Does winning an election against the popular vote represent the choice of the voters?

[The Romulan Republic]

Define "choice of the voters". Are you talking about the nation as a whole, whether the state/city/whatever got a representative that reflects the vote, or something else? For instance in a FPP system a candidate could get 30% of the popular vote and still be elected to represent everyone in his district, is that "democratic" since 70% of the people didn't vote for him? Or let's say we do proportional representation on a provincial/national level, and we get an even 3-way split between team Weiner-Holder, the Butt-Toucher party, and the Pussy-Grabbers. If I live in a city that's 90% Butt-Touchers, am I fairly represented?

Going back to this...

Well, my personal definition, in brief, would be a result that reflects the choice of the majority (or, if there is no majority behind a single candidate, at least the single largest block*) of the voters in a given race, in which all adult citizens had fair and equal access to voting.

For a Congressional midterm, for example, that would mean getting a representative that reflected the preferences of the voters in that district.

You have different representation at different levels. Your... Butt-Touchers Party would presumably be elected by a local Butt-Toucher Representative. However, at the national level, you would either get a President from whichever party squeaked out the most votes*, or, in a Parliamentary system, a PM from a coalition government, most likely.

For a Presidential election, since the President represents the whole nation and we are all supposed to have equal rights, it should, in my opinion, be based on nation-wide popular vote, though I know that many others would disagree.

And again, their are degrees of how democratic or undemocratic a system is. Its obviously not a simple choice of a) Democracy, or b) Despotism.

*I do think that there is a lot of merit to having run-off elections if no single candidate in a given race gets a majority, but I don't consider those a necessity for a system to be considered "democratic".

[Simon_Jester]

My starting principle with democracy is that every citizen gets an equal voice on voting day. There can be exceptions to that, but they must be justified.

So any system where the popular vote doesn't automatically resemble the outcome is not a system I'd call democratic. This rules out the US EC system for electing the president. FPP can produce results way out of line with the popular vote, even without obvious gerrymandering, so it's out.

This leaves only two ways of running elections that I'd consider democratic:
- For a winner takes all position like the President, it needs to be the popular vote. Preferably an STV system.
- For a system that elects multiple people to fill seats, proportional vote is the only option. District representatives can work, providing that electing them doesn't mess with the percentages of seats each party gets (eg, MMP)

That might be your personal way of viewing things, but from what I can tell, democratic systems seem to work perfectly fine without adhering closely to that rule and the degree of satisfactorily effective and democratic governance bears only a slight relationship to the degree the electoral systems conform to the ideals of PR advocates. PR systems in particular appear to be excellent at giving the appearance of a one-person one-vote system while effectively cedeing all real power on who holds power and represents the populace to the party bosses and backroom negoiations between parties to form coalitions. Meanwhile FPTP systems are a theoretical nightmare but give every appearance of working out about equally well to the alternatives in practice.

I'd consider the details of the system used to be quite secondary to the conditions of the civil society holding the elections in terms of real world results. Which is why I find the benefits of electoral system reform to be much more a plaything of poli sci nerds than any kind of pancea to practical aliments.

I think what it comes down to is that there are some situations where ceding real political power to backroom negotiations is better than the alternative (say, lunatic demagogues having disproportionate power). There are others where having relatively straightforward elections and limited backroom influence is better, instead (say, a chronically corrupt political culture a la Tammany Hall).