Tarandalation2/21/2021 Here's a boring science fiction story. Like all fiction, it is not based on anything real and you definitely shouldn't attempt to draw any real-world conclusions based on the story. I repeat: it is purely fiction. This sort of thing would never really happen. On planet Gorolbrax in a neighboring galaxy, there was a race of intelligent aliens with a culture as rich and complex as our own. Something interesting about Gorolbraxians is that about half of all of them were fuchsia and the rest were magenta -- and this ratio held true in every society on Gorolbrax. Among Gorolbraxians, there was some debate over which of the two groups was better at certain things, but everyone agreed that both the fuchsia and the magenta Gorolbraxians were vital parts of their planetary life and culture, and that neither group was inherently superior in terms of moral worth. And neither was hands down better at doing all the things Gorolbraxian society valued. Then a fun new activity swept Gorolbraxian society by storm! They called it "tarandalation" ... I.Anyone can learn to tarandalate, but to be really, really good at it is hard, and takes a lot of practice, and it looks like innate ability plays a pretty big role in determining just how good you can end up getting. Becoming a professional tarandelator takes around six years of intense, professional training, at which point it’s clear which tier you belong to. After this, it takes years of extra work to move up in the world rankings, and even then, it’s only one or two slots at best. After your six-year training period, you pretty much know what tier you belong to. Now, about those rankings. Every year, the Gorolbraxian Tarandelation Federation ranks the players who graduate from the training camps. The method of ranking is clear, objective, and uncontroversial. No one disputes the ranks of the players or the training camps. Everyone knows and agrees on who the number one ranked tarandelator is, which is the ninth best training camp, etc. The player at each rank has beaten the person immediately below them in at least two-thirds of their matches. When tarandelation was first introduced, magenta and fuchsia Gorolbraxians appeared equally good at it in terms of their innate abilities. Coaching pays off equally well for both. But a recent survey showed that more magenta Gorolbraxians than fuchsia Gorolbraxians seemed interested in tarandelation by a ratio of 70/30. We suspect that the only reason for this is the respective socialization that magenta and fuchsia Gorolbraxians receive. We wanted to do something about this, since the evidence we have suggests that being good at tarandelation correlates highly with success in other areas. Moreover, professional tarandelation is not only lucrative, but the pros also serve to inspire the next generation to get interested, and the very best pros coach at the elite tarandelation training camps. If tarandelation were to become dominated by the magenta Gorolbraxians, the worry is that fuchsia Gorolbraxians will be at a major disadvantage throughout their lives. We had to find a way to get more fuchsia Gorolbraxians into tarandelation! But how? II.We thought that a higher visibility of fuchsias in coaching roles at elite training camps would help shed the stigma around fuchsia tarandelators. More fuchsias in leadership roles would inspire more fuchsias to devote their efforts to tarandelating, which would bring the ratio of magentas to fuchsias closer to 50/50. This seems perfectly achievable, since magenta and fuchsia Gorolbraxians are equally capable, and the preferences they showed were entirely because of socialization. The five very best training camps (in order: A, B, C, D, and E) are very competitive, and any tarandelator would drop everything to coach at any one of them. The rest of the camps will take whom they can get, and coaches will work there if one of the top five jobs aren’t available. Last year, the big five made a commitment to hue inclusivity, and agreed that their new hires for coaches would be 50/50 magenta to fuchsia. They are each hiring the four best coaches they can find -- two magentas and two fuchsias. The top 100 tarandelators for last year were ranked. The thirty fuchsia tarandelators were distributed throughout, though strangely, they were at the very top of each decile so that within each tenth of the top 100, the rankings looked like this: 1F, 2F, 3F, 4M, 5M, 6M, 7M, 8M, 9M, 10M. We were excited by this news, as it looked very promising for our goals of hue equity... The big five tarandalation academies made their new hires, and the hue/ranking breakdown looked like this: Top Tier: A: 1F, 2F, 4M, 5M B: 3F, 11F, 6M, 7M C: 12F, 13F, 8M, 9M E: 23F, 31F, 15M, 16M Now it was time for the second tier to make their choices: F: 32F, 33F, 17M, 18M G: 41F, 42F, 19M, 20M H: 43F, 51F, 24M, 25M I: 52F, 53F, 26M, 27M J: 61F, 62F, 28M, 29M Followed by the third tier: K: 63F, 71F, 30M, 34M L: 72F, 73F, 35M, 36M M:81F, 82F, 37M, 38M N: 83F, 91F, 39M, 40M O: 92F, 93F, 44M, 45M By the time we hit the fourth tier, we’re out of fuchsias, so from now on, it’s all magentas: P: 46, 47, 48, 49 Q: 50, 54, 55, 56 R: 57, 58, 59, 60 S: 64, 65, 66, 67 T: 68, 69, 70, 74 And finally, the fifth tier (still all magenta): U: 75, 76, 77, 78 V: 79, 80, 84, 85 W: 86, 87, 88, 89 X: 90, 94, 95, 96 Y: 97, 98, 99, 100 The results of this division are harrowing. There is one training camp where the fuchsia coaches will regularly beat the magenta coaches. There is one training camp where one of the fuchsia coaches will be substantially better than the magentas and the other substantially worse. In the other twenty-three camps, the magenta coaches will completely dominate the fuchsias. Worse, in one third of the camps, the top fuchsia coach will be in a different decile than the other fuchsia coach, meaning that one of the fuchsias will be losing all of her matches handily, and the other will not find anyone at the camp to challenge her at her level. Both fuchsias will be substantially more isolated. What will become of the young tarandelators who attend the camps as students? Only the fuchsias who get into the two very best schools have a shot at seeing one of their fuchsia coaches regularly win in-camp games against a magenta coach. Think of the promising young fuchsia Gorolbraxians who are good enough to attend these elite training camps, but who don’t make it into the top 60%. A young fuchsia attending the fourth-tier training camp P will have no fuchsia coaches to personally encourage her. If she wants to find the first fuchsia who can regularly beat the magenta coaches at her camp, she must look eight full ranks above her own to training camp H -- which is two tiers above. These young players might have a meaningful life experience with the game, even if they never become top 100 players themselves (after all, by definition not everyone can do that). It is certainly worthwhile to encourage participation, even among those who never become professionals (remember that tarandelation helps develop skills in other domains that can help you succeed in life). But whatever they do after their time at the training camp, they will have no fuchsia coaches to serve as their role models while they are there. If we think that this is an important factor, then we must acknowledge that the program is lessening their experience. We have taken away the very coaches who would be in those camps if hiring were entirely merit-based. By putting the coaches in an element above their ability, we set them up to fail -- and to disappoint the very people they are meant to inspire. Because their would-be role models are now outmatched by their magenta counterparts at all but two schools, when these young fuchsia tarandelators look to the higher tier camps for heroes, they see fuchsias constantly being defeated by magentas from a lower-ranked camp than their own -- often drastically so. III.Recall that there is no innate difference between fuchsias and magentas in terms of playing ability, but only with the number of players interested in the game. This massive disparity happened even though the fuchsia tarandelators were the top players at each decile. But it turned out that it was a freak occurrence. The following year, thirty fuchsias were randomly distributed across the top 100 players in the following ranking:
When the training camps hired their coaches, they once again followed the two fuchsia, two magenta model. Each camp hired the highest ranked players available. This is how things turned out:
And now, once again, all the fuchsia coaches are gone after the third tier. Once again the last two tiers will be entirely magentas:
When the population of fuchsia tarandelators is randomly distributed, things can turn out even worse than when they lead every decile. In this scenario, there is no school where the fuchsia coaches will regularly beat their magenta counterparts. One of the magenta coaches at the very bottom training camp will be able to beat both fuchsia coaches at camp O -- two full tiers above him. Meanwhile, the magenta coaches at camp O are competitive with the fuchsias in camp F, at the very top of tier two. IV.Again, even though this scenario is substantially worse than the version where fuchsias are the top three out of every ten players, the magenta players in this ranking are not inherently better than the fuchsia players -- they are randomly distributed.* It’s just that there are more magentas who play. We started with uneven pools of players (thirty fuchsias to seventy magentas). When you siphon off pairs from each pool, you get to the bottom of the smaller pool before the larger one. We stated that it seems as though the only reasons fuchsias aren’t more interested in tarandelation are social. The goal of the hiring equity policy was to encourage more fuchsias to participate. But the result appears to be in danger of simply doing the opposite. A substantial argument could be made that everyone -- everyone -- would be better off by simply hiring the four best ranked coaches available, regardless of hue. By emphasizing equity, there are fewer camps where fuchsia coaches are present. And at those camps, the fuchsia coaches fare substantially worse than their magenta counterparts. None of this is because the magentas are any better. They aren’t -- remember that this happens when the fuchsias are the very best players at each decile. Rather, the disparity happens simply because of the greater number of magentas. When presented with this data, the GTF might propose requiring every school to have fuchsia coaches, and so the the fourth and fifth tier schools would be required to hire fuchsia coaches or be closed down. This would mean two things: First, all of the magentas at the fifth tier would be cut, in order to open positions for the fuchsias coming in. And second, the camps would have to find twenty more fuchsia tarandelators -- none of whom would be in the top 100 players. None of these fuchsia Gorolbraxians would be able to regularly beat any of the twenty magenta Gorolbraxians who were just cut from the ranks. Some of these twenty magentas who are slated to be cut are competitive with coaches at camps many ranks above them. They will be replaced by people who are significantly worse than that. Assuming the fuchsias from the next 100 players are in the top of each decile (as in our first arrangement), magentas ranked 75 and below will be replaced by fuchsias of the following ranks: 101F, 102F, 103F, 111F, 112F, 113F, 121F, 122F, 123F, 131F, 132F, 133F, 141F, 142F, 143F, 151F, 152F, 153F, 161F, and 162F. The lowest ranked magenta coach who was not cut will be 86 and 87 ranks above his fuchsia colleagues. This is a recipe for resentment. V.Alternatively, the Gorolbraxian Tarandalation Federation could consider quotas on the incoming students. Under such quotas, training camps would be required to admit the same number of fuchsia students as magenta students. If only thirty fuchsias were interested in being tarandelators, then they would only admit the same number of magentas. We might imagine that after a few generations of this, we could be on our way to hue parity. Of course, the training camps are also really competitive, so the players being admitted are ranked too. Those rankings will look a lot like the rankings of the coaches we just examined. The new admissions policy means, in effect that all of the players in tiers four and five will be cut, or else they will be admitted next to fuchsias from lower rankings, which is effectively the same as the previous consideration. The magentas will either be cut to make room for someone objectively not as good at tarandalation, or else they will work at a training camp next to fuchsia colleagues who can’t keep up, while fuchsias they have regularly beaten at matches are given positions above them at more prestigious camps. Young magenta (and fuchsia) Gorolbraxians will have an experience that teaches them that virtually all of their fuchsia coaches are inferior to their magenta counterparts. If quotas for students are imposed, they young magentas can be expected to defeat most of the fuchsias in their camps. This is a recipe for disaster. No one in these situations will be happy. It is a virtual guarantee that the fuchsias will be faced with unnecessary disappointment, and the magentas will be full of resentment. And who could blame either party? But the worst of it is that in every hallway of every camp, we will hear the one phrase we hoped to eradicate. And despite all the efforts of the GTF, all of the players will have an internalized sense that it is true. They will all say, “fuchsias can’t tarandelate.” VI.What would happen if instead, each training camp just hired the four best coaches available? This chart lists the magenta/fuchsia breakdown from the second, randomly distributed version of the top 100 ranking. I have omitted the numbers because they simply descend as you move down the camps. The coaches at camp A are ranked 1, 2, 3, 4; camp B are ranked 5, 6, 7, 8; etc.
This time there are only four camps without at least one fuchsia coach, and these camps are spread across multiple tiers. This is much better than two full tiers, comprising eight camps without a fuchsia coach. Moreover, there are eight camps at which the top player is a fuchsia (compared with zero when the same ranking of players is hired based on hue equity and only two when fuchsia players are at the top of each decile), and only five camps at which the bottom player is a fuchsia (compared to all of them or all but one). Best of all, everyone can believe that they earned their spot. No one is above them who doesn’t deserve to be. No magenta coach will be able to look at a fuchsia colleague and think, “she’s only here because she’s a fuchsia.” If he ever says it out loud, she can challenge him to a match, and there’s a much better chance in this setup that she’ll win her match! Notes:* I made this ranking with random.org by making a list of thirty Fs and seventy Ms and having their algorithm order the list randomly. That's right. I used up part of my daily quota of random data for this nonsense.
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