Well it's been nearly 6 months since my last post here and I thought I should get it back going again. I was going to post something about teaching swing dance in Nepal, a recipe for vegetable curry or something similarly relevant but then the ILHC scores came out.
Now for those of you who have followed this blog you'll note I'm slightly obsessed by both lindy hop and elections. ILHC presents a perfect opportunity to combine these two. All the scores of all the judges are published in addition to the complete rankings. It's rare that in an election (which is what a competition with multiple judges is, they're 'electing' the most skilled dancer/s) you're presented with all the ballot papers.
So I thought I'd rerun the comp results using a variety of different voting systems for a bit of fun and to point out some of the quirks with different electoral systems.
First up let me just say that this is just a hypothetical. I'm not suggesting that ILHC should change the way they calculate the positions. A lot of people have spent way more time and effort than me evaluating scoring systems and came up with one that fits a lot of criteria and works for ILHC. For more on the Relative Placement Method used by ILHC, check here, here and here.
I've deliberately steered clear of systems like plurality (first past the post) and instant runoff voting (such as STV), which rely on first preferences and aren't designed for circumstances where the ratio of voters to candidates is low. The two systems I've used are both designed for circumstances where all candidates receive a ranking from all voters.
The first is the Borda method. The raw ILHC scores are just that, scores. One could add them up to determine placings but this has problems, the judges may not be consistent in the spread of candidates scores (e.g. one might score all the way from 0 to 100, another might only go from 40-80). This is why the ILHC scores are converted to rankings before being combined. The Borda method converts those rankings back into scores and adds them together. The problem with Borda methods is that they are prone to being influenced by outlier scores and producing ties when you have a small voter pool.
The second is the Condorcet method. Condorcet methods are appealing for a dance contest because they simulate how some lindy comps (at least the finals) are run. These methods envisage a round robin series of head to head contests - whoever wins the most contests, wins the competition. The problem with Condorcet methods is that they tend to produce a lot of draws, particularly with a small voter pool. I've used the Small method to try and eliminate some of these draws, but the only way to fully resolve them is to have some sort of casting vote act as a tiebreaker. Note that the Small method returns the same results as the basic Condorcet method except where there are ties.
The full 'results' are at the end of the post but here's my summary: In 6 of the events (Balboa J&J, Balboa Strictly, Open Advanced and Champions Strictly Lindy and Pro-Am) the alternative systems make no difference (I've included cases where ties are involved, provided that order is preserved). In another 4 (All Star J&J, Lindy Hop Classic, Showcase and Teams) the only differences were in placings below 3rd.
For four of the events the systems disagreed over the third place getter, in some cases significantly:
In the Pro Lindy Classic, Condorcet gives the same result for 1,2 and 3 as Relative Placement. Only Borda disagrees, switching first (Todd and Ramona) and second (Sarah and Dax) In this case what we're really seeing is one of the failures of the Borda method, it is prone to influence in small voter pools of one or two outlier results.
For the Invitational Jack and Jill, both the Borda and Condorcet methods would place Sarah Breck and Pontus Persson first (who placed second), with Borda placing Peter Strom and Jo Hoffberg (who placed first) second and Condorcet Ramona Staffeld and Skye Humphries (who placed fourth). There's also a lot of variation throughout the remaining placings.
What's going on here? A glance at the scores for the Invitational J&J reveals substantial variation in the scores between individual judges. Nine out of the twelve contestants received a place (1,2 or 3) from at least one of the judges. This lack of consensus is exactly the sort of situation where differences in electoral systems become most pronounced. Perhaps in what some consider to be the pinnacle competition format in Lindy Hop (Jack and Jill simulating social dance) the skill level of the top international competitors is just so high that its becoming increasingly difficult to differentiate between them.
Fortunately dance contests rarely determine the fate of countries, but in the real world quirks in different electoral systems can have a big impact, such as the 2004 US Presidential Election or the previous Canadian Federal Election.
Here are the scores:
Now for those of you who have followed this blog you'll note I'm slightly obsessed by both lindy hop and elections. ILHC presents a perfect opportunity to combine these two. All the scores of all the judges are published in addition to the complete rankings. It's rare that in an election (which is what a competition with multiple judges is, they're 'electing' the most skilled dancer/s) you're presented with all the ballot papers.
So I thought I'd rerun the comp results using a variety of different voting systems for a bit of fun and to point out some of the quirks with different electoral systems.
First up let me just say that this is just a hypothetical. I'm not suggesting that ILHC should change the way they calculate the positions. A lot of people have spent way more time and effort than me evaluating scoring systems and came up with one that fits a lot of criteria and works for ILHC. For more on the Relative Placement Method used by ILHC, check here, here and here.
I've deliberately steered clear of systems like plurality (first past the post) and instant runoff voting (such as STV), which rely on first preferences and aren't designed for circumstances where the ratio of voters to candidates is low. The two systems I've used are both designed for circumstances where all candidates receive a ranking from all voters.
The first is the Borda method. The raw ILHC scores are just that, scores. One could add them up to determine placings but this has problems, the judges may not be consistent in the spread of candidates scores (e.g. one might score all the way from 0 to 100, another might only go from 40-80). This is why the ILHC scores are converted to rankings before being combined. The Borda method converts those rankings back into scores and adds them together. The problem with Borda methods is that they are prone to being influenced by outlier scores and producing ties when you have a small voter pool.
The second is the Condorcet method. Condorcet methods are appealing for a dance contest because they simulate how some lindy comps (at least the finals) are run. These methods envisage a round robin series of head to head contests - whoever wins the most contests, wins the competition. The problem with Condorcet methods is that they tend to produce a lot of draws, particularly with a small voter pool. I've used the Small method to try and eliminate some of these draws, but the only way to fully resolve them is to have some sort of casting vote act as a tiebreaker. Note that the Small method returns the same results as the basic Condorcet method except where there are ties.
The full 'results' are at the end of the post but here's my summary: In 6 of the events (Balboa J&J, Balboa Strictly, Open Advanced and Champions Strictly Lindy and Pro-Am) the alternative systems make no difference (I've included cases where ties are involved, provided that order is preserved). In another 4 (All Star J&J, Lindy Hop Classic, Showcase and Teams) the only differences were in placings below 3rd.
For four of the events the systems disagreed over the third place getter, in some cases significantly:
- Open Jack and Jill - Both Borda and Condorcet placed the actual 3rd place into 5th, replacing them with 4th or 5th.
- Advanced Jack and Jill - As with the Open Jack and Jill 3rd was switched with 4th or 5th.
- Invitational Strictly - Condorcet agreed with all the rankings, Borda switched 3rd and 4th.
- Solo Charleston - Condorcet agreed with all the rankings, Borda switched 3rd and 4th.
In the Pro Lindy Classic, Condorcet gives the same result for 1,2 and 3 as Relative Placement. Only Borda disagrees, switching first (Todd and Ramona) and second (Sarah and Dax) In this case what we're really seeing is one of the failures of the Borda method, it is prone to influence in small voter pools of one or two outlier results.
For the Invitational Jack and Jill, both the Borda and Condorcet methods would place Sarah Breck and Pontus Persson first (who placed second), with Borda placing Peter Strom and Jo Hoffberg (who placed first) second and Condorcet Ramona Staffeld and Skye Humphries (who placed fourth). There's also a lot of variation throughout the remaining placings.
What's going on here? A glance at the scores for the Invitational J&J reveals substantial variation in the scores between individual judges. Nine out of the twelve contestants received a place (1,2 or 3) from at least one of the judges. This lack of consensus is exactly the sort of situation where differences in electoral systems become most pronounced. Perhaps in what some consider to be the pinnacle competition format in Lindy Hop (Jack and Jill simulating social dance) the skill level of the top international competitors is just so high that its becoming increasingly difficult to differentiate between them.
Fortunately dance contests rarely determine the fate of countries, but in the real world quirks in different electoral systems can have a big impact, such as the 2004 US Presidential Election or the previous Canadian Federal Election.
Here are the scores:
Open Jack and Jill
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Pontus Spelmans & Melanie Ohl | 1 | 1 | 1 | 1 |
| Alexandre Abdoulaev & Lena Magnusson | 2 | 2 | 2 | 2 |
| Matt Richey & Sasha Anderson | 3 | 5 | 5 | 6 |
| Andrew Jose & Lily Susskind | 4 | 3 | 3 | 4 |
| Omar Myers & Beth Hartzel | 5 | 4 | 3 | 3 |
| Charles Wieprecht & Voon Chew | 6 | 7 | 7 | 7 |
| Phil Bourassa & Coralie Bazinet | 7 | 6 | 7 | 8 |
| Paulo Thierry & Mallory Grigg | 8 | 8 | 6 | 5 |
| Yossef Mendelssohn & Mirjam Johansson | 9 | 9 | 9 | 9 |
Advanced Jack and Jill
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Jean Baptiste Mino & Mette Herlitz | 1 | 1 | 1 | 1 |
| Michael Seguin & Nelle Cherry | 2 | 2 | 2 | 2 |
| Andrew Munoz & Sandra Klack | 3 | 4 | 5 | 6 |
| Dominique Pomeroy & Tatiana Udry | 4 | 3 | 3 | 3 |
| Peter Kertzner & Nicole Zuckerman | 5 | 5 | 3 | 4 |
| David Lee & Genevieve St-Laurent | 6 | 6 | 5 | 5 |
| Daniel Newsome & Anais Sekine | 7 | 7 | 8 | 8 |
| Kevin Clark & Shauna Marble | 8 | 8 | 7 | 7 |
All Star Jack and Jill
| Name | Relative Placing | Borda Count | Condorcet | Small |
| William Mauvais & Gabriella Cook | 1 | 1 | 1 | 1 |
| Patrick Szmidt & Maeva Truntzer | 2 | 2 | 2 | 2 |
| Andreas Olsson & Kate Hedin | 3 | 3 | 3 | 3 |
| Stephen Sayer & Teni Lopez-Cardenasv | 4 | 4 | 4 | 4 |
| Soochan Lee & Marie Ndiaye | 5 | 4 | 5 | 6 |
| Nalla Kim & Karen Turman | 6 | 6 | 5 | 5 |
| Michael Darigol & Natalia Rueda | 7 | 6 | 7 | 7 |
| Daryl Begin & Fancy Dougherty | 8 | 8 | 7 | 8 |
| Mindaugas Bikauskas & Brittany Johnson | 9 | 9 | 9 | 9 |
Invitational Jack and Jill
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Peter Strom & Jo Hoffberg | 1 | 2 | 3 | 3 |
| Pontus Persson & Sarah Breck | 2 | 1 | 1 | 1 |
| Dax Hock & Alice Mei | 3 | 4 | 4 | 5 |
| Skye Humphries & Ramona Staffeld | 4 | 3 | 2 | 2 |
| Thomas Blacharz & Kelly Arsenault | 5 | 5 | 4 | 4 |
| Todd Yannacone & Isabella Gregorio | 6 | 7 | 6 | 7 |
| Nick Williams & Alice Mei | 7 | 6 | 6 | 6 |
| Jeremy Otth & Annie Trudeau | 8 | 10 | 8 | 8 |
| Kevin St. Laurent & Laura Glaess | 9 | 8 | 10 | 10 |
| Mike Roberts & Mikaela Hellsten | 10 | 12 | 12 | 12 |
| Mikey Pedroza & Mia Goldsmith | 11 | 9 | 9 | 9 |
| Andy Reid & Naomi Uyama | 12 | 11 | 11 | 11 |
Balboa Jack and Jill
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Adam Speen & Mia Goldsmith | 1 | 1 | 1 | 1 |
| Andreas Olsson & Mette Herlitz | 2 | 2 | 2 | 2 |
| Javier Johnson & Nelle Cherry | 3 | 3 | 3 | 3 |
| Patrick Szmidt & Kate Hedin | 4 | 4 | 4 | 4 |
| David Lee & Heather Ballew | 5 | 5 | 4 | 4 |
| Nalla Kim & Gabriella Cook | 6 | 6 | 4 | 4 |
| Daniel Newsome & Teni Lopez-Cardenas | 7 | 7 | 7 | 7 |
Balboa Strictly
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Nick Williams & Kate Hedin | 1 | 1 | 1 | 1 |
| Adam Speen & Nelle Cherry | 2 | 2 | 2 | 2 |
| Robert White, III & Laura Keat | 3 | 3 | 3 | 3 |
| Andreas Olsson & Teni Lopez-Cardenas | 4 | 4 | 4 | 4 |
| Freddie Karlbom & Mette Herlitz | 5 | 5 | 5 | 5 |
| David Lee & Chelsea Lee | 6 | 6 | 6 | 6 |
| Patrick Szmidt & Natasha Ouimet | 7 | 7 | 7 | 7 |
| Javier Johnson & Heather Ballew | 8 | 8 | 8 | 8 |
Open Strictly Lindy
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Javier Johnson & Megan Damon | 1 | 1 | 1 | 1 |
| Paulo Thierry & Melanie Ohl | 2 | 2 | 2 | 2 |
| Jack Park & Minyoung Choi | 3 | 2 | 2 | 2 |
| Intaeck Joo & Jina Lee | 4 | 4 | 2 | 2 |
| Jaewon Jang & Young Kang | 5 | 5 | 5 | 5 |
| Yossef Mendelssohn & Beth Hartzel | 6 | 5 | 6 | 6 |
| Jack Chen & Brittany Calavitta | 7 | 7 | 7 | 7 |
Advanced Strictly Lindy
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Jean Baptiste Mino & Tatiana Udry | 1 | 1 | 1 | 1 |
| Alain Fragman & Anais Sekine | 2 | 2 | 2 | 2 |
| Jon Tigert & Heather Ballew | 3 | 3 | 3 | 3 |
| Markus Rosendal & Sandra Klack | 4 | 4 | 4 | 4 |
| Peter Kertzner & Mallory Grigg | 5 | 5 | 5 | 5 |
| Alex Dreyer & Fancy Dougherty | 6 | 6 | 6 | 6 |
Champions Strictly Lindy
| Name | Relative Placing | Borda Count | Condorcet | Small |
| William Mauvais & Maeva Truntzer | 1 | 1 | 1 | 1 |
| Stephen Sayer & Chandrae Roettig | 2 | 2 | 2 | 2 |
| Nicolas Deniau & Mikaela Hellsten | 3 | 3 | 3 | 3 |
| Andreas Olsson & Mette Herlitz | 4 | 4 | 4 | 4 |
| Jakob Bergelin & Anna Fors | 5 | 5 | 5 | 5 |
| Soochan Lee & Hyunjung Choi | 6 | 5 | 6 | 6 |
| Patrick Szmidt & Natasha Ouimet | 7 | 7 | 7 | 7 |
| Nalla Kim & Jessica Yoon | 8 | 8 | 8 | 8 |
Invitational Strictly Lindy
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Pontus Persson & Isabella Gregorio | 1 | 1 | 1 | 1 |
| Mikey Pedroza & Annie Trudeau | 2 | 2 | 2 | 2 |
| Peter Strom & Naomi Uyama | 3 | 4 | 3 | 3 |
| Dax Hock & Sarah Breck | 4 | 3 | 4 | 4 |
| Thomas Blacharz & Alice Mei | 5 | 5 | 5 | 5 |
| Todd Yannacone & Ramona Staffeld | 6 | 7 | 7 | 7 |
| Nick Williams & Laura Keat | 7 | 6 | 6 | 6 |
| Jeremy Otth & Kelly Arsenault | 8 | 8 | 8 | 8 |
| Mike Roberts & Laura Glaess | 9 | 9 | 9 | 9 |
Lindy Hop Classic
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Joshua Welter & Melanie Huot-Lavoie | 1 | 1 | 1 | 1 |
| Jamin Jackson & Sonia Ortega Betriu | 2 | 2 | 2 | 2 |
| Jean Baptiste Mino & Tatiana Udry | 3 | 3 | 2 | 3 |
| Michael Darigol & Brittany Johnson | 4 | 6 | 4 | 4 |
| Soochan Lee & Hyunjung Choi | 5 | 4 | 5 | 6 |
| Andreas Olsson & Mette Herlitz | 6 | 5 | 5 | 5 |
| Alain Wong & Anais Sekine | 7 | 7 | 7 | 7 |
| Ryan Calloway & Ann Mony | 8 | 8 | 8 | 8 |
| Junsik Kong & Olivia Jo | 9 | 10 | 9 | 9 |
| Andrew Hsi & Mary Freitag | 10 | 9 | 10 | 10 |
| Jack Park & Minyoung Choi | 11 | 11 | 11 | 11 |
| Mark Godwin & Shauna Marble | 12 | 12 | 13 | 13 |
| Adam Lee & Elaine Silver | 13 | 13 | 12 | 12 |
Lindy Hop Pro Classic
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Todd Yannacone & Ramona Staffeld | 1 | 2 | 1 | 1 |
| Dax Hock & Sarah Breck | 2 | 1 | 2 | 2 |
| Pontus Persson & Isabella Gregorio | 3 | 3 | 3 | 3 |
| Mike Roberts & Laura Glaess | 4 | 4 | 4 | 4 |
| Peter Strom & Naomi Uyama | 5 | 5 | 6 | 6 |
| William Mauvais & Maeva Truntzer | 6 | 6 | 5 | 5 |
| Nick Williams & Laura Keat | 7 | 7 | 7 | 7 |
| Kevin St. Laurent & Jo Hoffberg | 8 | 10 | 10 | 10 |
| Zack Richard & Annie Trudeau | 9 | 8 | 8 | 8 |
| Nicolas Deniau & Mikaela Hellsten | 10 | 9 | 9 | 9 |
| Thomas Blacharz & Alice Mei | 11 | 11 | 11 | 11 |
| Nathan Bugh & Giselle Anguizola | 12 | 12 | 12 | 12 |
Showcase
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Thomas Blacharz & Annie Trudeau | 1 | 1 | 1 | 1 |
| William Mauvais & Maeva Truntzer | 2 | 2 | 2 | 2 |
| Jeremy Otth & Laura Keat | 3 | 3 | 3 | 3 |
| Pontus Persson & Isabella Gregorio | 4 | 5 | 4 | 4 |
| Fabien Vrillon & Lisa Clarke | 5 | 4 | 5 | 5 |
| Patrick Szmidt & Natasha Ouimet | 6 | 6 | 6 | 6 |
| Jakob Bergelin & Anna Fors | 7 | 8 | 7 | 7 |
| Daniel Newsome & Gabriella Cook | 8 | 7 | 8 | 8 |
| Nalla Kim & Jessica Yoon | 9 | 9 | 9 | 9 |
| Soochan Lee & Hyunjung Choi | 10 | 10 | 10 | 10 |
| Jon Tigert & Mandy Spencer | 11 | 11 | 11 | 11 |
| Justin Hill & Olivia Taylor | 12 | 13 | 14 | 14 |
| Markus Rosendal & Sandra Klack | 13 | 11 | 12 | 12 |
| Mark Godwin & Shauna Marble | 14 | 14 | 13 | 13 |
Pro-Am
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Dominique Pomeroy & Laura Glaess | 1 | 1 | 1 | 1 |
| Adam Brozowski & Adrienne Weidert | 2 | 2 | 2 | 2 |
| Davis Thurber & Annie Breault | 3 | 3 | 3 | 3 |
| Nirav Sanghani & Nicole Frydman | 4 | 3 | 3 | 3 |
| Gabriel Indurskis & Annie Trudeau | 5 | 5 | 3 | 3 |
| Davis Thurber & Roxanne Lemay | 6 | 6 | 6 | 6 |
| Alain Wong & Daphna Harel | 7 | 7 | 7 | 7 |
Solo Charleston
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Pontus Persson | 1 | 1 | 1 | 1 |
| Nathan Bugh | 2 | 2 | 2 | 2 |
| Jon Tigert | 3 | 4 | 3 | 3 |
| Gabriella Cook | 4 | 3 | 4 | 4 |
| Robert White, III | 5 | 5 | 5 | 5 |
| Giselle Anguizola | 6 | 6 | 6 | 6 |
Teams
| Name | Relative Placing | Borda Count | Condorcet | Small |
| Lindy Hoppers Dozen | 1 | 1 | 1 | 1 |
| Swinging Air Force | 2 | 2 | 2 | 2 |
| Northern Lights | 3 | 3 | 3 | 3 |
| Cement Mix‐A‐Lot | 4 | 4 | 4 | 4 |
| Night and Day | 5 | 5 | 5 | 5 |
| Fly Rights | 6 | 6 | 7 | 7 |
| The Sweetheart | 7 | 7 | 6 | 6 |
| Groove Juice Speical | 8 | 8 | 8 | 8 |
| SAF Batillion | 9 | 9 | 9 | 9 |
| The Bees Knees of Boston | 10 | 10 | 10 | 10 |
| Sin Nombre | 11 | 11 | 11 | 11 |
I'm slightly obsessed with dance contests (mostly WCS) and elections.
ReplyDeleteYou may find the following paper by Xavier Mora interesting. He is a mathematician from Spain who is also a DanceSport judge.
http://mat.uab.cat/~xmora/articles/iss2Aen.pdf
You might also find this Westie Discussion of the Day thread on Relative Placement interesting.
https://www.facebook.com/WestieDiscussion/posts/549118701832617
I'll be back. ;)