In fact, the OBO system is not only even more complex than the current ordinal system, but it does not solve the flip-flop problem, either. The OBO system may even introduce flip-flops that would not have occurred under the current system.
This article begins with some background and a summary of the ISU's actions concerning the OBO proposal. This is followed by an overview of how the OBO system works and why it is more computationally complex than the current system. In the third part, some specific examples of flip-flops derived from simulations of the results of the 1998 World Junior Championships, 1998 European Championships, and 1998 Olympic Games are presented. I conclude with some editorializing.
In the men's free skate at the 1997 European Championships, there was a dramatic reshuffling of placements owing to the fact that, in a very close competition, the marks given to the last skater caused one of the previous competitors to lose a majority for the place he had temporarily been holding. This "flip-flop" in the standings was surprising to many people who did not understand how the ordinal-based scoring system used in figure skating works, or who were not paying close attention to the scoring as the event unfolded. Complicating the situation, the press covering the event seemed to be at a complete loss to explain the scoring system or results to the public.
Following the event, Ottavio Cinquanta, president of the International Skating Union, stated that he thought the current scoring system was unsatisfactory and should be changed. Cinquanta has made repeated statements to the press that the scoring system must not permit "flip-flops" in the standings, where the relative placements of two competitors who have already skated are changed by the marks given to a competitor who skates later, such as what happened at 1997 Europeans. (Most recently, at the 1997-98 Champions Series Final in Munich, Cinquanta was quoted in press reports as stating unequivocally that "If one skater is in front of another, he should remain there.") Also getting into the act was IOC chair Juan Antonio Samaranch, who has made public statements to the effect that the system used to score figure skating at the Olympics must be understandable to the public.
In fact, the ISU's own regulations did not allow changes to the scoring system to be adopted in time for the 1998 Olympic Winter Games. In the meantime, while various other alternatives were presented, Cinquanta focused on the "OBO" proposal for a new scoring system presented to the ISU by Andreas Sigurdsson and sponsored by the DEU (the German federation).
The ISU technical committees were instructed to allow the DEU to test the OBO system at the Nebelhorn Trophy competition in August, 1997. The results of that test were inconclusive and subject to dispute as to what a "change of position" really was. A second test was later commissioned in the form of a simulation: the results of the 1998 World Junior championships were to be recalculated under OBO during meetings of the technical committees at the Champions Series Final in Munich in December, 1997. However, before the technical committees could submit their report, Cinquanta announced to the press that OBO had been approved!
Meanwhile, at the Munich meeting, Cinquanta claimed that the provision in the ISU Constitution permitting the Council to assign tasks to the technical committees and another provision to the effect that the Vice-President for Figure Skating "oversees" the work of the figure skating technical committees in essence gave the President the authority to "direct" the outcome of work by the committees. On that basis, the committees were instructed to approve OBO unless it had a "major flaw". They were further informed that problems identified in the simulation and in prior examination of OBO (including flip-flops, significantly different outcomes, problems with manual calculation, high costs of software for the new system, etc.) did not constitute "major flaws". Thus, any further technical evaluation of the OBO proposal by the ISU was effectively squelched and to a large extent the only "evaluation" done was strictly limited to what Cinquanta permitted the technical committees to do.
Even more incredibly, Cinquanta then issued a statement to the ISU membership (Circular Letter No. 536) claiming that the evaluation based on the World Junior Champions had "officially been made", and further implying that the technical committees had endorsed the OBO proposal as a result of the test. The truth of the matter is that the results of the second evaluation were simply discarded and that the proposal was "accepted" by the committees only as a result of political maneuvering, over any and all technical objections.
As a result of these actions, the OBO proposal is now on the agenda (as items 414, 415, 416, and 417) for consideration at the ISU Congress in June 1998. It must be approved by a 2/3 vote of ISU member organizations in order to take effect.
|OBO: What it is, how it works|
OBO stands for "one-by-one". The general idea behind this scoring system is to compare the skaters pairwise and rank them according to which has the most total "wins" in these pairwise comparisons. Some people may find the idea of ranking skaters according to a "who-beat-who" criteria appealing, but this is definitely not how the OBO system works. It is quite possible under OBO for skater X to place ahead of skater Y even if Y beat X in a head-to-head comparison of marks, for example.
The OBO system does not introduce any changes to the marking used by the judges. Under OBO it is also convenient to compute ordinals in the same way as for the current scoring system since this simplifies the later computations somewhat. However, the manner of using the ordinals from the different judges to calculate standings is completely different than for the current system. Although statements from Cinquanta and others that have been reported in the press suggest OBO is just a minor change to the method of computing running standings to prevent flip-flops, the two systems can produce dramatic differences in the final standings.
If there are N skaters participating in the event, the OBO system requires building an N-by-N table, with a row and column for each skater. The entries in the table are filled in by comparing each skater against all the others. In comparing skater X against skater Y, there are two pieces of information that have to be filled in each table entry: whether X skater has "won" a majority of judges when compared to Y, and the number of judges that voted for X over Y (this is called "judges in favor", or "JiF"). Then the total number of "wins" for each skater is added up, as is the total number of "judges in favor". The skaters are ranked by total wins with total JiF used as the tie-breaker.
Here's an example involving a small event with only 6 competitors (derived from the actual marks given to the top 6 finishers in the free skating in the men's event at 1997 Europeans). The first step is computing the ordinals in the usual way. Suppose this works out to give us:
A 1 1 1 1 1 2 1 1 1 B 3 2 5 2 3 3 5 6 6 C 5 5 4 4 2 4 2 2 3 D 4 3 3 6 4 6 4 3 2 E 2 4 2 3 6 5 3 4 5 F 6 6 6 5 5 1 6 5 4The OBO comparison table might look like this:
|| A | B | C | D | E | F || total wins || total JiF ----++-----+-----+-----+-----+-----+-----++--------------++------------- A || | 1/9 | 1/9 | 1/9 | 1/9 | 1/8 || 5 || 44 ----++-----+-----+-----+-----+-----+-----++--------------++------------- B || 0/0 | | 0/4 | 1/5 | 0/4 | 1/6 || 2 || 19 ----++-----+-----+-----+-----+-----+-----++--------------++------------- C || 0/0 | 1/5 | | 1/5 | 1/5 | 1/8 || 4 || 23 ----++-----+-----+-----+-----+-----+-----++--------------++------------- D || 0/0 | 0/4 | 0/4 | | 0/4 | 1/7 || 1 || 19 ----++-----+-----+-----+-----+-----+-----++--------------++------------- E || 0/0 | 1/5 | 0/4 | 1/5 | | 1/6 || 3 || 20 ----++-----+-----+-----+-----+-----+-----++--------------++------------- F || 0/1 | 0/3 | 0/1 | 0/2 | 0/3 | || 0 || 10 ----++-----+-----+-----+-----+-----+-----++--------------++-------------So in this case the results would be A, C, E, B, D, F. (Under the current scoring system, the results were A, B, C, D, E, F; so you can see that the OBO system does indeed produce results that are quite different.)
Aside from any questions regarding the effectiveness of the OBO scoring system, such as whether or not it is resistant to judging errors or prevents flip-flops in the standings during the course of an event, it is immediately obvious that it is much more complex from a computational point of view than the current system. The current system requires only a linear scan of the ordinals given to each competitor to compute the ranking criteria (the majority, total ordinals of majority, and so on). The OBO system, on the other hand, requires an order N-squared comparison followed by a linear scan.
The additional computational complexity may not appear to be a big issue in the age of ubiquitous computers, but in fact many skating fans who attend competitions can and do work out the results by hand using the scoring sheets provided in the program booklet. At competitions that do not have electronic displays of running standings, fans often work out the results by hand long before the official results are posted. Under the OBO system, doing this would at best be very impractical. Certainly, at an event like the World Championships when there are up to 30 competitors, a very large sheet of paper would be necessary to work out or display the 30-by-30 table of results, and it would be extremely tedious and error-prone to have to do at least an additional 3,915 comparisons by hand, along with repeated additions of 30 columns of numbers, to fill in the table.
A further problem regarding the complexity of the OBO system is one of the issues that initially led to the search for a new scoring system: the complaint that the scoring system was too complex for the TV-viewing public to understand or for the media to explain. Introducing a scoring system that is even more complex, and that in many instances produces results that are just as counter-intuitive, is certainly not going to solve this problem.
|So what about flip-flops?|
In fact, the OBO system does not prevent flip-flops in the event standings -- instances where the relative placements of two skaters change because of the placements given to a third skater by the judges.
To show how the OBO system might work in a real-life competition situation, simulations were performed (independently of the tests commissioned by the ISU) using the marks and skate orders from the 1998 World Junior and 1998 European championships, available on the web at http://www.wige.de/Skating/index.htm, and similar information from the 1998 Olympic Games, available at http://www.nagano.olympic.org/. (Recall that the OBO system doesn't change the interpretation of the judges' marks from the current rules, only the manner in which the results are computed from the marks.) These simulations showed that, under the OBO system, flip-flops would have occurred in seven of the fourteen competition segments at World Juniors; three of ten competition segments at Europeans; and four of ten competition segments at the Olympic Games. Specifically:
At the World Junior Championships:
It is interesting to observe that Nikodinov actually scored a head-to-head "win" over Fivian, who finished two places ahead of her in the simulation.
In this event as well, there were instances where the overall placements of the competitors concerned did not reflect the "wins" in head-to-head comparisons: e.g., Vlandis & Guzman actually "won" over Lefrancois & Osseland, and at one point in the competition were ahead of them by total "wins".
Wins JIF 6. HRAZSKA / PROCHAZKA 16 138 7. ROMANIUTA / BARANTSEV 15 132 8. SILVERSTEIN / PEKAREK 14 130Kristina Kobaladze & Oleg Voiko's marks created a very interesting situation: they scored "wins" over Gabriela Hrazska & Jiri Prochazka and Natalia Romaniuta & Danil Barantsev, but not over Jamie Silverstein & Justin Pekarek. This created two ties on "wins" and caused S&P to move ahead of R&B on "judges in favor":
Wins JIF 6. HRAZSKA / PROCHAZKA 16 142 7. KOBALADZE / VOIKO 16 141 <=== new 8. SILVERSTEIN / PEKAREK 15 135 <=== changed 9. ROMANIUTA / BARANTSEV 15 134 <=== changed
Closer examination of this flip-flop situation reveals that there were actually five couples involved in a near-tie situation that could not be resolved without reversing "wins": K&B and R&B both also scored "wins" over Kristina Kobaladze & Oleg Voiko, who "won" over Gabriela Hrazska & Jiri Prochazka, who in turn "won" over the three other couples involved. Again in this competition segment, it was observed that a single judge who gave marks that were out of line could have a significant effect in the overall standings due to the "judges in favor" tie-breaker. For example, S&P's higher "judges in favor" count could be attributed to the scattering of 5th, 6th, and 7th place votes they received although they had a majority only for 10th place. Meanwhile, R&B's one 11th-place vote among their majority for 8th place essentially meant that the one judge cost them three "judges in favor" points.
The fun started when Alexei Kozlov skated. Before this, the standings for the top 10 were:
Wins JIF 1. Derrick DELMORE 15 132 2. Sergei DAVYDOV 14 122 3. Vitaly DANILCHENKO 13 123 4. Taijin HIRAIKE 12 108 5. Yosuke TAKEUCHI 11 96 6. Emanuel SANDHU 10 87 7. Ben FERREIRA 9 72 8. Matthew DAVIES 8 68 9. Alan STREET 7 66 10. Vakhtang MURVANIDZE 6 54Kozlov was given a mixed bag of marks that gave him "wins" over Ferriera and Davies but not Street or Murvanidze. This meant that Davies, Street, and Kozlov now all had 8 "wins", and moreover, Davies and Street were in an absolute tie with the same total "judges in favor". Note that at this point Kozlov was behind two of the skaters he beat in head-to-head competition, and ahead of one who beat him!
Wins JIF 1. Derrick DELMORE 16 141 2. Sergei DAVYDOV 15 131 3. Vitaly DANILCHENKO 14 132 4. Taijin HIRAIKE 13 117 5. Yosuke TAKEUCHI 12 105 6. Emanuel SANDHU 11 95 7. Ben FERREIRA 9 76 8. Alan STREET 8 72 <=== changed 8. Matthew DAVIES 8 72 <=== changed 10. Alexei KOZLOV 8 65 <=== new 11. Vakhtang MURVANIDZE 7 59These relative standings remained unchanged after the next two skaters, Alexei Gruber and Michael Amentas, who finished farther down the list. Next up was Kyu-Hyun Lee, who received marks that gave him "wins" over Sandhu and all the skaters below him. However, the individual judges' placements of Lee compared to Davies and Street broke the tie on "judges in favor" between them: judge #5 voted for Street over Lee, while all the judges had Davies behind Lee. So now, the placements of Davies and Street flip-flopped:
Wins JIF 1. Derrick DELMORE 19 168 2. Sergei DAVYDOV 18 158 3. Vitaly DANILCHENKO 17 159 4. Taijin HIRAIKE 16 144 5. Yosuke TAKEUCHI 15 129 6. Kyu-Hyun LEE 14 124 <=== new 7. Emanuel SANDHU 13 116 8. Ben FERREIRA 11 93 9. Alan STREET 10 89 10. Matthew DAVIES 10 88 <=== changed 11. Alexei KOZLOV 10 81 12. Vakhtang MURVANIDZE 9 72The next skater was Juraj Sviatko. His marks placed him even farther up the standings than Lee, but this time Davies picked up one judge on him, thanks to his generous marks from judge #6. So, Davies and Street were back in an absolute tie!
Wins JIF 1. Derrick DELMORE 20 177 2. Sergei DAVYDOV 19 167 3. Vitaly DANILCHENKO 18 167 4. Taijin HIRAIKE 17 151 5. Juraj SVIATKO 16 137 <=== new 6. Yosuke TAKEUCHI 15 133 7. Kyu-Hyun LEE 14 126 8. Emanuel SANDHU 13 119 9. Ben FERREIRA 11 93 10. Alan STREET 10 89 10. Matthew DAVIES 10 89 <=== changed 12. Alexei KOZLOV 10 81 13. Vakhtang MURVANIDZE 9 72The next skater after this was Lukas Rakowski. Rakowski's marks were also high enough to place him well above the skaters involved in the tie, but once again Davies' high marks from judge #6 were enough to give him one more vote and break the tie with Street yet again, this time in his favor rather than Street's. Davies then retained this lead for the remainder of the competition.
Rakowski's placement is interesting in another way: judge #4 gave him the identical marks as Sviatko, and since the other 8 judges were split evenly, this also caused an absolute tie in determining the "win" in the head-to-head comparison between them. This in turn led to a tie in the number of "wins", which was broken by "judges in favor".
Wins JIF 1. Derrick DELMORE 21 186 2. Sergei DAVYDOV 20 176 3. Vitaly DANILCHENKO 19 176 4. Taijin HIRAIKE 18 159 5. Juraj SVIATKO 17 142 6. Lukas RAKOWSKI 17 139 <=== new 7. Yosuke TAKEUCHI 15 136 8. Kyu-Hyun LEE 14 128 9. Emanuel SANDHU 13 123 10. Ben FERREIRA 11 94 11. Matthew DAVIES 10 90 <=== changed 12. Alan STREET 10 89 <=== changed 13. Alexei KOZLOV 10 81 14. Vakhtang MURVANIDZE 9 72
In this instance, Sandhu was clearly hurt by a 16th-place ordinal from judge #5; no other judge had him lower than 12th. Again, this shows the fragility of the OBO-tie breaking mechanism with regards to inappropriate marks from a single judge.
After Katerina Blohonova skated, her marks put in next-to-last place over Jekaterina Golovatenko, like this:
Wins JIF 5. Katerina BLOHONOVA 1 11 <=== new 6. Jekaterina GOLOVATENKO 0 11These relative placements remained unchanged until Anina Fivian, the third of the competitors involved in the tie situation, skated. Her marks caused Golovatenko to move ahead of Blohonova, into a tie with Fivian.
Wins JIF 7. Anina FIVIAN 1 16 <=== new 7. Jekaterina GOLOVATENKO 1 16 <=== changed 9. Katerina BLOHONOVA 1 15 <=== changedThe next skater was Valeria Trifancova. Although her marks were generally much higher than the three skaters we're looking at, one of the judges had her behind Blohonova. This caused a three-way tie at the bottom of the standings:
Wins JIF 8. Anina FIVIAN 1 16 8. Katerina BLOHONOVA 1 16 <=== changed 8. Jekaterina GOLOVATENKO 1 16 <=== changedAfter Noemi Bedo skated, the judges gave her marks that put her in last place. However, she won one judge each over Fivian and Blohonova, which caused Golovatenko to break out of the tie:
Wins JIF 10. Jekaterina GOLOVATENKO 2 25 <=== changed 11. Anina FIVIAN 2 24 <=== changed 11. Katerina BLOHONOVA 2 24 <=== changedSimilarly, Salome Chigogidze won one more judge over Blohonova than Fivian, causing their tie to be broken, while Golovatenko remained in front:
Wins JIF 15. Jekaterina GOLOVATENKO 3 32 16. Anina FIVIAN 3 31 17. Katerina BLOHONOVA 3 30 <=== changedBut, when Kaja Hanevold skated, the tie returned:
Wins JIF 19. Jekaterina GOLOVATENKO 4 40 20. Anina FIVIAN 4 36 20. Katerina BLOHONOVA 4 36 <=== changedAnd finally, it was broken again after Marta Senra skated:
Wins JIF 23. Jekaterina GOLOVATENKO 5 48 24. Anina FIVIAN 5 44 25. Katerina BLOHONOVA 5 43 <=== changedIn summary, Blohonova was originally in front of Golovatenko and actually "won" the one-by-one comparison against her, but wound up finishing two places behind her and failed to finish in the top 24 as a result. Blohonova also moved in and out of a tie five times during the course of the event! In the real-life competition, it was Fivian who failed to make the cut rather than Blohonova.
Another very curious effect of the OBO scoring system is that it reversed the placements of the 2nd and 3rd place finishers in this competition segment from the actual results under the current ordinal system. The ordinals for the two skaters involved are:
Surya BONALY 5 4 2 2 5 2 1 1 4 Irina SLUTSKAYA 2 3 3 1 4 3 4 2 3Under the current scoring system, Bonaly had a majority of five votes for second place, while Slutskaya had only three votes for second place or better. However, under the OBO simulation, Slutskaya was placed ahead of Bonaly, primarily because Slutskaya "won" over Bonaly by a 5-4 split in a direct comparison of their marks.
Wins JIF 1. Irina SLUTSKAYA 21 182 2. Tanja SZEWCZENKO 20 181 3. Elena LIASHENKO 19 167 4. Julia SOLDATOVA 18 168 5. Krisztina CZAKO 16 136 <=== new 5. Julia LAUTOWA 16 136 <=== changed 7. Yulia VOROBIEVA 16 135However, when Surya Bonaly skated, Czako scored a "win" over her, while Lautowa did not, moving Czako definitely over Lautowa, who was moved into another tie with Vorobieva. Perhaps most surprisingly, in spite of Czako's "win" in the one-by-one comparison with Bonaly, she still wound up behind Bonaly in the final standings due to the OBO tie-breaking rules! In the actual competition using the current scoring rules, Bonaly finished behind Czako.
Wins JIF 1. Maria BUTYRSKAYA 23 207 2. Irina SLUTSKAYA 22 191 3. Tanja SZEWCZENKO 21 190 4. Elena LIASHENKO 20 176 5. Julia SOLDATOVA 19 175 6. Surya BONALY 17 142 <=== new 7. Krisztina CZAKO 17 141 8. Julia LAUTOWA 16 139 <=== changed 8. Yulia VOROBIEVA 16 139 <=== changed
Wins JIF 2. SHMERKIN, Michael 3 25 3. WEISS, Michael 2 25 <=== newVidrai, skating later, then scored a "win" over Shmerkin while Weiss "won" over Vidrai, giving all three skaters an equivalent number of "wins". At this point, Vidrai and Weiss were also tied with 63 "judges in favor" with Shmerkin ranked behind both of them with 60.
Wins JIF 6. VIDRAI, Szabolcs 7 63 <=== new 6. WEISS, Michael 7 63 <=== changed 8. SHMERKIN, Michael 7 60 <=== changedEventually, however, Weiss pulled ahead of Vidrai on "judges in favor", picking up one additional judge over each of Dmitri Dmitrenko, Igor Pashkevitch, and Michael Tyllesen. Moreover, Weiss scored a "win" over Pashkevitch while Vidrai did not, giving him a clear lead on "wins" alone. In the end, Weiss, who had originally been placed behind Shmerkin, wound up finishing two places above him.
Wins JIF 11. WEISS, Michael 17 153 12. VIDRAI, Szabolcs 16 150 13. SHMERKIN, Michael 16 144This case is particularly interesting because it shows a flip-flop on "wins", not just one caused by skaters moving into a tie on "wins" and the order being changed by the "judges in favor" tie-breaker which is much more sensitive to fluctuations caused by strange marks from one or two judges.
The second flip-flop in this competition segment involved Igor Pashkevitch and Yamato Tamura. Pashkevitch had originally been placed behind Tamura on "wins", although he had a greater number of "judges in favor". When Pashkevitch scored a "win" over Viacheslav Zagorodniuk and Tamura did not, they were thrown into a tie on "wins" that was broken in Pashkevitch's favor. Both Pashkevitch and Tamura, incidentally, received a huge spread of ordinals -- from 8th to 18th for Pashkevitch, and 8th to 17th for Tamura!
Both of these two flip-flops involved the same group of six skaters who had scored "wins" over one another in a cyclical fashion: Weiss, Vidrai, Shmerkin, Pashkevitch, Tamura, and Zagorodniuk. Any possible ranking of these six skaters would have reversed at least one "win".
The final flip-flop involved Margus Hernits, Cornel Gheorghe, and Roman Skorniakov. Gheorghe initially led Hernits on "wins" and in the head-to-head comparison, but Hernits scored a "win" over Skorniakov while Gheorghe did not, throwing all three skaters into a tie with 6 wins apiece. At this point, the tie was broken by "judges in favor" in the order: Skorniakov, Hernits, Gheorghe. Skorniakov, however, later lost a judge to Kyu-Hyun Lee (who was well below the others in the overall standings), dropping him into a tie with Hernits. To complicate things further, all three skaters were thrown into an absolute tie when both Skorniakov and Hernits lost a judge to Anthony Liu (again, a skater who was placed well below the three tied skaters). In short, Gheorghe moved from being ahead of Hernits to being behind him to being tied with him; while Skorniakov wound up in a tie with two skaters he had initially led.
A look at the ordinals shows that Langdon probably lost at least one place in the overall standings because of the single 15th-place ordinal he received from judge #2. In the OBO simulation, Langdon finished 11th in this competition segment, while in the actual competition under the current scoring rules, he was ranked 10th.
Here again it was obvious that a stray ordinal from a single judge had a disproportionate impact on the results -- in this case, it was the 5th-place ordinal given to Moniotte & Lavanchy from judge #2 which lifted them above the two other teams. (Most of their other marks were for 9th and 10th place.) In the actual competition under the current rules, M&L finished this competition segment in 10th place behind both of the other teams.
First of all, it is very obviously the case that the OBO system does not eliminate flip-flopping within the standings. It is possible that it may even introduce more flip-flops than the current scoring system, although more statistical analysis of the two systems would have to be performed to determine this.
In situations where there is no clear consensus among the judges about the placements of skaters, the simulation shows it is quite common for the eventual results of the OBO system to place a skater behind another competitor in spite of "winning" a head-to-head confrontation with that competitor. Some of the scenarios discussed above even included instances where a skater "won" against the competitors who finished two and three places above him. This is troubling even in instances where it does not actually cause a flip-flop in the standings, because it indicates situations where additional flip-flops could have occurred if a different skating order had been drawn. It also means that OBO as a system is not internally consistent as to the significance of one-on-one "wins".
Another disturbing problem with the OBO system lies with using "judges in favor" as the sole tie-breaking mechanism. (Mathematically, "judges in favor" is actually equivalent to the "total ordinals" criteria that is used as the final tie-breaker in the current scoring system, after the "greater majority" and "total ordinals of majority" rules.) The problem is that a single judge who gives an ordinal that is greatly out-of-line with rest of the panel can wind up having a disproportionate effect should skaters wind up tied on the number of "wins". And ties on "wins" seem to be quite common in cases where the judging panel is split between a group of three or more skaters.
From a theoretical point of view, OBO is therefore just as flawed in this way as the current system, or indeed as any other ordinal-based scoring system that could possibly be devised. The decision about which system is "better" has to be based on other criteria: perhaps computational simplicity and resistance to judging errors, which are both areas of comparative weakness for OBO, as we have seen.
It is clear that the OBO proposal does not represent an improvement over the current scoring system, considered purely on technical grounds. It meets neither of the supposed criteria for a new scoring system -- being easy to understand, and eliminating flip-flops. It is also inferior to the current system in that judging errors are more likely to affect the overall standings.
In addition, there are three disadvantages inherent in any change to the scoring system:
It is also very disturbing that Cinquanta has attempted to suppress any methodical investigation of OBO by the technical committees and that the only official information about the proposed rules change that has been provided to the ISU members up until now has been in the form of vague generalities. It's my hope that the analysis and commentary contained in this article will make it possible for the ISU members to make a more informed decision on this issue at the upcoming ISU Congress.
This article incorporates revised and updated text from two of my earlier articles which were originally published on the Internet. These articles, along with the computer program, input data, and complete results for the simulations, are available on the web at http://www.frogsonice.com/skateweb/obo/.
I am indebted to Michael Stob (email@example.com) for supplying the connection to Arrow's Theorem.
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