From Merriam-Webster
SPORT: 1 a : a source of diversion : RECREATION b : sexual play c (1) : physical activity engaged in for pleasure (2) : a particular activity (as an athletic game) so engaged in
(I think we can agree that definition 2 is the one we're talking about in relationship to the Olympics)
ATHLETIC: 2 : characteristic of an athlete; especially : VIGOROUS, ACTIVE
GAME: 3 a (1) : a physical or mental competition conducted according to rules with the participants in direct opposition to each other
Let's look at Scrabble. Recreation? yes. Game? yes. Athletic? no.
Let's look at Poker. Recreatoin? yes. Game? yes. Athletic? no.
Let's look at ditch-digging. Athletic? Possibly. Recreation? not if you're sane. Game? no.
Let's look at hockey. Recreation? yes. Athletic? yes. Game? yes. IT'S A SPORT!
Let's look at figureskating. Recreation? yes. Athletic? yes. Game? yes. IT'S A SPORT!
Let's look at beauty pageants. Recreation? yes. Game? yes. Athletic? no.
Let's look at shuffleboard. Recreation? yes. Game? yes. Athletic? probably not; if it is, it could be a sport.
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These guidelines seem pretty clear to me, although at their edges they may start to break down. But figureskating is clearly athletic; it's clearly engaged in for recreation; and it's clearly competitive. It's central to the definition. Scrabble, poker, beauty pageants all fail terribly at one of the key parts of being a sport: namely, they're not athletic.
Now, there's at least one additional consideration. The Olympics are biased toward spectator sports: sports that are fun to watch, and that have a fair number of people who are willing to watch the competitors. Again, figure skating is a great example of a spectator sport.
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Storm Raven, I think you have a fairly strong argument when you focus on the corruption of the skating judges, although this may be my ignorance about the judging system popping up (I have a much better grasp of linguistics than I have of Olympic history). When you argue that the skating judge system is so corrupt that it should be retired from the Olympics, I think that's worth considering.
But given that we have a working definition of sports that includes what people expect it to include, and excludes what people expect it to exclude; and given that your definition excludes what many folks expect it to include and includes what everybody expects it to exclude; I think that's not so strong an argument.
Daniel