[EM] Fragmented Condorcet doesn't imply DPC
From off-list conversation, I discovered an example of that my tentative multiwinner criterion, Fragmented Condorcet, doesn't imply DPC. Consider this bullet-voting situation: 400: A 400: B 400: C 300: D Three to be elected. The Droop quota is 375. So, according to DPC, A, B, and C should be elected. There's at least one way of splitting these votes into three bundles so that the right candidates (A, B, and C) get elected, and so that each contains 500 ballots (1500/3). For instance, first bundle: 400 A, 100 D second bundle: 400 B, 100 D third bundle: 400 C, 100 D but there's also a way that isn't proportional: first bundle: 300 A, 100 B, 100 C A beats B and C, A wins second bundle: 300 C, 100 B, 100 A C beats A and B, C wins third bundle: 300 D, 200 B D beats B, D wins The parallels to packing and cracking are obvious. I suppose I shouldn't be surprised, since Condorcet doesn't imply mutual majority, either, but this allows for the possibility that Fragmented Condorcet contradicts the DPC. If it does, the construction would probably be something like: arrange a setup so that there's only one way of arranging Condorcet winners in each bundle, all others causing cycles in at least one bundle. Then modify this arrangement so that the only CW-permitting partitioning contradicts the DPC. I don't know if that's possible, though, and it would have to use full preference votes (e.g not just bullet votes). - In general, I think my surprise at this confirms what I've suggested before: that it's not enough to technically satisfy criteria, one must also gracefully fail towards them. Clone independence isn't worth much if the system is remove clones then run Borda. Similarly, if it's possible to pass both FC and the DPC, then the method, for a ballot set where DPC and FC provide no constraints, must elect results that are in some fashion close to a ballot set where they would provide constraints. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Chris, --- En date de : Lun 12.1.09, Chris Benham cbenha...@yahoo.com.au a écrit : Kevin, You wrote (11 Jan 2009): There are reasons for criteria to be important other than how easy they are to satisfy. Otherwise why would we ever bother to satisfy the difficult criteria? Well, if as I said none of the criteria were incompatible with each other then presumably none of the criteria would be difficult. That's not what I meant. I meant: Why do we *currently* ever bother to satisfy difficult criteria? What do we mean when we say we value a criterion? Surely not just that we feel it's cheap? With mono-add-top and Participation, the quasi-intelligent device in reviewing its decision to elect X gets (possibly relevant) information about other candidates besides X. How can it be relevant? X was winning and X is the preferred candidate on the new ballots. You know that Condorcet is incompatible with mono-add-top (and so of course Participation), Condorcet isn't incompatible with mono-add-top. Only top tiers probably are. so if we value compliance with the Condorcet criterion information about candidates ranked below X must sometimes be relevant. I didn't realize that whether information is relevant depends on whether a valued criterion requires the information. If you need to identify majorities, then the fact that a ballot shows no preference between Y and Z, is relevant information. But even if the quasi-intelligent device is mistaken in treating them as relevant, then that is a much more understandable and much less serious a blunder than the mono-add-plump failure. Ok. I still don't really see why, or what makes the difference. It's absurd that ballots that plump for X should in any way be considered relevant to the strength of the pairwise comparison between two other candidates. This absurdity only arises from the algorithm specifically using (and relying on) a majority threshold. We have Mutual Majority and beatpath GMC displaying the same phenomenon. No. I don't accept that 'being tossed out of the favoured (not excluded from winning) set' is exactly the same phenomenon as 'being joined by others in the favoured set'. The latter is obviously far less serious. In an actual election method it would be exactly the same phenomenon. Removed from that context it isn't clear how any of this is serious, let alone obviously far more/less serious. The logical problem is the same, that according to you, the new ballots only contain information on one candidate and should only affect that one candidate. I guess you imagine the win as a pie that has to be split up, and it's better for the candidate to get a smaller piece than none at all. Never mind, that the logic causing this is still just as bad, or that real elections don't award divisible pies. Anyway, you already said there was no way to explain why it isn't completely absurd for Mutual Majority to behave as it does. I don't think that whether Mutual Majority's behavior is absurd should depend on whether you remember that Mutual Majority has this behavior. I don't feel there's an advantage to tending to elect candidates with more approval, because in turn this should just make voters approve fewer candidates when they doubt how the method will use their vote. And why is that a negative? I value LNHarm as an absolute guarantee, but in inherently- vulnerable-to-Burial Condocet methods, I think it is better if they have a watch who you rank because you could help elect them Approval flavour. This is a negative because it suggests that your positional criterion will be self-defeating. How can it possibly be self-defeating? What is there to defeat? I thought there was some intention behind your criterion. You talk about the clearly strongest candidate so I assumed this idea is important to you. If insisting on electing the clearly strongest candidate creates incentives that *change* who this candidate is, then what have you accomplished? From your earlier post: In the three-candidate case, at least, I think it's a problem to elect a candidate who isn't in the CDTT. Why? Because in the three-candidate case this is likely to be a failure of MD or SFC, or close to it. I'm happy to have MD, and I don't care about SFC or close failures of MD. Regarding SFC: It's a bit strange to elect Y when a majority of the voters prefer X to Y, but there's no majority that prefers anybody to X. There could be a good reason for it, but that doesn't mean it wouldn't be better if we never had to do that. I would say that I don't think the CDTT is that much more valuable, than the combination of MD and SFC, especially if you use pairwise definitions of these two. In the three-candidate case it's also compatible with LNHarm. By adding a vote for your second choice, you can't inadvertently remove your first preference from the CDTT.
