(As a side note, discussing the US is always a pain for me because of their silly habit of calling their provinces 'states'. This is tricky enough for anyone who wants to distinguish the state of Georgia from the state of Georgia, but it's extra tricky for me, because we had it hammered into us in first year politics that the correct technical term is not 'country' but 'state', so I'm perhaps more inclined than most to run into this linguistic obstacle. And don't even get me started on the American demonym problem!)
Anyway, the maths thing got me thinking about where you'd have the strongest single vote, where your 1 vote would (without cheating) count for the greatest possible percent of the whole. And obviously the answer is any decision that you get to make solo, where your 1 vote constitutes 100% of the electorate's will. Easy. Or we could insist that a democracy by definition has to include multiple voters, in which case the smallest case would be two. And there are plenty of examples of business partnerships and very small municipalities and things like that where there are very few people who get a vote. It's actually not quite such a weird situation, in reality.
But what about formal states (not states, but states!), the elections individuals can participate in at the highest level? Still a wee bit complicated. The smallest microstate by population listed on wikipedia, the Vatican, is not a democracy, so we can ignore it. The next smallest population belongs to the Republic of Nauru, with a little over 9,000 humans (or 12,000, 10 years ago; it seems they booted out a lot of foreigners in 2006, due to shrinkage in their phosphate industry). They have all the key structures of a modern democracy, with a president (acting as both head of government and head of state, which is a distinction that means a lot more when you've got a politics degree), an 18-seat parliament, a separate judiciary and, quite sensibly, no formal party system - each MP is effectively an independent, although 3 parties do exist for support purposes.
|The entire Republic of Nauru.|
Voting is compulsory (as it should be!) for anyone aged 20 and over, but annoyingly I can't find the exact figure of how many individuals that works out to, but let's guess it's close to half: 4,500 adult human citizens. In that case, your single Nauruan vote is worth a 0.0222222% share of control of the Nauruan government. That's 4,700 times as potent as a South African vote or 52,400 times the strength of a US vote. Holy shit, Naurauns, careful where you swing those votes! Someone could get hurt.
Of course, we generally pay more attention to democracies with large total populations, rather than those with high concentrations of electoral power per capita, which is why I literally couldn't go more than 5 minutes after waking up this morning before learning who had won yesterday's election in the US, while I had to go out of my way (a relatively small bit, thanks to the efficiency of Wikipedia) to be reminded that Nauru even exists, never mind that it's the smallest independent democracy. And yet a compare-and-contrast between the US and Nauru (just for the fun of it) yields some surprising results. Nauru is possibly more industrial per capita, though phosphate mining has plummeted in recent years, and is certainly less hospitable to most critters, leading to lower biodiversity, despite appearing to be an isolated tropical paradise. Nauruans are also statistically the fattest national population in the world, with around 95% of them classified as overweight or obese, way above the 58% of adult Americans classified the same. On the positive side, Nauru has no military of its own, and as far as I know, no intention of invading anywhere either. And they used to have a president called Ludwig Scotty, which is a name that pleases me.