First, this message directly only replies to Steve's reply. I'll try to get to
(at least some of) Mike's reply this weekend. Second, I think that if these interchanges of messages are to have any merit, we need to be as specific and precise as reasonably possible. One way to do this is to point out places in messages where increased precision would be more helpful than harmful. I think that Steve's reply to me does exactly this. Third, "specific and precise" does not rule out judgments. What, in my opinion, it does rule out is treating judgments as facts. Making judgments as clearly labeled judgments is fine. Let me try to do that here. On Apr 3, 8:25pm, Steve Eppley wrote: > Subject: Re: Reply on EM to Mike's Reply on ER > Bruce Anderson: > >I don't think I ever said that (in my notation) Smith//Condorcet is > >too complicated to propose to the public. I said that it is > >significantly more complicated than just Condorcet. >> I also said that it is significantly better than just Condorcet. I also said that I thought that there are still other voting methods that are both better and simpler than Smith//Condorcet. None of these statements mean that Smith//Condorcet is too complicated for public use. In fact, I think that it is too simple, and that the public could accept the slightly more complex method I denote by Smith//Condorcet//Plurality. I presume that Mike thinks that Smith//Condorcet is slightly more complicated and slightly better than just Condorcet. Maybe we'll never reach agreement on "slightly" >>versus "significantly," but maybe we can agree on the unmodified "more." > How do you define significantly more complicated, then? Does your > definition relate to whether the public can be persuaded to approve > it when it's offered in state initiatives? (To me, that seems the > practical benchmark.) I certainly agree that I could have more clearly labeled these remarks as being personal judgments, not scientifically or mathematically proven facts. In particular, it is my judgment that Smith//Condorcet is significantly more complicated than just Condorcet. The following are my main reasons for making this judgment. First, Smith//Condorcet involves two fundamentally different methods, so it involves explaining and asking people to understand and accept two different methods. Condorcet alone, of course, does not. Second, in attempting to advocate Smith//Condorcet, one has to explain, if asked, why Condorcet alone is not good enough. In my opinion, such an explanation is quite simple, for example, for either Condorcet//Plurality or Copeland//Plurality; namely, Plurality is quite poor as an initial voting method, but it serves well as a tie-breaker. In my opinion, the corresponding statement for Smith//Condorcet (i.e., Condorcet is quite poor as an initial voting method, but it serves well as a tie-breaker) is much more difficult to accept. Third, while neither Smith nor Condorcet, alone, is extremely complex, neither one is all that simple either. As evidence of this, note that erroneous or vague statements of these methods frequently appear on these lists. In fact, I'm not sure I ever seen a technically correct definition of the Smith set (i.e., of the set of winners according to the Smith voting method). With two exceptions, one such definition is as follows. DEFINITION: An alternative is a winner according to the Smith voting method if that alternative is a member of the smallest non-empty subset of the alternatives such that each alternative in that subset pairwise beats each alternative not in that subset. The two exceptions are: 1) "pairwise beats" needs to have been defined, and 2) to be a valid definition, it must be shown that such a subset always exists and is always unique (it does and it is, but this still needs to be shown). As are as Condorcet goes, it seems to me that most people on this list, except for Mike, say (as you imply below) that the Condorcet winner is the candidate whose worst pairwise defeat is the smallest, whenever there is no candidate that pairwise beats every other candidate. There are two problems with this statement. First, there can be two or more such candidates, which this statement does not allow. Admittedly, it is not hard to construct a more complex correct statement, but complexity is the issue here. Second, consider the following example. 46: A, (B & C tied) 6: B, A, C 4: B, C, A 44: C, B, A Then #(A>B) = 46 and #(B>A) = 54, so B beats A by 54-46 = 8. Also #(A>C) = 52 and #(C>A) = 48, so A beats C by 52-44 = 6. Also #(B>C) = 10 and #(C>B) = 48, so C beats B by 48-10 = 38. A says: "I scored 46 in my only defeat, while C only got 44, and B only got 10. So my worst pairwise defeat was the smallest." B says: "My opponent only scored 48 in my one defeat, while C's opponent got 52, and A's opponent got 54. So my worst pairwise defeat was the smallest." C says: "I lost by only 6 in my one defeat, while A lost by 8, and B lost by 38. So my worst pairwise defeat was the smallest." This is simple? At best, it's understandable only if it's very carefully explained. And the need for such a vary careful explination is part of my argument for complexity here. It's late in EST, I'm tired, and it took me several hours to get this far. I'll try to continue tomorrow (unless I get an offer I can't refuse, which does't take much these days). I still have two more reasons to present; and then there's the rest of Steve's letter. And then Mike says he wants to know why I like Copeland//Plurality better than Smith//Condorcet. Does anyone really care? Bruce > >Determining which standards are most desirable would be a good > >topic to debate--too good to try to rush out in a "quick-and-dirty" > >e-mail posting. > > Did you receive the Glossary of standards I posted about a week ago? > It's overly inclusive of standards. If you have more standards you > want added, though, I'd like to hear them so I can add them. > > Several weeks ago we had two proposals for how to proceed here. > Both involve our voting on the order in which we will discuss > standards (and how well the methods score on each standard). > Maybe we'd vote all at once on the complete order, or maybe just > periodically pick the next few. To be considered in the voting, > they should be in the Glossary. > > >As an aside, in my notation X-Y either means a particular voting > >method jointly proposed by X and Y, or it means a particular voting > >method where X and Y alone have no intrinsic meaning. X//Y means > >that X and Y are both ranked-ballot single-winner voting methods > >where, if X produces a single winner, then that winner is the X//Y > >winner; while if X results in tied winners, then the result of > >applying method Y to this set of tied winners yields the overall > >X//Y winner(s). > > So with this syntax the order of the two (or more) methods is > important. Smith//Condorcet and Condorcet//Smith would be two > different systems. In Smith//Condorcet, if the Smith set doesn't > have exactly one candidate, then smallest worst defeat breaks the > tie. > > Smith//Condorcet has three cases: > > 1. Smith set is empty: Condorcet picks from the candidates not in > the set (i.e., picks from all the candidates). > > 2. Smith set contains exactly one candidate: This is the winner. > > 3. Smith set contains more than one candidate: Condorcet picks from > the candidates in the set. > > >In fact, I have never used and I strongly oppose the use of the > >term "Instant Runoff" to mean MPV/STV/Hare voting. Runoff has an > >established meaning, at least it does in the United States--it's > >the pairwise match between the top two plurality leaders, if > >neither has a strict majority. So an "instant runoff" should be > >that pairwise match based on the voters ranked ballots. > > How about "Instant Runoffs"? > > But I'd rather reserve this moniker for pairwise methods, since the > pairings are just as much (maybe more so) "runoffs" as MPV's > attrition runoffs. And maybe reserve it for one particular pairwise > method, so it can be used before the public when it's campaign time. > > --Steve > >-- End of excerpt from Steve Eppley |
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