we've seen in these last few turns, a lot of designs have been proposed and we've had some ties, some vast majorities, and some designs that only get one vote. Typically the vote of the proposer. To prevent someone for voting for the idea they think is most appropriate stifles the process (a process which is not broken and doesn't need fixing by the way).
I really fail to see your reasoning here. As far as I can tell, if it only got a vote from its proposer, then it was either a bad idea for the time, impractical, misunderstood genius, or a victim of politics. No matter how you look at it, they almost certainly could have spent their vote better, and were probably dulled by much the same phenomena that renders proof-reading more effective if you give it some time to become less familiar. Ties, on the other hand, are more likely with fewer voters, which is precisely why we would benefit from reducing the single-votes for a personal project. Instead of five different proposals with one vote each, you will tend to get one with three and one with two and everything else with nothing because when you take away the appeal of it being your own product, and the magic of it being exactly what you thought of to deal with things, there isn't enough left for anyone else to think it is the best proposal.
Basically, every time that a proposal gets only the vote of its proposer, I feel that we see a vote that might have been spent to get a result that they wanted instead of buoying something that is not going to happen. They would, themselves, benefit, if everyone does it. And every tie that could be broken by all the proposers taking away their self-vote and putting it in as a best-of-the-rest vote is an example of freeing up votes that are spread out in order to focus them down to the consensually-agreed "pretty good" proposals. If you still get a tie after all the votes are directed to just a couple of ideas, then you have a tie because those ideas are really close in preference, and there really isn't much that can be done about that without restricting people's ability to express themselves...
Voting against attacking the eastern theatres. They have a combat bonus there due to controlling the Eastern Sea, so we'll be throwing away our men for nothing. Unless taking them by surprise counts for a lot.
I think that we should hit the sea to stop them from pushing into our own sea and cutting off our sea bonus on the tundra... Breaking their horsies would be fun if we can do it quickly, so I am on the fence about the plains.
Oh, Waffles! You were asking about something to defeat their luck magic. If you don't mind my asking, what is wrong with my antiluck charms?
The idea of rendering our important forces completely luckless seems like it would work. I mean, how can you say that randomly being the only person in the whole unit to get a rock land on you due to magical influence being anything other than magically-afflicted bad-luck? I mean, sure, they only cast the spell on their own people, but it has repercussions on our own luck and reasonably couldn't exist if our own luck didn't exist, all without actually needing to learn how to manipulate luck directly, rather just tweaking our brute-suction charms from the 'visible spectrum' of magic to the 'microwaves' of luck. Which presumably must exist because otherwise how would luck magic even work... And then we can revise in some statistical analysis to reduce the effect of equipment failures as exploding boilers stop being a matter of blind luck and start being a matter of complex patterns that can be somewhat predicted...