> restricting it to Smith Set when there is no Condorcet Winner (only
>> helpful when there is no Condorcet Winner) or having a Runoff of the IRV
>> Winner vs the MMPO winner, both of which introduce some later harm
>> potential. Or alternately Dropping all choices lower in approval than
>> the first choice votes for the plurality leader (while fixing Plurality
>> it does not guarantee to eliminate the Condorcet loser) also introduces
>> a later harm concern.
> About the only thing MMPO has going for it is that it, indeed, meets
> LNHarm and Participation. The cost is a very strong Plurality failure.
> But if you try to fix the Plurality failure by modifying MMPO, then
> it'll no longer meet either LNHarm or Participation. In that case, why
> not use another method?