Friday, February 21, 2014

Fairness, part 1

I've found myself thinking a lot about fairness lately. Most of us would agree that fairness, as we define it, is among our core values; we react viscerally to what we perceive as injustice - yes, in particular injustice done to ourselves or those we care about, but I'd like to think most of us are more broad-minded than that.  Very few of us would not like to see a fairer world, and while we're here, we'd like to make the world a little fairer if we can. But there are so many definitions of "fairness", and of related ideas such as "justice", that we have a hard time coming to any sort of consensus about how to resolve complex situations fairly.

So what I'd like to do, if I find the time, is write a few entries examining fairness in different arenas and from different perspectives, to help me (and perhaps you the reader) frame some of the many questions related to the idea of fairness. We'll see what I get to; I have a lot going on these days, even as part of me feels it isn't enough. I'm sure you can relate.

I'll start in the world of games, since I know that world better than I know many others - in particular, games that are competitive and attempt to rank individual players, such as chess or Scrabble. What do we as players want from our competitive environment? We want it to reflect the relative abilities of the players, with as much fidelity as possible. That means we want small differences in ability to lead to small differences in winning percentage and rating and large differences in ability to lead to large differences in those things, roughly on a proportional scale. We want the best players to be identified as best over a sample of games large enough to feel right to us.

Chess uses what's called the Elo rating system, which assigns a numerical rating to players based on their winning percentage adjusted for the strength of their opposition. Scrabble also does this, though it sets the curve a bit differently, taking into account the variance in the quality of tile draws in the game. To illustrate, if Player A is rated 350 points higher than Player B in Scrabble, the rating formula expects player A to win about three out of four games. In chess, a 350-point difference means that the higher-rated player is expected to win about seven out of eight. Why is chess not eight out of eight, you may wonder; after all, there's no luck involved in chess. Shouldn't the superior player always win? Well, a 350-point difference in Player A's favor does not mean that Player A will always play better than Player B does. Abilities aren't static - they fluctuate. Player A might play like a 2200 player in one game, and more like a 1600 player in the next, particularly if the first game offers themes and positions that Player A is much better at solving than the second. Or maybe Player A didn't have enough caffeine or rest in game two, or has some sort of inferiority complex with certain opponents; humans are weird.

Is it inherently unfair that an inferior player might win a game? In Scrabble, you'd better get used to it. No one would deny that 350 points of rating represents a significant difference in skills. If you took a bunch of 2000-rated players - there are about 15 players in North America rated that high - and evaluated them on word knowledge, anagramming, board vision, strategic skill and ability to handle tournament pressure, every 2000 player would come out ahead of every 1650 player in every area almost all the time. But the 1650 player will win a quarter of the time, the chance of flipping two heads in two coin flips. Easy to do once or twice, but the more games in the event, the more difficult it becomes for the lower-rated player. A 1650 player, assuming the rating is accurate, wouldn't be expected to win the U.S. Nationals (31 games) given a million tries. So while on some level Scrabble is "unfair", a large enough sample restores the fairness, and if you look at who has finished in the top five of a Nationals over the years, you're not going to find anyone there who isn't at least 1850 strength or so, and in most cases the top five will be 1950 or better. But on the other hand, every year there are surprises in the top 20. (The size of the top-division field at Nationals has varied over the years, but is usually about 100.) I take both of these as good signs.

I think Scrabble achieves the balance pretty well now, though maybe there are ways to improve it. I play about 150 tournament games a year, and my rating range over the past eight years has been somewhere between 1875 and 2025. Unless I'm atypical (don't think so), it's reasonable to assume that I'm a 1950 player. That feels fair, even when I'm busy losing a game to a 1200 player or beating 2250-rated Nigel Richards (I've done both). It's true that in chess, were I similarly skilled, I'd just about never lose to the 1200 player, but I'd just about never beat the Nigel Richards of chess, either. I'm not sure we can say that one scheme is fairer than the other - in fact, I'd say both are appropriate. If you want to reduce the luck involved in Scrabble, or increase it in chess, there are ways to do that. But again, what we want to avoid - because it feels unfair to us - is either of two situations: where small differences in ability yield excessively large advantages, or large differences in ability yield too-small advantages.

What am I on about here? Real life is a hell of a lot more complex than a game like Scrabble or chess is, and the luck factor is self-evidently MUCH larger. Bill Gates might be ten thousand times as rich as your local successful infotech entrepreneur, but he's not a hundred times as skilled, or diligent, or smart, or anything of the sort, and I'm sure he'd admit as much. He's more of all of those things, maybe, but not TEN THOUSAND TIMES more by any reasonable method of measurement. Most of the wealth difference is attributable to circumstances outside of Gates's control. (Malcolm Gladwell's "Outliers" makes this point, to some degree.) Which brings us to a fundamental of fairness: do we not bristle when players are rewarded or penalized for things they didn't have control over? This is not to begrudge Gates his success - I see no reason to say he shouldn't be at the top of the mountain. It's the size of the mountain that's in question. Even a fivefold advantage in skill shouldn't lead to hundredfold rewards, and when it does, shouldn't our alarm bells be going off? But in our culture such disproportionate rewards happen all the time. I'm not suggesting we should do anything draconian to fix this, but we need to recognize that it's a feature of our Monopoly world - that minor advantages in skill can snowball into massively dominant positions in a hurry, which tend to ossify over time. According to the idea of fairness we talked about above, that's not ideal; a 51-49 or even 60-40 advantage in skill shouldn't ever end up as winner take all - rather, it should be reflected as the ratio it is, or at least closer to it than our society now manages.  The problem with the just world theory behind laissez-faire, ultimately, is that it's fatalistic. We end up rewarding good fortune more than we reward anything else, and to me, that's not sensible.

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