This list of US ‘faithless electors’ suggests that things sometimes go awry in the electoral college system.
You’re free to use the word in that sense, but you’re disregarding millennia of established use.
The correct word for “representative democracy” is “representative democracy”. Republic means something completely different. You can clearly be a republic without being in any sense a democracy (North Korea, for example). I’m curious, though, as to what word you use to describe the class of governments that have no hereditary head of state yet which are not democracies?
A very good and reasonable question. ‘Dictatorship’ is my usual catch-all for all countries run by a single guy, and ‘single-party state’ or possibly ‘oligarchy’ for countries run by a single group of people who can’t be voted out. You can subdivide into things like ‘military junta’ and ‘theocratic dictatorship’ and so on if you want, but in general terms it often doesn’t really matter. Sometimes it makes sense to group communist countries into their own category, with things like ‘communist dictatorship’ or ‘communist single-party state’ being able to convey a lot of useful information about which kind of Cold War-era government you’re talking about.
Everyone else: OK, I’m willing to back down on this. Sure. My real point is that the US and the UK are a lot more similar than they are different if you ignore things that could happen and focus on what does happen, especially on a day-to-day basis. Putting them in two different groups simply makes no sense unless you’re really getting into it.
Except a monarchy by definition is not a republic.
You can have democratic, constitutional monarchies, but that doesn’t make them republics.
Derleth: You’re missing a category: oligarchy – rule by a small self-perpetuating group, the leader of which may appear to be a dictator. But his power is not absolute; power is distributed among the members of the small group. The Soviet Union after 1953 was such a system; Japan’s structure between the Meiji Restoration and Hiroshima defies easy categorization, but comes closest to oligarchy. Saudi Arabia is arguably another example.
As for the distinction between Republic and Monarchy, it’s more a philosophical one than a seat-of-power one. In a republic, either the people or something symbolic of the social contract of the people is conceived of as the source of sovereignty. Who actually wields power in a republic and how they get the job may vary, but their power is conceived of as being drawn on in the name of and with the at least tacit consent of the people. In a monarchy, no matter how little power the constitutional monarch may have, he or she is conceived of as the source of governing power. This can very rarely have practical application, as when QE2 twice resolved what didn’t rise to the level of constitutional crisis, but might fairly be termed constitutional hiccup, in 1957 and 1963, by taking advice in the literal, non-euphemistic sense and then selecting a prime minister who could command a majority in Commons, or when Haakon VII of Norway gave voice to the united will of his people in rejecting collaboration with the invading Nazis in 1940.
Basically, as I understand it, each party puts forth a slate of electors, and the voters elect one slate over another; in most states, the whole slate goes to college for the party with the most votes. Not a perfect system (ask Gore) but the voters select who will then select the president and VP. Not much different on some levels than a party nominating a slate/list of candidates for proportional representation in parliament, a system like Germany(?), Italy, Israel, etc. have.
Strictly speaking, nine unelected people got to decide who should have been President. 
Those dates are too early. William III* was able to refuse assent to more than one parliamentary bill. That pushes us up until the 1690s or so. And as late as William IV’s reign the Sovereign was able to curtail parliamentary discussion by prorogation made purely on his own authority; since prorogation at the time killed off any bills still in progress, that pushes us up until the 1830s.
*I don’t believe the oft-cited example of Anne not assenting to the Scotch Militia Bill is relevant here, as to the best of my knowledge her refusal was on ministerial advice.
I knew that someone here would stumble into this assumption!
[QUOTE=Article 2 of the Constitution of the Irish Free State]
All powers of government and all authority legislative, executive, and judicial in Ireland, are derived from the people of Ireland and the same shall be exercised in the Irish Free State (Saorstát Eireann) through the organisations established by or under, and in accord with, this Constitution.
[/QUOTE]
The Constituent Act enacting the afore-mentioned Constitution also states in its words of enactment:
(Emphases added.)
The Irish Free State was, of course, a constitutional monarchy.
@ A Gwilliam (since a quote would be less than useful):
My stance there is that the Irish Free State was a republic which, like Sparta, retained the historic office of King – not a monarchy in the strict sense, where the Crown, however constrained by democratic institutions, is the official source of power.
But the constraints upon the monarchy by democratic institutions in (say) New Zealand were the same as those in the Irish Free State.
This website claims the oldest continuous democracies in the world are, in order:
- “Britain”
- USA
- Canada
- Switzerland
- Sweden
- Australia
I’m not I’d put much stock in that website but there’s some alternative contenders. This site, hosted by the Guardian, has a huge discussion. One commenter claims:
Some commenters claim that New Zealand was the first to have universal suffrage, but another commenter says the Isle of Man had actually established it years earlier. Australia and New Zealand are suggested quite a few times overall.
The oldest Parliament is apparently Iceland since 930, although the Isle of Man has had a continuous Parliament since 979.
Switzerland gets a few mentions, with arguments that it’s the closest to being truly, directly democratic.
One commenter says that Finland gave full voting rights to women 1906, supposedly before anyone else.
The Faroe Islands get mentioned a few times, although with the caveat that it was always under the control of Denmark. Some make the claim that they in fact had the oldest Parliament…
San Marino is mentioned, as others here have said.
And finally: