You'll force the majority to lose to their second choice if none of them do the math.
How does that work? Examples:
mahority proposal: 10 votes(v)
Minority proposal: 8v
lesser minority proposal: 6v
Everyone's second choice: 24/2=12v
In the above, everyone agreed that the winner was good enough, and no single group was large enough to get their favourite to win. Thus democracy was served by deferring to a compromise, as that was what the people agreed to. Is it really so bad to think that democracy might sometimes try to be 'good enough' for everyone rather than purely pandering to the majority community?
Majority idea: 6 votes
Minority idea: 4 votes+6 half-votes=7v
The mahority all liked the good thing, but were okay with the alternative. The minority were militant fanatics who insisted on withholding their votes in order to give their favourite a better chance of winning, or they just really hated the majority idea. If team 'withhold votes so my idea wins' is distributed that unevenly, then something weird is going on, the majority(or some portion of them) could have done the same thing. If the majority were all okay with the minority idea, and the minority all felt that the majority favourite was a vile chunk of refuse, then their feelings on that matter have been reflected and I feel that the correct result has been provided. I mean, it is not as though the majority didn't like the minority idea, just that they wanted something else more.
I just don't see a scenario in which not doing the maths is going to result in an unwanted outcome, unless supporters of one thing are all trying to metavote and the supporters of the other thing are all just voting for what they want. Which would be odd, because everyone can metavote if they want to, it shouldn't be skewed that much.
Seriously though, if most people think something is the best choice, then that one wins.
Radar-guided missiles: 6 votes+5halves=8.5v
Ship-mounted radar-scanners: 5 votes + 6 halves=8v
Orion drive: 7v
There are 11 people who want some sort of radar and will want both missiles and scanners soon, and 7 people who want bomb-based propulsion. Most people think radar is the best choice, but do not agree on which sort of radar. Bomb-drive wins if we rely upon primary votes only...
If there's a tie, you hold a tiebreaker. Then you consider measures like split votes (You have 4 quarters. Spend them as you will) or something. Until then, it should be a simple-majority thing, in order to keep things simple.
I feel as though this is simple 'enough'. People can just vote for one thing if they want. It is a little tricky to look through three times as many votes and to track two types of votes, but that still seems pretty easy to me. There are lots of more complex systems that could be used, I went for something that was still very simple. "Vote for what you want, but you get to make little votes for a couple of other things. If people keep failing to vote coherently then I will concede that we cannot have nice things.
How many experience points is democracy worth?
Ooooh, I wonder if we can research class and skill levels...