My post is made with big games in mind, not small, so the presence of aliases is a given in any situations I describe.
Lynches barely matter in multifaction negotiation. It's true. Until you've reached lategame (at which point it's less a matter of collecting information and more about acting on the information you have) if your faction is losing a man to a lynch, your ally is just going to tell you to suck it up. No team would want to put their guys on the line in this manner unless absolutely necessary. Most of the multifaction alliance forming and negotiation revolves around the night roles, the communication, the sharing of information. It has NOTHING whatsoever to do with lynches. So that isn't even an argument for keeping lynches around in multifaction.
Positive voting seems like an interesting concept, mainly because EVERY team would likely have a vested interest in the result of the vote, which isn't the case when it comes to lynching to kill, since there is only really one team that has any real incentive to fight back, and fighting back on your own is probably not going to yield any results against an alliance of enemies going after you. This would certainly go some way towards solving the problem that you usually see of people not bothering to post on the anonymous main forums at all.
If you going with the policy change variant that Mekkah suggested, you might actually see dynamic alliances, since different teams might react to different changes differently, adding ANOTHER layer to the the politics already involved in big games. Just saying, this might not be a positive thing in everyone's eyes.
If you go with the weapon etc idea, then you would just see more aggressive voting than you do atm, since every team would want said weapon in the hands of their own alliance of factions, rather than the enemy's. Either way it would spice things up, and probably have a visible impact on gameplay I think.
Positive lynching is definitely an idea to consider IMO.
[23:11:41] <@LightWolf> Oda rested on the seventh chapther, and saw it was good