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Hasse diagram of the 2008 Olympic medal table


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With all that scope for reasonable disagreement, is there anything we can all agree on? How much of the hierarchy in the medal table is indisputable, and how much depends on your point of view? So we want to say that one country has done strictly better than another if the medal score of the latter can be transformed into the former by a sequence of medal additions and medal upgrades. A bit of thought shows that this is exactly equivalent to defining a partial order on triples of medals, in which a triple (G,S,B) is considered at least as good as another triple (g,s,b) if and only if it satisfies the three conditions * G ≥ g * G + S ≥ g + s * G + S + B ≥ g + s + b

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