How many countries can a citizen visit without a visa? [Bonus Economist Graph Edition]

I have considering the titular question for some time, and today The Economist did its job of answering it for me by relaying the findings of Henley and Partners, who apparently “are the world’s leading specialists in international residence and citizenship planning”, as well as being tax avoidance advisers, by their own reckoning. I’m proud to advertise their services.

A graph showing some of the more notable countries and interesting statistics is at The Economist’s website, while H&P’s full list is in PDF form at their site.

Some of the most interesting finds for me are:

• Afghanistan comes last, followed by Iraq. Is this because of the American invasions? They rank even lower than Somalia and North Korea.
• What causes some of the small discrepancies between the countries whose citizens have greatest freedom to travel? To take the most obvious example, what is that extra country that gave Denmark the sole lead with 157 countries not requiring a visa from its citizens? Which countries let in Portuguese but not Brits?
• Courtesy of the cat: If one could have two passports from any on the list, which ones should be chosen in order to maximise the number of visa-less countries one could travel to? Denmark’s might not necessarily be one of them, of course. Similarly for three passports, and so on. And so what is the minimum number of passports needed in order to visit every country in the world without a visa, assuming it’s possible? Is it possible?
• Even more interesting would be to list the countries in order of how many other countries’ citizens can enter them freely. I suspect it’d look quite different from this one, maybe even to the extent that merely listing them in the opposite order to the current one would almost suffice…

A 0-1 matrix showing which countries let in which other countries’ citizens will answer most of the questions. Come on, Economist, I’m waiting…