The trick is that:
The countries are all wrong! They are almost right, but all wrong.
What is it then?
It is one of their neighbours.
Portugal France, lets take Spain.
Instead of Cuba, lets take USA.
Instead of New Zealand, lets take Australia.
Instead of Turkey, lets take Greece.
Instead of Mongolia, lets take China.
Instead of France, lets take UK.
Instead of Paraguay, lets take Brazil.
What this do?
Barcelona, Spain, 1992 - over 20 years ago.
Atlanta, USA, 1996.
Sydney, Australia, 2000.
Athens, Greece, 2004.
Beijing, China, 2008.
London, UK, 2012.
Rio de Janeiro, Brazil, 2016.
So the next one is:
Tokyo, Japan, 2020.
Since the country is on purpose wrong, then I should choose a nearby wrong country, a VERY wrong, TERRIBLY WRONG country...
Also I want to eliminate the 1988 country because the list must be kept being wrong.
[Take 1] So I'll choose:
But rand said that this is not correct. Thinking about how to fix the algorithm...
It seems related to distances. After a lot of head smashing, I conclude that the country is the nearest one to the olympic city, excluding the host country of course.
France's border is at 106 km from Barcelona. Andorra's is at 126 km. Portugal is at 700 km. Algeria is at 511 km. Italy's Sardinia is at 505 km. So, France is the nearest.
Atlanta is at 935 km from the nearest point in Bahamas. But let's forget Bahamas. At roughly 1181 km we reach Cuba shores. Mexico's Yucatán is at 1391 km and the extreme tip of Mexico's border with Texas is at 1494 km. Canada's extreme south, near Detroit, is at 905 km in Pelee Island or 928 if you don't count the island, but screw up Canada too.
Sydney is at 1974 km from New Zealand's shores in northern island and 1853 km from southern island. 1673 km from the isolated Norfolk Island (part of Australia, so doesn't count). 1938 km from New Caledonia. So, New Zealand is the nearest country.
Crossing the sea, from Athens, Turkey is at 227 km. Albania is at 356 km. Macedonia at 370 km and Bulgaria at 379 km. So, Turkey is the closest.
Mongolia is at 564 km from Beijing. North Korea is at 671 km. South Korea is at 889 km. So, Mongolia is the closest.
London is at 137 km from France. 190 km from Belgium. 242 km from Netherlands. 176 km from Wales. 437 km from Scotland. So, France is the nearest.
Paraguay nearest border to Rio de Janeiro is at 1129 km. But Argentina beats it with 1111 km. I guess that rand got this one wrong since the difference is so small. Bolivia is at 1543 km. Uruguay is at 1446 km.
Tokyo is at 915 km from South Korea. 1059 km from North Korea. 944 km from Russia (near Vladivostok).
So the next country is: