# [EM] Minmax ranked method

Juho Laatu juho.laatu at gmail.com
Wed Nov 8 17:44:04 PST 2017

```> On 08 Nov 2017, at 23:52, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:

> However, I would want the system to have some reasonable resistance to point number two. I seem to value tactical nomination resistance higher than say, Mike, who values strategic voting resistance more highly.

Do you have some nice clone and nomination related (real life large political election) example where Minmax/Simpson would be in trouble?

The first example in my mind is a case where one party nominates three equally liked candidates that end up in a loop, and therefore none of them wins, although one of them would have won without the loop. This is however not really a bad problem because it can be solved by nominating only two similar candidates. The probability of this kind of a loop is also very low (especially if there are clear differences between candidates, i.e. they are not indistinguishable to the voters).

Next example. There are three left wing parties that each have one candidate, and they end up in a loop as above. In this case it is not possible to tell one of the parties not to nominate any candidates. Since there are only three left wing parties, it is possible that those candidates have mutual majority. They could be the top three candidates in all the votes of the leftist voters. Now we have two cases. Either the looped votes indicate that there would be considerable dissatisfaction among the leftist voters (and others) if any of their candidates will be elected, in which case a right wing candidate could be a better winner. Or alternatively the looped votes are just an accident, and actually all left wing voters would be very happy to elect any of the leftist candidates. Since we have only ranked votes, we can not tell which one of those explanations is closer to the truth. Typically it is also not possible to check if the looped candidates have mutual majority (or are in ranked next to each others in many votes). It is thus hard to tell how "clone like" the looped candidates are, and if the loop vas a result of having "clone like" candidates, or just a loop that indicates unwillingness to elect the other candidates in the loop.

Observations:
1) loops are quite rare (especially when candidates have considerable differences (i.e. when they are not seen by voters as "all identical"))
2) if there is a loop, it is not easy to tell if it is a loop of "clone like" candidates or an indication of other kind of cyclic preferences
3) the preference matrix can't tell us if clones (votes where the looped candidates were ranked next to each others) had a major role in creating the loop
4) it can be better not to elect one of the top looped candidates (if being looped indicates interest to change that candidate to someone better, and there is a candidate that is more "stable")
5) if you use a clone proof method, it will always assume that top looped candidates are clones (in the sense that one of them must win), and that could sometimes be a mistake / unwanted result
6) three clones within one party can be avoided (if they are considered a risk)
7) from minmax point of view it is important to discuss if the target of the election is to elect a candidate that loses to others as little as possible, even in the presence of loops (is friendly fire an essential risk, or should pairwise losses be always counted as enemy fire)

If my party (or wing) had three serious potential winners, it would probably make sense to nominate them all, since the risk of not winning because of the loops is probably much lower than the risk of not winning because of not nominating a potential winner. Candidates may be nominated also for other reasons, like keeping the party in the limelights and hoping to win in the next election.

Juho

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