[EM] MOP-F2 / ties

[Juho Laatu]

> On 08 Jul 2019, at 21:01, Juho Laatu <juho.laatu at gmail.com> wrote:
> 
>> On 08 Jul 2019, at 17:36, C.Benham <cbenham at adam.com.au> wrote:
> 
>>> Margins provide good results with sincere votes, so why not use margins...
>> I don't see how egregious failures of the Plurality  and Later-no-Help (and even Non-Drastic Defense) criteria constitute "good results"
>> irrespective of whether the votes are "sincere" or not.
> 
> I googled the Non-Drastic Defense criterion and this example.
> 
> 46 A>C
> 10 B>A
> 10 B>C
> 34 C=B
> 
> Non-Drastic Defense criterion:    if on more than half the ballots X is voted both above Y and below no other candidate (i.e. no lower than equal-top) then Y must not win
> 
> The Non-Drastic Defense criterion says that A should not be elected.
> 
> If no cutoffs are used, MOP-F2 is the same as the base method, i.e. Minmax(margins), and elects A. But if those 34 voters that seem to consider C and B to be clones indicate this in their votes (as they probably should) by voting C=B>>, C>B>>, or B>C>>, then B wins.
> 
> I guess it would be ok in MOP-F2 not to support use of "=" in the vote (explicitly) since in this case since they can vote also C>B>>, or B>C>>, and by doing this, indicate that these two candidates should be seen as clones / their mutual defeats should be seen as weak defeats.

Few more words on different options in handling ties in MOP-F2.

Every vote that ranks A above B makes B's defeat to A one point stronger. But if both A and B are protected (above the cutoff), both B's defeat to A and A's defeat to B will be made two points weaker. As a result ranking one's favourites does not harm them (in the sense that they would be worse off in comparisons if there is a top loop).

Someone might try to maximise the protection of one's favourites by not giving any preference between them, but vote those candidates equal in order to avoid any defeats between one's favourites. This could be achieved by casting a A=B>>... style vote. In principle I don't like any incentives to hide preferences in ranked elections, so let's see what possible alternatives there are.

First alternative could be to not allow use of "=" in the votes (except implicitly between the truncated candidates). That would make sense if the used ballots are such that supporting use of "=" would just introduce additional technical problems and unnecessary complexity in the voting process. Not being able to use "=" is no problem since voters can easily replace it with ">". Usually there is a small preference difference anyway. And if there really is none, then flipping a coin is a good solution. In some other ballot types marking candidates as tied may however be a very natural (e.g. if there is a fixed number of positions/ratings/columns/slots to use), and even unavoidable if e.g. the number of slots is smaller than the number of favourite candidates. This approach is thus quite good for some ballot types. It is not a problem not to support explicit ties ("=" between ranked candidates) if it is easier to implement the voting process without them.

Another approach would be to handle A=B>> style voting so that both candidates will lose to each others (not very pretty). Or alternatively one could give only one point of protection to candidates that are tied or at the winning end of a ">" relation. The calculation process would be a bit more complex than in the original MOP-F2. It may be easier to voters to understand the simple protection rules of the original MOP-F2 than this kind of nuances.