In accordance with the suggestion, I'm asking this different, broader question than my previous one, in relation to the same problem.
Situations in Which Problems Occur
Many times, a group needs to pick one out of several contradictory or even mutually exclusive courses of events or actions. This can involve PCs\$^1\$ deciding between multiple things to do based on their personal values and motivations, or players deciding which plot would be more interesting to play (especially with more shared-storytelling types of campaigns), or even choices that span both the IC\$^2\$ and OOC\$^3\$ decision (such as when PC motivations reflect player interests).
Which of the choices is taken seems to have a major effect on the narrative, so such decision-making moments can easily be as important as - or even more important than - the 'mainline' mechanics of a game (and than the corresponding mechanical balance).
The Main Part of the Problem
For an N-sized group of players (GM\$^4\$ being distinct from players), in my experience it is common for one player (when N>=3), or sometimes even two players (if N==5), to be proportionally underrepresented in terms of narrative balance, i.e. getting significantly less than 1/N 'weight' in terms of influencing the narrative (again, both in cases where influencing the narrative happens through purely IC decisions, and when meta-influencing the narrative through OOC suggestions and the like). This seems to be occurring whenever 2-3 players and/or characters have a similar preference that leans in a direction opposite of some other player.
The Secondary Part of the Problem
There is a factor which also aggravates it: the underrepresented member may not be able to get proportional influence even on issues subjectively more important to the player/character. Inability to have stronger narrative weight in a personally-subjectively more important issue can be a drawback to everyone, but it seems to be even more unfun when one already has disproportionally reduced influence.
What Outcome Would Be Preferable
It would be nice to maintain a proportional narrative balance. E.g. in an N==5 party, for each party member to have a roughly 20% weight of influencing the narrative on average. It would also be nice to have the personal/subjective importance of an issue be evaluated and quantified, and to make a participant gain higher influence with subjectively more important issues and lower influence with subjectively less important ones (but in a way that doesn't allow just claiming that all issues are super-important). Given the failures experienced with other solutions (below), I'm seeking a solution that is tangible, actionable, enforceable.
A Solution Considered But Not Tried
I have considered a bidding mechanic (and asked about it in the previous question), but did not get a chance to try it out.
I have witnessed or been part of (as a player) or personally tried (as a GM) several unstructured solutions and have found them wanting.
'Just talk about it'. Probably the vaguest / least informative of the advice ever given for the problem, and most unstructured. Also tried out the most. And IME\$^5\$, it shares some characteristics of UN GA\$^6\$: an issue is raised, people express their deep concern, a consensus and joint resolution are seemingly reached, but then later things keep happening the way they did, and people start saying how they understood the joint consensus differently, or forgot, or broke it unintentionally, or 'that was agreed under different circumstances which no longer apply' or or many others that are not as well remembered. End result: a lot of wasted time and effort, but increased frustration. Essentially the solution fails because it isn't really actionable or enforceable in the long term (and not even necessarily due to malice!). Also, IME people pushing for this solution seem to have a tendency to do that in a very condescending and uninformative way.
'Vote on it'. Less insidiously frustrating than just talking, but also largely ineffective, because it means that, for example, for N==4, having 50% of the vote (2 members with matching preferences) tends to result in having 100% of the influence in most situations with multiple choices. Also, totally fails to differentiate levels of personal subjective importance of issues.
'Spend 30 minutes on each player/character at a time, and start over when you run out of players'. Mixed results. It gives everyone a proportional activity time, which mitigates the worst possible outcome of outright sitting in a corner . . . but not even always that (I have seen cases where the overall direction of the campaign results in the underrepresented player just not having anything to do when the turn comes). It also tends lead to a split party (either partially or completely) for its duration, making it so that, for example, for N==2, the similar-preference duo gets their 60 minutes of working together and getting chances for fun interactions, while the underrepresented one gets 30 minutes of solo activity. The duo working together can still get a disproportionately higher influence on the overall campaign narrative.
I'm interested in trying out solutions other than the ones I have tried and found wanting, as well as any advice about implementations thereof. Could you help me with that?
\$^1\$ PCs: player characters.
\$^2\$ IC: in character.
\$^3\$ OOC: out of character.
\$^4\$ GM: Game Master.
\$^5\$ IME: in my experience.
\$^6\$ UN GA: United Nations General Assembly.