Re: Finding the probable best candidate
Forest: Most preferred according to the information in the ordinal preference ballots. SB --- In [EMAIL PROTECTED], Forest Simmons [EMAIL PROTECTED] wrote: On Mon, 18 Feb 2002, Steve Barney wrote: Yes, of course we have limited information by which to determine the group's best candidate, but what if we focus on nothing but the information which is contained in an ordinal preference ballot? [...] In that case, the best candidate may be defined as the one who is most preferred according to the information contained in fully ranked ordinal preference ballots. Most preferred according to which measure of preference? The preferences are given as vector valued functions. For maximization, those vectors have to be turned into scalars. There are infinitely many different ways of doing this, each yielding a different measure of preference. [...] Forest __ Do You Yahoo!? Yahoo! Sports - Coverage of the 2002 Olympic Games http://sports.yahoo.com
Re: [EM] Re: Finding the probable best candidate?
On Tue, 19 Feb 2002, Adam Tarr wrote: Basically, whoever starts in first place in the cyclic tie wins, since whoever makes it up to challenge them must be the candidate that loses to them. So insofar as Borda seeded bubble sort uses Borda count to decide things, it has the same strategic problems as Borda. Two things: (1) Bubble sort starts from the top and works down: If the Borda order is A B C , then Bubble compares A and B first, and then advances C as far up as possible, one comparison at a time. So in circular ties Bubble can alter the Borda order if the Borda order is opposite to the cyclic order. (2) Borda's strategic problems are no worse than those of Ranked Pairs when it comes to three way circular ties. In other words, Black is as good as Ranked Pairs in three way races. Forest
Re: [EM] Proof Borda Count best in the case of fully ranked preference ballots
On Tue, 19 Feb 2002, Steve Barney wrote: Forest: What do you think of circular triplets, such as: ABC BCA CAB, and reversals, such as: ABC CBA. If that is all the information that we have to go on (when ordinal preference ballots are used, it is ), shouldn't either of these profiles cancel out completely and yield a tie? The Borda Count is the only method which always does that, according to Saari's analysis. From that simple fact, argues Saari, come voting paradoxes such as non-monotonicity, etc. The two examples that you give yield ties in every serious method of which I am aware. Forest
Re: Finding the probable best candidate
On Wed, 20 Feb 2002, Steve Barney wrote: Most preferred according to the information in the ordinal preference ballots. I don't think you are saying that we should choose the candidate that contributes the most (or least) information to the ballot. Example: 51 ABCD 49 DBAC B's rank is constant, and therefore contributes the least information. D's rank has the most variation, and therefore contributes the most information. Yet A is the winner according to Borda. Just what aspect of the information are we supposed to maximize to find the best candidate according to the information? Forest
Re: [EM] Re: Finding the probable best candidate?
On Wed, 20 Feb 2002, Adam Tarr wrote: Forest wrote: (1) Bubble sort starts from the top and works down: If the Borda order is A B C , then Bubble compares A and B first, and then advances C as far up as possible, one comparison at a time. So in circular ties Bubble can alter the Borda order if the Borda order is opposite to the cyclic order. My mistake. So my examples were wrong. In a three way cyclic tie, 3rd in Borda can never win; whoever wins the first vs. second matchup wins. For more complicated cyclic ties, the lowest candidate who beats every candidate above them wins. This seems reasonable, I suppose. (2) Borda's strategic problems are no worse than those of Ranked Pairs when it comes to three way circular ties. In other words, Black is as good as Ranked Pairs in three way races. I believe this is not the case. Ranked Pairs is (at least in some cases) more clone independent. Adding a candidate to the race that is listed just after one of the leaders on every ballot will boost that leading candidate's Borda count, while not changing anything in the pairwise matchups. If this boost brings the candidate from third to first in a three-way cyclic tie, they will win the election where they would have lost it. But adding a candidate changes the race from three way to four way. Note that I didn't claim that Black was as good as Ranked Pairs in four way races. In three way races Black, Ranked Pairs, and SSD all give the same answer if there are no truncations, so none has any possible advantage over the others in three way races without truncations. It seems to me that SSD's advantages are mostly due to truncation serving as an Approval cutoff detector, although the winning vote aspect, and the chain is no stronger than the weakest link idea probably contribute. I'm not an expert on the fine points of SSD and Ranked Pairs. I certainly don't consider Borda Seeded Bubble Sort to be in the same league as the big boys. As I said before, I don't believe in pure preference ballot methods. Like Demorep I think we have to look at both the pairwise preferences and the Approval scores to get good results in the gamut of cases that are likely to happen. And (as I said before) the only reason I proposed Bubble Sorted Borda was to find a simple method that would beat Black along the same lines as Black. After I forgot about it Rob LeGrand reminded me of the unfinished business. I thought it would be a good way of introducing the idea of Bubble sorting, which can be applied to other seedings (Bubble Sorted Approval, Bubble Sorted CR, etc.) and make use of pairwise matrices from other style ballots such as Five Slot Grade Ballots and Dyadic Ballots. To set the record straight I owe an apology to Tom Ruen. As I remember, his proposal of Inverse Nanson was the impetus for my suggestion of Borda Seeded Single Elimination, later modified to Bubble Sorted Borda. After experience with all of these four (and other closely related) methods I believe that Inverse Nanson (an iterated form of Borda Runoff) is the best of these four methods based on Borda. Forest
Re: Finding the probable best candidate?
Forest wrote: In three way races Black, Ranked Pairs, and SSD all give the same answer if there are no truncations, so none has any possible advantage over the others in three way races without truncations. What about the election 9:ABC 8:BCA 6:CAB B wins under Black but A wins under Schulze and Ranked Pairs (plus Baldwin, Dodgson, Nanson and Minmax). And (as I said before) the only reason I proposed Bubble Sorted Borda was to find a simple method that would beat Black along the same lines as Black. Unfortunately, at least according to my simulations so far, BSBS is much worse at SU given sincere votes than BSSE or Black. But it's not bad; it's about on par with Schulze and is better than Ranked Pairs. By the way, I think the sort BSBS uses is actually called an insertion sort, not a bubble sort. After experience with all of these four (and other closely related) methods I believe that Inverse Nanson (an iterated form of Borda Runoff) is the best of these four methods based on Borda. What is Inverse Nanson again? How is it different from regular Nanson (or Baldwin)? Is it monotonic? = Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/honky98/ __ Do You Yahoo!? Yahoo! Sports - Coverage of the 2002 Olympic Games http://sports.yahoo.com
Re: Finding the probable best candidate?
Rob: First, I really never thought of Buchanan as a clone of Bush, just as I didn't think of Gore as a clone of Bush (Nader may have, but I didn't). In fact, in that election it always seemed to me that the fairly strong vote for Nader in Florida and other states, in spite of the obvious spoiler problem for Gore, was an indication that there where more voters on Gore's side of the political spectrum than Bush's, where right wingers like Buchanan did poorly in comparison to Nader. It seemed to me that the presence of a strong third party candidate on the left is evidence of more overall voter support for the left than the right. I wonder sometimes whether the BC's sensitivity to clones (failure to satisfy the IIA criterion) might not be such a bad thing, as long as there is actually no such thing as a human clone. Perhaps this is just too a radical idea for us at first blush, and perhaps we need to open our minds up to new political world with many choices and colors to choose from (human clones do not actually exist - yet). Perhaps it would be good to be faced with the opposite problem - too many candidates spanning the political spectrum (again, at least for now human clones remain a fantasy), rather than too few. Given that the plurality procedure's spoilage is bad, perhaps the opposite of that, the BC's sensitivity to clones or non-IIA, is good. I don't know, but it is not beyond the realm of possibility, is it? Maybe, just maybe, part of the problem is that we are sort of prejudiced in favor of majoritarian systems, and too uncritically accepting of the majority rules ideal. Perhaps we should start experimenting with it on a small scale, such as school elections, and see what happens over time. Several schools are already doing just that, including one governing body at my own campus - thanks to a visit by Donald Saari (guess who organized that visit): Alternative Voting Systems in Student Governments http://www.fairvote.org/irv/studentgov.htm The argument against Fran, in your other example: 63:EricFranGary 37:FranGaryEric can be turned on its head. Let's say: 1,000,001:EricFranGary 1,000,000:FranGaryEric or 1,000,000:EricFranGary 1,000,000:FranGaryEric In that case Fran is the 1st or 2nd preference of all the voters. Whereas Eric is despised by about half, and nobody despises Fran. Do you see what I mean? -Steve Barney University of Wisconsin Oshkosh --- In [EMAIL PROTECTED], Rob LeGrand [EMAIL PROTECTED] wrote: Steve, [...] So, what's the point? Well, looking at the ranked votes, do you think Bush is the best candidate? I don't. Bush's Borda score is propped up by his near-clone Buchanan. Borda is the only ranked-ballot method I know (besides Black) that gives the win to Bush. As a simpler example, consider an election with three candidates. Eric is freedom-loving and Fran and Gary are socialist. 63% of the voters are freedom-loving, 37% are socialist and all of the voters prefer Fran to Gary because of a scandal involving Gary, so the ranked votes are 63:EricFranGary 37:FranGaryEric Borda gives the win to Fran even though Eric received a majority of first-place votes and would have won in a landslide if Gary hadn't run. Borda encourages a party or ideology to run lots of candidates. Some methods, like Simpson (i.e. Minmax, Condorcet(EM)), fail clone independence only in contrived cases, but Borda fails badly. [...] = Democracy?: http://www1.umn.edu/irp/images/postcardAd2.jpg AR-NewsWI, a news service for Wisconsin animal advocates: http://groups.yahoo.com/group/AR-NewsWI/ __ Do You Yahoo!? Yahoo! Sports - Coverage of the 2002 Olympic Games http://sports.yahoo.com
Re: Finding the probable best candidate?
On Wed, 20 Feb 2002, Rob LeGrand wrote: Forest wrote: In three way races Black, Ranked Pairs, and SSD all give the same answer if there are no truncations, so none has any possible advantage over the others in three way races without truncations. Oops! What about the election 9:ABC 8:BCA 6:CAB B wins under Black but A wins under Schulze and Ranked Pairs (plus Baldwin, Dodgson, Nanson and Minmax). A wins under Borda Seeded Bubble Sort as well. And (as I said before) the only reason I proposed Bubble Sorted Borda was to find a simple method that would beat Black along the same lines as Black. Unfortunately, at least according to my simulations so far, BSBS is much worse at SU given sincere votes than BSSE or Black. I knew that, but that's part of the inevitable tradeoff. The higher the SU in this class of methods, the less likely that the votes will be sincere. My guess is ... SU:Borda Black BSSE BSBS Inverse Nanson Schulze Likelihood of sincere ballots : Borda Black BSSE BSBS Inverse Nanson Schulze Black has SU to spare, but it is still too manipulable in my opinion. But it's not bad; it's about on par with Schulze and is better than Ranked Pairs. By the way, I think the sort BSBS uses is actually called an insertion sort, not a bubble sort. Usually in insertion sort the new guy is tested against the middle of the previously sorted guys. Bubble sort starts the new guy at the bottomn an lets him work up one place at a time. Insertion sort is efficient on the order of n*log(n) comparisons, while bubble sort requires about n*n/2 comparisons. Sink sort is bubble sort in reverse. It was surprising to me at first that sink sort and bubble sort don't always give the same order. You wouldn't expect insertion sort to give the same order because it skips over some of the comparisons, assuming the transitive consistency that is lacking in Condorcet ties. After experience with all of these four (and other closely related) methods I believe that Inverse Nanson (an iterated form of Borda Runoff) is the best of these four methods based on Borda. What is Inverse Nanson again? How is it different from regular Nanson (or Baldwin)? Is it monotonic? Sets aside the Borda winner, then sets aside the Borda winner of the remaining, etc. down to until one candidate is left. That candidate is the first to be eliminated. This first eliminated candidate will always be in the reverse smith set. The process is repeated among the uneliminated candidates, until there is only one uneliminated candidate, the Inverse Nanson winner, which will always be a member of the smith set. I think it is monotone, but I haven't proven it. Forest
Re: Finding the probable best candidate?
Steve, The term clones refers to candidates who are together on every ballot in an election. In other words, on no ballot does any other candidate separate them. (Markus has a good formal definition.) The term doesn't imply that the candidates are actually alike in any way, much less that they're clones in the genetic sense. :-) Being independent of clones is different and much easier than being independent of irrelevant alternatives. In fact, no Condorcet method is independent of irrelevant alternatives, although many are independent of clones, which I see as an important advantage over Borda. Maybe, just maybe, part of the problem is that we are sort of prejudiced in favor of majoritarian systems, and too uncritically accepting of the majority rules ideal. Just as a quick point, every reasonable ranked-ballot method I know of is equivalent to plurality when there are only two candidates. So all of them, from Borda to Condorcet, can be thought of as generalizations of plurality in that sense. As for your sample elections . . . 1,000,001:EricFranGary 1,000,000:FranGaryEric Eric, the freedom-loving candidate, wins a squeaker using Condorcet, and no voter would have reason to regret his vote. If Borda were used, though, Fran would win by a large margin, and the freedom-loving voters would have *plenty* of reason to regret voting Fran second. If they'd all voted Fran last, their favorite would have won. Doesn't it bother you that Borda encourages insincere voting to such an extreme? 1,000,000:EricFranGary 1,000,000:FranGaryEric This one should be a tie between Eric and Fran. Do you really think Fran should win decisively just because the socialists ran two candidates? Would you honestly like to see parties or ideologies benefit by running lots of candidates? As much as I hate the vote-splitting that occurs using plurality or IRV, at least it limits the confusion and complexity. Surely the proliferation of candidates that would occur using Borda would be much more nightmarish. But that's just my opinion. If it doesn't convince you, then stick with Borda. Believing that Borda is the best method is perfectly logical if certain criteria are considered more important than others, but aren't Saari's criteria far removed from real-world concerns? = Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/honky98/ __ Do You Yahoo!? Yahoo! Sports - Coverage of the 2002 Olympic Games http://sports.yahoo.com
Re: Finding the probable best candidate?
Forest wrote: Unfortunately, at least according to my simulations so far, BSBS is much worse at SU given sincere votes than BSSE or Black. I knew that, but that's part of the inevitable tradeoff. The higher the SU in this class of methods, the less likely that the votes will be sincere. My guess is ... SU:Borda Black BSSE BSBS Inverse Nanson Schulze Likelihood of sincere ballots : Borda Black BSSE BSBS Inverse Nanson Schulze Very interesting! Has anyone come up with an objective measure of manipulability? Nanson itself has an average SU much worse than Schulze or even Ranked Pairs, and Baldwin (Borda-elimination) is even worse. I wonder whether Inverse Nanson would really beat Schulze on SU. Worth a try, though . . . Usually in insertion sort the new guy is tested against the middle of the previously sorted guys. Bubble sort starts the new guy at the bottom and lets him work up one place at a time. Insertion sort is efficient on the order of n*log(n) comparisons, while bubble sort requires about n*n/2 comparisons. Sink sort is bubble sort in reverse. I see. Your sink sort is what I've heard called bubble sort, and your bubble sort I've heard called insertion sort. I'd never seen an O(n log n) insertion sort before, but the scheme you describe certainly makes sense. I'd guess that the number of actual swaps would still be O(n^2), though. = Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/honky98/ __ Do You Yahoo!? Yahoo! Sports - Coverage of the 2002 Olympic Games http://sports.yahoo.com
Re: [EM] Finding the probable best candidate?
I wrote and Markus responded, Shwartz Sequential Dropping is better. The only differences as far as I can tell are that 1) You only deal with the Smith Set 2) You consider number of voters in favor of the defeat, not the margin of the defeat. I don't understand this paragraph. Do you want to say that the difference between RP and SSD is that the latter one meets the Smith criterion When I say, you only deal with the Smith Set, I merely mean that SSD throws out all candidates outside the Smith set before it starts dropping defeats. I am not directly attempting to imply anything about the Smith criterion. It seems obvious, however, that this will force a member of the Smith set to win. I'm not sure if this is true of Ranked Pairs. and measures the strength of a pairwise defeat by the number of voters in favor? Yes, that's what I meant. Could you post those examples where RP and not SSD produces those seemingly undesirable results? I can't find those old messages in my archives, but here's a very simple example: 49: Bush 24: Gore 27: Nader,Gore Bush beats Nader 49-27 Nader beats Gore 27-24 Gore beats Bush 51-49 With ranked pairs, the Gore-Bush defeat is overturned, and Bush wins, despite a true majority preferring Gore to Bush. In SSD the Nader-Gore defeat gets overturned, and Gore wins, which seems more intuitive to me. -Adam
[EM] Re: Finding the probable best candidate?
Mr. LeGrand wrote in part- The term clones refers to candidates who are together on every ballot in an election. In other words, on no ballot does any other candidate separate them. (Markus has a good formal definition.) The term doesn't imply that the candidates are actually alike in any way, much less that they're clones in the genetic sense. :-) - D- Any dictionary of election method words and phrases ??? Cloneness is like unanimity on *disputable* issues -- very scarce -- especially in *large* elections. A range of possible results -- 100 A B 0B A 99 A B 1 B A Etc. 51 A B 49 B A Etc 51 B A 49 A B Etc. 99 B A 1 A B 100 B A 0 A B A and B are not exactly clones just by being next to each other even in the 100 to 0 cases.
[EM] [instantrunoff] Vote for the Oscars with IRV online!
Here's a new site where you can vote for the Oscars online. http://www.tedsowinski.com/cgi-bin/irv_vote.cgi?c=oscarsb=aa74 Try it out so we can work out any bugs. Thanks to Ted Sowinski for creating this poll! Dan Yahoo! Groups Sponsor -~-- Get your FREE credit report with a FREE CreditCheck Monitoring Service trial http://us.click.yahoo.com/ACHqaB/bQ8CAA/ySSFAA/YgSolB/TM -~- Kill the 'wasted vote' syndrome by ranking candidates (1, 2, 3) and requiring a majority of votes to win. Help end plurality elections. To subscribe or unsubscribe, send a small note to [EMAIL PROTECTED] For more information: www.fairvote.org, www.midwestdemocracy.org, www.instantrunoff.com MAKE YOUR VOTE COUNT! (Take five minutes every day for some IRV activism -- we'll only get better elections with your persistent, patient work. Word-of-mouth is your most powerful political weapon: use it!) Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
[EM] Winning-votes intuitive?
Adam wrote: 49: Bush 24: Gore 27: Nader,Gore Bush beats Nader 49-27 Nader beats Gore 27-24 Gore beats Bush 51-49 With ranked pairs, the Gore-Bush defeat is overturned, and Bush wins, despite a true majority preferring Gore to Bush. In SSD the Nader-Gore defeat gets overturned, and Gore wins, which seems more intuitive to me. I think the reason the winning-votes method seems more intuitive in this case is that, looking at the votes, there seem to be 49 Bush voters and 51 Gore/Nader voters, so a Bush result seems wrong. But that's misleading. The 24 Gore voters don't prefer Nader to Bush. If they had voted GoreNaderBush, then I'd agree that Bush should lose. But, if you ask me, the above election is more accurately expressed as 49:BushGore=Nader 24:GoreBush=Nader 27:NaderGoreBush which should be equivalent to 49:BushGoreNader 49:BushNaderGore 24:GoreBushNader 24:GoreNaderBush 54:NaderGoreBush Now Bush wins using Schulze and Ranked Pairs, not to mention Borda, Dodgson, Nanson and Minmax. I'm not a winning-votes fan, and this has been a hotly debated topic on the list in the past, so there are several who won't find my reasoning convincing. But if I were one of the Nader voters (*shudder*) and a winning-votes method were being used, I'd vote Nader=GoreBush. Winning-votes methods may discourage truncation, which is nothing more then tied rankings at the bottom, but they strongly encourage tied rankings at the top. In fact, I'd vote ties in the top half or so of my ballot, even if I had *zero* information about the other voters' preferences! Margins methods don't encourage tied rankings like that on average, although of course there will be situations that reward insincere voting in any method. I don't think of using margins at all, though; to me a tie in a ballot should simply result in half a pairwise vote each way. That's the way I do it in my online ranked-ballot voting calculator at http://www.onr.com/user/honky98/calc.html . Has anyone tried it out? It's not completely finished yet, but I'd love some feedback (preferably private, of course). = Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/honky98/ __ Do You Yahoo!? Yahoo! Sports - Coverage of the 2002 Olympic Games http://sports.yahoo.com
