A Tool to Enable Consensus Decision Making

• Problem: your group fails to make timely decisions due to a consistent failure to reach a consensus
• Desired Remedy: A tool that helps alleviate this detriment to fun gaming.
• Proposed Tool: Options Identification Process and Voting Tool (see below)
• Requirements: Buy-in from GM and players on the particular voting tool that will be used.

A voting tool can resolve all four problems if your group and your DM agree to use a voting tool. We don't know the interpersonal dynamics in this group. (It matters). I will assume that you are all friends or at least on friendly terms.
Note about reality: Who the "alpha dog" in your group is may color your success in agreeing on a decision aid.

What you seek is an in-game usable form of Consensus Decision making

A generic process is illustrated by this fluxograma and the previous link is a concise summary of the process that is subject neutral. (Not TTRPG centric, but process/tool set used in many walks of life).

Per your comment that the group is all adults, you could just stop here and look at the summary in the first link, and tailor your own tool. But we'll proceed ...

Apply the voting tool when you find yourselves in the dilemmas you described in the question.

Primeiro:

• Identify how many different actions or choices are being proposed.
  • If you don't identify what your options are, you can't make a decision.
  • You can die roll to see who states his case first, with the DM as facilitator.
    • (Or, and better, IMO)
  • Take turns as pointed to by the DM, as that disrupts play less.

Segundo:

• each player proposing an option states it, along with a brief "why" for that choice.

Terceiro:

• With DM facilitating, you all vote on each option.
  • Each player has 2 votes available. You cannot apply two votes to a single option.
  • Use a d6 to indicate your vote, in front of you at the table:
    • 1 pip is no, 6 pips is yes.
  • A brief "why not" for a no vote is an option here
  • Rinse and repeat for each option.

DM keeps track of votes received. (as neutral facilitator).

If there were more than two choices to start with, drop option with lowest score, vote on remaining choices per above.

Fourth: Vote To Determine the Group Decision

Voting Criteria For Success:

Unanimous agreement
Unanimity minus one vote
Unanimity minus two votes
Person-in-charge decides

Pick from one of the above criteria. Your group has to agree on the level of consensus that is acceptable to all(See Social Contract comment further down).

For the final vote, I suggest Unanimity Minus One or Unanimity Minus Two.

If you end up with a hung jury due to which protocol was chosen (like Unanimous) you have two last resort options to get a decision.

1. "Person in Charge decides." You can roll for, or each night designate, someone as "person in charge" and accept their decision for hung juries.

2. Roll the dice (high wins) or flip a coin to decide between the last two choices.

Your problem statement indicates that you want the group to make decisions. The above is a time tested method, adapted for your described table, that will get you decisions.

Summary of Benefits: (to address your stated problems)
- Vote on choices to keep play moving by making decisions.
- Don't split the party.
- You'll have less wasted time.
- Each player participates in making decisions for the group when the group needs a decision.
- The GM doesn't pull his hair out.

Caveat to this answer:

1. If you are the only person at the table concerned about this, the above as a decision aid is probably doomed.
2. If the other players care, then you have something to discuss within your group and get buy-in.
3. Getting buy-in on collaborative processes like this is part of your Social Contract, which from your problem statement is not robust in your group -- at least in this area.

Experiência:

Small group dynamics and decision making have been in my professional life for a few decades. I'll use an informal group example of a decision process following the same steps tailored to a different situation:

• RL example: seven men, one van, Friday night, which bar to go to? Thumbs up and thumbs down rather than dice. Same basic process, different objective, small social group dynamics.

Give the party a way to identify these situations where an argument is ongoing with no new information is being introduced, and a mechanism to decide on a particular course of action regardless of the individual members preferences. Fortunately, when all relevant arguments and points have been put forth, mature players will recognise it. Or at least, they'll recognise it if it's pointed out to them or they think about it for a moment. Once that's happened, all you need is a way to get each party member to agree to follow the same course of action even if they personally prefer one of the alternatives.

The traditional tool for this is to have a "party leader" whose job it is to step in and have the final word in discussions and thereby cut them short once no new arguments are being introduced. (The excellent game Ryuutama makes this a codified player role, but I've also seen it come up in other systems.) Leaders can be permanent or temporary, or even just whichever-player-isn't-involved-in-the-argument-and-seems-fair-minded. There are also other methods of making decisions when an argument's points have been made, such as the group agreeing to vote or to a coin flip.

The important thing is that the players agree in advance to cede the decision to the specified authority if they're unable to come to a consensus... And most players will, as long as they perceive the decision-making authority to be fair.

(That said, if your party ever gets into an argument where one or more sides adamantly refuse to abide by the decision of such an authority, there's a high chance that you've stumbled across an irreconcilable conflict between different characters' values. As far as I'm aware, no method of shortening discussions will help these situations; The party may have to escalate the conflict until one or the other sides is incapable of resisting, or agree to disagree and go their separate ways.)

If you get a chance, I'd recommend checking out the game Divinity: Original Sin.

It features a mechanic based around exactly this sort of problem. When the two players disagree on a particular approach, they can each declare how they'd go about solving the problem - this allows the two characters to build up their relative scores in various attributes. One might gain a point in Romantic while another would gain a point in Pragmatic - each of which alters your stats ever so slightly. Then, there's a rock-paper-scissors approach to determining who "wins the argument" and various points spent in social skills will improve the odds of you winning the fight - because each win in the rock paper scissors matchup is worth a certain number of points, up to the goal of ten or so, where the person who got ten rockpaperscissors points wins the argument.

This allows both players to feel like they gained something out of roleplaying their approach to the situation, while also allowing the game to progress. The most impressive feature of it is that it allows the encounter to be meaningful at the same time that it advances the story.

So, you could say something like: "okay guys, pick an option and paper rock scissors to see who wins." And after a winner is decided, award points toward some imaginary track and tell everyone that they got something cool for their roleplaying. You might be surprised at how positive their reaction is.

(If I remember correctly, "Romantic" gave a 1% bonus to critical chance or something like that, so you can safely give them something like +1 to use rope checks on the weekends or something like that - Knowing players, they'll remember. And they'll love exploiting it)

One tool that can be used in many situations is to make the discussion happen in character. If the players want to, they can argue all they want, but their discussion can be heard by NPCs and game time advances while the players talk.

So while the players are arguing about whether to climb the ladder, mobs might hear them and attack.

This can be facilitated by fitting environment design. So, considering your first example. If the players are in a place where there are no other people and where they cannot be approached by anyone, advancing game time will not do any good. But if you don't give the players any completely empty/safe space, but instead either place NPCs nearby or let NPCs/Mobs roam the place, advancing game time now does make a difference again. So in your first example, if the players are discussing what to do in their sound-proof room in the inn, this method could not be used. But if the room in the inn has thumb-wide cracks in the floor, someone downstairs could be easily listening. Or don't give them their own room, but rather a huge room where many people sleep.