That is a really interesting idea.
Picture a body where there's 4 members. A has a voting power of 10. B and C have a voting power of 6 each. D has a voting power of 3.
It's easy to see that once A, B and C have cast their yes/no vote, the issue will be decided no matter how D votes. D has 3 out of 25 "voting weight", but no power at all. We can say this for sure without knowing anything about the ideology of the participants.
> D has a share in "voting weight", but no power at all. We can say this for sure
This is interesting in a different way. D's ability to vote has no power at all. That's true. You're taking a leap when you extrapolate that D has no power; by that argument, lobbyists have no power either. Is that something you believe?
It also occurs under most 'normal' voting systems in safe seats.
That this is a problem with party whipping in parliaments too, doesn't mean it's not a problem.
Btw, parties and how they work in specific electoral systems are (at least partially) a function of how general voting works in those systems.
If you have a sortition system, parties might work rather differently, if they would be present at all. MPs submit to the whip's party discipline, because they need the resources of the party to get re-elected etc. Under sortition, the incentives are all different.
You could run parliament on probabilistic lines, too.
More realistically, I agree with thaumasiotes: this is exactly how forming a government works in most parliamentary systems around the world (eg both in the UK parliament and the German Bundestag.)
My instinct is that this would have significantly more negative effects, to do with the ease under that system of making radical policy changes.
Though more likely, it would fall into a pathological state where most votes are votes on whether to retake other votes.
And you can also still have safeguards, like constitutional guarantees etc.
Of course, if A, B, C and D are groups of people with less than perfect party discipline, the people in D may still have some power.
The paradox is that they get a good deal of power being pivotal, but only on issues they don't really care so much about.
No. That's only true in a deterministic parliament that works by majority rule.
You could have your parliament make decisions by lot (with probabilities weighted by what MPs vote for).
Or you could give your parliamentarians a steady stream of tokens they could use for voting; small parties could save up their tokens for a while, to have a decisive influence on something they care about.
(You'd have to work out a lot of kinks in such a token system..)
Approval voting and range voting come pretty close.
However, your first link only seems to critique deterministic voting systems. It's fairly easy to sidestep these critiques (especially Arrow's theorem) with a probabilistic systems:
Eg this variant of sortition: every voter chooses a preferred candidate on their ballot, and we draw n ballots at random to fill up parliament. (Pick whatever system you prefer for resolving one candidate getting picked multiple times, eg give them extra voting power in parliament, or pick the voter's next choice on the ballot etc.)
If you can find a way to vote 'tactically' in this scheme, please let me know.
I believe it's fair in some sense, and free of the pathologies outlined in your links. You are always better off voting for the candidate you prefer.
(I specifically mention using this scheme to fill up parliament with a few hundred people in it. If you want to pick a single position, like a president, the low of large numbers won't kick in, and you might have a greater variance than you'd like from your voting system.
But even for picking a president, a randomised system can still avoid the pathologies mentioned.)