To be honest the premise of my argument is that a static equilibrium wouldn't be reached given uncertainty about others' preferences, risk aversion and a multi-stage game, but here's a simple edge case scenario
Imagine a scenario in which there are N Jews, N neoNazis (for simplicity: example works if the Jews simply believe the number of Nazis is approximately equal) and yN ordinary citizens. Each individual in those groups has an equal budget to distribute between initiatives V(1)...V(X), where X > 2.
neoNazis desire a "yes" vote for both initiatives V(1) and V(2) - let's call them "internment" and "pogroms" - so strongly that they are (or are believed to be) willing to forego all votes on initiatives V(3)...V(X) to pass them
Jews have similarly strong views on not being interned or the victim of pogroms, but in the absence of adequate information on how the neoNazis will use their votes cannot be assured of allocating their voting budget between V(1) and V(2) in a way sufficient to negate the votes of the neoNazis on both issues.
(Note also that the existential threat posed by V(1) and V(2) sitting on the [future] referendum list also deters the Jews from using part of their budget to influence votes on V(3)...V(X) in ways which might improve their individual utilities)
If ordinary citizens have a preference for a "no" vote which would be sufficiently strong for them to vote against it in a regular referendum, but insufficiently strong for them to allocate voting budget that could otherwise purchase decisions on initiatives V(3)...V(X) the moderate majority will not provide the same bulwark against extremism as they do under a 1 person 1 vote system. If all or most Jews decide that pogroms are significantly worse than incarceration and are sufficiently risk averse to warrant allocating all their budget to eliminate the possibility of an equal number of Nazis enacting V(2), it's surprisingly easy and inexpensive in terms of voting budget for the Nazis to pass V(1). The only way I can see the Jews avoiding both initiatives being passed is to put the neoNazis on the defensive with an equally vicious anti-Nazi counter-proposal - assuming Nazis can be targeted as effectively as Jews - but I'm not convinced that mutually assured destruction is the ideal way of resolving voting conflicts.
Unfortunately, this also applies to less extreme examples where balloting is secret and intentions uncertain: in order to shift the Nash equilibrium of a particular proposal in your favour you simply raise the spectre of an [additional, and credible] proposal you anticipate your adversaries will like even less.
This is why there is a nominating procedure. I don't think this is a great forum for hashing this all out without a white board, but I would be happy to do it with a whiteboard. I think I could persuade you that there is no case where this can happen in an equilibrium of any model, including with uncertainty about preferences, risk-aversion, etc. to a significant extent and over a reasonable range of cases more than happens in 1p1v. One has to average over a reasonable range of cases to compare different systems. 1p1v can extremely easily lead to a nazi equilibrium as we have seen in practice: http://en.wikipedia.org/wiki/First_they_came_...
Imagine a scenario in which there are N Jews, N neoNazis (for simplicity: example works if the Jews simply believe the number of Nazis is approximately equal) and yN ordinary citizens. Each individual in those groups has an equal budget to distribute between initiatives V(1)...V(X), where X > 2.
neoNazis desire a "yes" vote for both initiatives V(1) and V(2) - let's call them "internment" and "pogroms" - so strongly that they are (or are believed to be) willing to forego all votes on initiatives V(3)...V(X) to pass them
Jews have similarly strong views on not being interned or the victim of pogroms, but in the absence of adequate information on how the neoNazis will use their votes cannot be assured of allocating their voting budget between V(1) and V(2) in a way sufficient to negate the votes of the neoNazis on both issues. (Note also that the existential threat posed by V(1) and V(2) sitting on the [future] referendum list also deters the Jews from using part of their budget to influence votes on V(3)...V(X) in ways which might improve their individual utilities)
If ordinary citizens have a preference for a "no" vote which would be sufficiently strong for them to vote against it in a regular referendum, but insufficiently strong for them to allocate voting budget that could otherwise purchase decisions on initiatives V(3)...V(X) the moderate majority will not provide the same bulwark against extremism as they do under a 1 person 1 vote system. If all or most Jews decide that pogroms are significantly worse than incarceration and are sufficiently risk averse to warrant allocating all their budget to eliminate the possibility of an equal number of Nazis enacting V(2), it's surprisingly easy and inexpensive in terms of voting budget for the Nazis to pass V(1). The only way I can see the Jews avoiding both initiatives being passed is to put the neoNazis on the defensive with an equally vicious anti-Nazi counter-proposal - assuming Nazis can be targeted as effectively as Jews - but I'm not convinced that mutually assured destruction is the ideal way of resolving voting conflicts.
Unfortunately, this also applies to less extreme examples where balloting is secret and intentions uncertain: in order to shift the Nash equilibrium of a particular proposal in your favour you simply raise the spectre of an [additional, and credible] proposal you anticipate your adversaries will like even less.