"Great Britain includes both Northern Ireland and Eire."

No it doesn't but at the Olympics people from Northern Ireland qualify for 'either' GB or the Republic of Ireland. It is up to them. I suppose by competing as the UK we would be automatically including Northern Ireland. To make things more complicated at the Commonwealth Games we compete not as the UK or GB but as seperate Scottish, English, Welsh and Northern Irish teams - as we do in international football. At international rugby Scotland, England and Wales compete as seperate countries but neither Northern Ireland or the Republic do as they compete as a united Ireland at that sport. It is complicated right enough!