Richard did not quote my introduction to the post he responds to, so I copy that here:
> I got into this thread because of comments as to what voters might > understand. > > So, I put my voter hat on again to respond to the following. > AND, I do the same in most of this, unless I precede something with "DWK". On Sun, 28 Apr 2002 19:05:14 -0700 Richard Moore wrote: > Dave Ketchum wrote: > >>> Preferences that are expressed in Approval tend to be strongly held >>> preferences, while preferences that are expressed in ranked ballots >>> are of unknown strength (and sometime negative strength, particularly >>> in non-Condorcet methods such as IRV and Borda). Thus, the voters may >>> end up with a CW who is favored by a majority of voters to all other >>> candidates, but who doesn't have any voters that have a strong >>> preference for that candidate over their next choice. When the CW and >>> the AW (Approval Winner) are different, the better choice is probably >>> the AW, since it is likely that, for the majority that prefer the CW >>> to the AW (as indicated on rank ballots), that preference is a weak >>> one -- otherwise that preference would be expressed in the Approval >>> vote as well. For the minority who approved the AW without approving >>> the CW, this was more likely to be a strong preference. >> >> >> >> >> I get dizzy, and suspicious, trying to sort that out. > > > Hmm, I might suggest a little more effort, rather than simply dismissing > an argument because it makes you "suspicious". Still, I guess more clarity > wouldn't hurt (I wasn't intentionally trying to be confusing, but I can > see that my words came out less clear than I intended). Point is, you might as well keep such for the genius community - we do not have time. > > So, let's say you have an election in which two sets of ballots are taken > simultaneously: one ranked set, and one approval set. The ranked ballots > are counted to find the CW, and the approval ballots are counted to find > the AW. If CW and AW are the same, then neither method has bested the > other. If CW and AW are different, then... > > 1) there is a majority N1 of voters who prefer CW to AW. Some of these > will have approved of CW and disapproved of AW; call this number N1A. > > 2) there is a minority N2 of voters who prefer AW to CW. Call the number > of voters within this group that approved of AW and disapproved of CW > N2A. DWK: This even sails over my head. If I read it right, it says CW should win a runoff between AW and CW, suggesting that looking for CW is preferable to looking for AW. So, what are we arguing over? > > For simplicity I'll assume nobody voted any tied preferences between > AW and CW. > > Since AW is the approval winner, we know that N2A > N1A. We also know > that N1 > N2, meaning that (N2A/N2) > (N1A/N1). That is, the voters > who prefer CW to AW are less likely to express that preference on an > approval ballot, than the voters who prefer AW to CW are to express > that preference on an approval ballot. In other words, we have a good > reason to believe that the median strength of the CW>AW preferences > is less than the median strength of the AW>CW preferences. > > I don't claim that the Approval winner is always more strongly preferred > than the Condorcet winner when the two differ, but I think I've shown > that such will be the case more often than not. Hence, I am more willing > to trust Approval than Condorcet. > > (On the other hand, I can't think of a single argument to justify the > IRV winner over the Condorcet winner, when those two methods give > different results.) > >> Truly the decision as to winner is a public choice, but it needs to >> be, as close as possible, the sum of the private choices of the >> voters. For that to work, knowing more of what each voter's private >> choice is needs doing so far as practical. > > > "...as far as practical" -- indicating that there are practical limits > to allowing individual expression. I think Approval does at least as > well as Condorcet at aggregating individual choices. If I have a weak > preference for A>B, and a strong preference for B>C, then voting a > ranked ballot of A>B>C adds more noise than voting an Approval ballot > of AB. BOTH ballots showed least preference for C. The Approval ballot did not let me indicate a preference for A>B, no matter how strong it might be, without giving up my right to show C as less preferred than either. > >>> If it's individual expressivity you want, then Cardinal Ratings are >>> for you. You'd be perfectly free to sacrifice instrumental voting power >>> to make a more exact statement about your evaluation of the candidates' >>> merits. >> >> >> >> >> This one scares me. I would worry about losing to those who could figure >> out a strategy to give themselves extra power over those of us who are >> not up to strategy. > > > I suggested CR as a counter-example to the notion that maximizing individual > expressive power should be an end goal of choosing an election method. > > Actually my worry about CR is the corollary to yours. While I would simply > vote an Approval-style ballot in CR, if other voters who are on my side > aren't up on this strategy, and vote their actual ratings, then I could > lose. Approval is a way of doing CR that levels the playing field between > the strategy-aware and non-strategy-aware voters. Elsewhere I seem to see agreement that strategy gets you little, if anything, in Condorcet. > >>> If you are unable to decide whether to approve or disapprove some >>> candidate, because that candidate is somewhere close to the strategic >>> borderline between approval and disapproval, then the strategic value >>> of your vote for that candidate is close to zero (relative to your >>> strategic values for the high- and low-utility candidates). Therefore >>> the strategic cost of making the wrong choice on this particular >>> candidate is very low. >> >> >> >> >> I think you are saying it is not important whether I get it exactly >> right - could be, but I am not sure where the ballpark is, to be close >> to being right. > > > That's pretty much what I was saying. A wrong choice made near the > utility extremes could negate the power of your ballot altogether, but > you aren't likely to make a wrong choice there. Near the middle of your > utility range is where you are most likely to make a wrong choice, but > the damage to the value of your ballot is going to be very minimal in > such a case. > >> Adam was more helpful, with a rule I could follow: Approve whichever >> candidate I prefer among the expected front runners, and approve all >> the candidates I like better than that one. > > > I thought the various simplified approval strategies had already gotten > a lot of exposure on this list in recent weeks, so I didn't want to be > too repetitive. > > -- Richard -- [EMAIL PROTECTED] http://www.clarityconnect.com/webpages3/davek Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026 Do to no one what you would not want done to you. If you want peace, work for justice. ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
