I just realized I didn't give my IRV3/AV3 variant system a name. I think I'll call it 3-2-1 voting, because it is a pretty natural way (in my mind at least) to eliminate down in that fashion.
2011/11/6 Jameson Quinn <jameson.qu...@gmail.com> > Forest: I think your system (Bubble IRV, in the sense of bubble sort?) > would have some good properties in terms of results. But honestly, I don't > really see the point. We have a number of systems which give good results. > To me, the point of designing new systems is to give good results while > gaining some combination of (in roughly descending importance) > > - Simplicity of explanation > - Simplicity of counting (summability, etc.) > - Simplicity of voting (ballot design, minimal strategy > considerations, etc.) > - Broad appeal (For instance, a method that would appeal to both IRV > and Condorcet suppporters) > - New, unexplored mathematical properties ("just for fun") > > I think your Bubble IRV doesn't really give any of the first three, and > not too much of the last two. > > It does, however, inspire me to present my own proposal, a simple > modification of David's IRV3/AV3. My only change from his system is that > equal ranking would be allowed. In the IRV part, equal-ranked-top would be > counted as a full first-place vote for both (all) of the top candidates. > > What does this do to summability (one of the main advantages of David's > proposal over IRV)? It actually works fine. You'd keep three tallies: top > ranks, approvals, and a Condorcet matrix. Since with three candidates > there's only one true IRV elimination, equal-ranking doesn't cause the > logistical headaches it would with full IRV. > > What does it do to simplicity of explanation? In my opinion, it's at least > as good as its predecessor IRV3/AV3. "Keep the three top approvals; discard > the one with fewest top ranks; and use preferences to see who'd win between > the remaining two." In a certain sense, that's actually simpler than even > giving a full explanation of IRV. > > What does it do to simplicity of voting? It is much better for ballot > design. With equal-ranking allowed, you'd simply eliminate the problem of > spoiled ballots, which seems to me to be a real concern for IRV. And > allowing equality makes it possible to vote a ratings-style ballot, which > is cognitively easier. > > How about strategy? Additional votes at level 2 or 3 would essentially be > a way to make the approval part of this method freer, without the arbitrary > limit of three approvals. Additional votes at top level would be a way for > a solid majority coalition to ensure that their principal enemy is > eliminated. The chicken dilemma still applies, so it would rarely (never?) > be "strategically optimal" from a first-order perspective to vote two > candidates at top ranking; but on the whole, I think it's good to allow > voters the option to explicitly say that they don't care about such > first-order strategic considerations between two candidates they consider > to be clones. > > In terms of results, I think this system would tend to give the IRV > winner, with perhaps a small step in the direction of MJ. That's not my > favorite place to be; it still allows for self-perpetuating two-party > domination. However, I think that there's a real possibility that this > system would allow for smoother transitions if the set of top two parties > changed at a local level. So ... well, perhaps it's my "I invented it" > bias, but I think it's good enough. > > Thoughts? > > Jameson > > ps. One more minor comment on Forest's Bubble IRV proposal, below: > > 2011/11/5 <fsimm...@pcc.edu> > > Dear EM Folks, >> I’ve been very busy, while watching postings on the EM list out of the >> corner of my eye. I was very >> happy to notice Mike Ossipoff’s interesting contributions. In particular >> his promotion of a variant of IRV >> where equal rank counts whole strikes me as promising in the context of >> the “chicken problem.” >> >> On a related note I have been thinking about how to make a monotone >> variant of IRV. Perhaps the two >> ideas could be combined without sacrificing all of the other nice >> features that IRV(=whole) seems to have. >> >> It is well known that certain kinds of elimination methods cannot satisfy >> the monotonicity criterion. The >> basic variant of IRV is of that type, namely what I call the “restart >> with each step type” of elimination >> method. This means that when one candidate is eliminated, the next stage >> starts all over again without >> learning from or memory of the eliminated candidate. Range elimination >> methods that renormalize all of >> the ballots at each stage are of this type, too, since the >> renormalization is an attempt to eliminate the >> effect of the eliminated candidates on the remaining stages of the >> process. >> >> But some methods of elimination that do not suffer from the “restart >> problem” turn out to be monotone. >> For example, approval elimination where the original approvals are kept >> throughout the whole elimination >> process; trivially the highest approval candidate is the last one left. >> >> Now here’s what I propose for an IRV variant: >> >> 1. Use the ranked ballots to find the pairwise win/loss/tie matrix M. >> This matrix stays the same >> throughout the process. >> >> 2.Initialize a variable U (for Underdog) with the name of the candidate >> ranked first on the fewest number >> of ballots, and eliminate U from the ballots. >> >> 3.While more than one candidate remains, eliminate candidate X that is >> ranked first on the fewest >> number of ballots after the previously eliminated candidates’ names have >> been wiped from the ballots (as >> in IRV elimination) and then replace U with X, unless U defeats X, in >> which case leave the value of U >> unchanged. >> >> 4. Elect the pairwise winner between the last value of U and the >> remaining candidate. >> >> Note that a simplified version of this where you just eliminate the >> pairwise loser of the two candidates >> ranked first on the fewest number of ballots in NOT monotone. We have to >> remember the previous >> survivor and carry him/her along as "underdog challenger" to make this >> method monotone. >> >> Note also that this method satisfies the Condorcet Criterion. So we gain >> monotonicity and CC, but what >> desireable criteria do we lose? It still works great on the scenario >> >> 49 C >> 27 A>B >> 24 B >> >> Candidate A starts out as underdog, survives B, and is beaten by C, so C >> wins. > > > Wouldn't B be the underdog initially here? (Not that it matters to the > result or to the further analysis below.) > > >> But if B supporters >> really prefer A to C they can make A win. On the other hand if the A >> supporters believe that the B >> supporters are indifferent between A abd C, they can vote A=B, so that B >> wins. >> >> When I have more time, I'll sketch a proof of the monotonicity. >> >> Comments? >> >> Thanks, >> >> Forest >> ---- >> Election-Methods mailing list - see http://electorama.com/em for list >> info >> > >
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