As a long time fan of Margin Sorted Approval (AKA Approval Sorted Margins <https://electowiki.org/wiki/Approval_Sorted_Margins>), I've been thinking about various ways to improve it. I started thinking about how one might implement an automatic approval cutoff, designed to give each ballot its own strategically optimal cutoff. One reasonable strategy in Approval Voting generally is to determine, for each ballot, the highest ranked candidate(s) who are in the Smith Set, and then put the Approval Cutoff below that rank. But what happens if there is a Condorcet cycle, and the candidate who would ordinarily win in Approval voting ("A") using that strategy is cloned ("A1, A2, A3"). and there is a cycle in that clone set? With the strategy.above, the approval cutoff will be placed just below the top clone on the ballot. This would cause a split of approval for the A# candidates, affecting not only Margin Sorted Approval but also Approval Voting more generally. This special case seems highly unlikely, but it points to a cloning resistance issue with any Approval augmented Condorcet method. Thoughts?

A couple quick thoughts on this. I see two risk factors to the vote split eventuating. The first is how lenient one is in setting the approval cutoff within the Smith Set in general: on one end, you approve of all members except the least favorite (least risk) and on the other you approve of the top member only (most risk). The second is whether, in your scenarios, the original set of ballots that elected A had A as the CW or as a member of Smith Set to begin with. If the later, A’s clones will likely cluster higher within the Set from the pov of the voter compared to the other, non-A Set members, so will be likely all approved (but again, depends on the first factor above). If A was the CW though and was the last candidate still approved off originally, at least some of the clones won’t be approved by various voters, hence splitting. Depending on how these two factors interact, you could get vote splitting in such scenarios(?). Or maybe this is entirely off the mark. Regards, Etjon On Tue, Oct 22, 2024 at 9:32 AM Ted Stern <dodecatheon@gmail.com> wrote: > As a long time fan of Margin Sorted Approval (AKA Approval Sorted Margins > <https://electowiki.org/wiki/Approval_Sorted_Margins>), I've been > thinking about various ways to improve it. > > I started thinking about how one might implement an automatic approval > cutoff, designed to give each ballot its own strategically optimal cutoff. > > One reasonable strategy in Approval Voting generally is to determine, for > each ballot, the highest ranked candidate(s) who are in the Smith Set, and > then put the Approval Cutoff below that rank. > > But what happens if there is a Condorcet cycle, and the candidate who > would ordinarily win in Approval voting ("A") using that strategy is cloned > ("A1, A2, A3"). and there is a cycle in that clone set? With the > strategy.above, the approval cutoff will be placed just below the top clone > on the ballot. This would cause a split of approval for the A# candidates, > affecting not only Margin Sorted Approval but also Approval Voting more > generally. > > This special case seems highly unlikely, but it points to a cloning > resistance issue with any Approval augmented Condorcet method. > > Thoughts? > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >

Ted, > As a long time fan of Margin Sorted Approval (AKA Approval Sorted > Margins <https://electowiki.org/wiki/Approval_Sorted_Margins>), I've > been thinking about various ways to improve it. To solve what "problem"? > > I started thinking about how one might implement an automatic approval > cutoff, designed to give each ballot its own strategically optimal cutoff. Not possible with just ranking information. To revisit the classical example: 49 A        (presumably sincere, but maybe sincere is A>C) 24 B        (sincere may be B>C, that is what the C supporters believe) 27 C>B    (sincere, but could be C>B>>>A or C>>>B>A) If we claim that we are trying to elect the sincere CW and therefore avoid giving the voters a strong truncation incentive then the approval cutoffs need to be explicit and manual so as to squash any post election complaints from losers. > > One reasonable strategy in Approval Voting generally is to determine, > for each ballot, the highest ranked candidate(s) who are in the Smith > Set, and then put the Approval Cutoff below that rank. In the above example that would mean we interpret the C>B ballots as giving approval to both C and B, giving the win to B (as the sole winner by Double Defeat).  But then the C supporters could have a semi-reasonable complaint: "We didn't mean to really approve of B. We only expressed our weak B>A preference because we assumed (or were led to believe) that the B supporters would return the favour by voting B>C.  We object to them being rewarded for their treacherous defection." But if the approval cutoffs are explicit any complaint like that gets a crushing rejoinder.  If they voted C>B|>A giving the win to B, it is "Your complaining about the election of a candidate you explicitly approved of? You could have prevented B from being elected by not approving B. You cannot reasonably expect the voting method to read minds and call C the winner.  C was Doubly Defeated  by A." Or if they voted C|>B  causing A to win and their complaint is "But we prefer B to A and B pairwise beat A" then the rejoinder is "If you really wanted B to defeat A why didn't you approve of B? If you had, then B would have won." With an explicit approval cutoff there is no clone issue because when the method has a ratings element candidates have to have the same ratings (here being on the same side of the approval cutoff) to qualify as clones. So either we say to the voters "This is an Approval-ish high SU method, so we are not interested in your rankings among unapproved candidates" or we say "We are interested in whatever ranking you care to express and if there is a top cycle then your approval cutoffs will help determine the winner". I am open to both but prefer the second because it allows greater voter expression.  In the first case we need a method that meets Double Defeat (Implicit) and in the second one that meets Double Defeat(Explicit). My favourites are MSA(implicit) and MSA(explicit),  but the two versions of Smith//Approval also fill the bill and are not bad. Chris Benham On 22/10/2024 9:02 am, Ted Stern wrote: > As a long time fan of Margin Sorted Approval (AKA Approval Sorted > Margins <https://electowiki.org/wiki/Approval_Sorted_Margins>), I've > been thinking about various ways to improve it. > > I started thinking about how one might implement an automatic approval > cutoff, designed to give each ballot its own strategically optimal cutoff. > > One reasonable strategy in Approval Voting generally is to determine, > for each ballot, the highest ranked candidate(s) who are in the Smith > Set, and then put the Approval Cutoff below that rank. > > But what happens if there is a Condorcet cycle, and the candidate who > would ordinarily win in Approval voting ("A") using that strategy is > cloned ("A1, A2, A3"). and there is a cycle in that clone set? With > the strategy.above, the approval cutoff will be placed just below the > top clone on the ballot. This would cause a split of approval for the > A# candidates, affecting not only Margin Sorted Approval but also > Approval Voting more generally. > > This special case seems highly unlikely, but it points to a cloning > resistance issue with any Approval augmented Condorcet method. > > Thoughts? > > ---- > Election-Methods mailing list - seehttps://electorama.com/em for list info