Monday, August 13, 2012

Olympic Medals and Lexical Ordering

Those familiar with Rawls's political philosophy will no doubt be familiar with the notion of lexical (or lexographical) ordering, the standard example of which is dictionary alphabetisation. Football league tables offer another example, usually with points scored lexically prior to goal difference, which is in turn lexically prior to goals scored.

I thought it worth noting that the Olympic medals table offers another fine example. For some particularly clear examples:
South Korea (13/8/7) comes 5th, ahead of Germany (11/19/14).
Kazakhstan (7/1/5) comes 12th, ahead of Netherlands (6/6/8).
North Korea (4/0/2) comes 20th, ahead of Spain (3/10/4).
Norway (2/1/1) comes 35th, ahead of Canada (1/5/12).
And, just to show that silver medals carry some weight, Australia (7/16/12) comes 10th, ahead of Japan (7/14/17).

It's a further question, of course, whether this lexical ordering is justified. Does one gold medal really outweigh any number of silvers?

I'm told by Canadian friends that Canadian reporting switched from using the lexical ordering to reporting the total number of medals, a measure on which Canada (36th) came ahead of Hungary (9th, with 8/4/5). This doesn't seem right either, since it counts a gold as being as good as (but no better than) a bronze.

Perhaps a better ordering would be one giving differential weight to different medals, but this (unlike either lexical ordering or equality) requires us to specify how much better gold is than bronze. If we were to say gold = 3 points, silver = 2 points, bronze = 1 point then we would get one result; but we'd get a quite different table if we said gold = 5 points, silver = 3 points, bronze = 1 point. (If that's not clear, compare two countries with the profiles (1/0/0) and (0/2/0) under each of these schemes.)

p.s. This is based on the table after the immediate conclusion of the games. Apparently the medal standings won't be absolutely final until 2020! (Maybe even longer: see update here.)

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At 7:48 pm, Anonymous jim rogers farmland said...

Huh - not final until 2020?

At 12:56 pm, Blogger Ben said...

Apparently not: competitors can still be disqualified for drugs offences (based on new as yet untried tests) until the statute of limitations expires. (See the link.) As such, medal standings may alter.

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